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@minrk
Created February 2, 2014 19:15
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>Week_1_Finite_differences</title>
<style type="text/css">
.clearfix{*zoom:1}.clearfix:before,.clearfix:after{display:table;content:"";line-height:0}
.clearfix:after{clear:both}
.hide-text{font:0/0 a;color:transparent;text-shadow:none;background-color:transparent;border:0}
.input-block-level{display:block;width:100%;min-height:30px;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}
article,aside,details,figcaption,figure,footer,header,hgroup,nav,section{display:block}
audio,canvas,video{display:inline-block;*display:inline;*zoom:1}
audio:not([controls]){display:none}
html{font-size:100%;-webkit-text-size-adjust:100%;-ms-text-size-adjust:100%}
a:focus{outline:thin dotted #333;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}
a:hover,a:active{outline:0}
sub,sup{position:relative;font-size:75%;line-height:0;vertical-align:baseline}
sup{top:-0.5em}
sub{bottom:-0.25em}
img{max-width:100%;width:auto\9;height:auto;vertical-align:middle;border:0;-ms-interpolation-mode:bicubic}
#map_canvas img,.google-maps img{max-width:none}
button,input,select,textarea{margin:0;font-size:100%;vertical-align:middle}
button,input{*overflow:visible;line-height:normal}
button::-moz-focus-inner,input::-moz-focus-inner{padding:0;border:0}
button,html input[type="button"],input[type="reset"],input[type="submit"]{-webkit-appearance:button;cursor:pointer}
label,select,button,input[type="button"],input[type="reset"],input[type="submit"],input[type="radio"],input[type="checkbox"]{cursor:pointer}
input[type="search"]{-webkit-box-sizing:content-box;-moz-box-sizing:content-box;box-sizing:content-box;-webkit-appearance:textfield}
input[type="search"]::-webkit-search-decoration,input[type="search"]::-webkit-search-cancel-button{-webkit-appearance:none}
textarea{overflow:auto;vertical-align:top}
@media print{*{text-shadow:none !important;color:#000 !important;background:transparent !important;box-shadow:none !important} a,a:visited{text-decoration:underline} a[href]:after{content:" (" attr(href) ")"} abbr[title]:after{content:" (" attr(title) ")"} .ir a:after,a[href^="javascript:"]:after,a[href^="#"]:after{content:""} pre,blockquote{border:1px solid #999;page-break-inside:avoid} thead{display:table-header-group} tr,img{page-break-inside:avoid} img{max-width:100% !important} @page {margin:.5cm}p,h2,h3{orphans:3;widows:3} h2,h3{page-break-after:avoid}}body{margin:0;font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;line-height:20px;color:#000;background-color:#fff}
a{color:#08c;text-decoration:none}
a:hover,a:focus{color:#005580;text-decoration:underline}
.img-rounded{border-radius:6px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px}
.img-polaroid{padding:4px;background-color:#fff;border:1px solid #ccc;border:1px solid rgba(0,0,0,0.2);-webkit-box-shadow:0 1px 3px rgba(0,0,0,0.1);-moz-box-shadow:0 1px 3px rgba(0,0,0,0.1);box-shadow:0 1px 3px rgba(0,0,0,0.1)}
.img-circle{border-radius:500px;-webkit-border-radius:500px;-moz-border-radius:500px;border-radius:500px}
.row{margin-left:-20px;*zoom:1}.row:before,.row:after{display:table;content:"";line-height:0}
.row:after{clear:both}
[class*="span"]{float:left;min-height:1px;margin-left:20px}
.container,.navbar-static-top .container,.navbar-fixed-top .container,.navbar-fixed-bottom .container{width:940px}
.span12{width:940px}
.span11{width:860px}
.span10{width:780px}
.span9{width:700px}
.span8{width:620px}
.span7{width:540px}
.span6{width:460px}
.span5{width:380px}
.span4{width:300px}
.span3{width:220px}
.span2{width:140px}
.span1{width:60px}
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.offset11{margin-left:900px}
.offset10{margin-left:820px}
.offset9{margin-left:740px}
.offset8{margin-left:660px}
.offset7{margin-left:580px}
.offset6{margin-left:500px}
.offset5{margin-left:420px}
.offset4{margin-left:340px}
.offset3{margin-left:260px}
.offset2{margin-left:180px}
.offset1{margin-left:100px}
.row-fluid{width:100%;*zoom:1}.row-fluid:before,.row-fluid:after{display:table;content:"";line-height:0}
.row-fluid:after{clear:both}
.row-fluid [class*="span"]{display:block;width:100%;min-height:30px;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box;float:left;margin-left:2.127659574468085%;*margin-left:2.074468085106383%}
.row-fluid [class*="span"]:first-child{margin-left:0}
.row-fluid .controls-row [class*="span"]+[class*="span"]{margin-left:2.127659574468085%}
.row-fluid .span12{width:100%;*width:99.94680851063829%}
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.row-fluid .offset2:first-child{margin-left:17.02127659574468%;*margin-left:16.914893617021278%}
.row-fluid .offset1{margin-left:10.638297872340425%;*margin-left:10.53191489361702%}
.row-fluid .offset1:first-child{margin-left:8.51063829787234%;*margin-left:8.404255319148938%}
[class*="span"].hide,.row-fluid [class*="span"].hide{display:none}
[class*="span"].pull-right,.row-fluid [class*="span"].pull-right{float:right}
.container{margin-right:auto;margin-left:auto;*zoom:1}.container:before,.container:after{display:table;content:"";line-height:0}
.container:after{clear:both}
.container-fluid{padding-right:20px;padding-left:20px;*zoom:1}.container-fluid:before,.container-fluid:after{display:table;content:"";line-height:0}
.container-fluid:after{clear:both}
p{margin:0 0 10px}
.lead{margin-bottom:20px;font-size:19.5px;font-weight:200;line-height:30px}
small{font-size:85%}
strong{font-weight:bold}
em{font-style:italic}
cite{font-style:normal}
.muted{color:#999}
a.muted:hover,a.muted:focus{color:#808080}
.text-warning{color:#c09853}
a.text-warning:hover,a.text-warning:focus{color:#a47e3c}
.text-error{color:#b94a48}
a.text-error:hover,a.text-error:focus{color:#953b39}
.text-info{color:#3a87ad}
a.text-info:hover,a.text-info:focus{color:#2d6987}
.text-success{color:#468847}
a.text-success:hover,a.text-success:focus{color:#356635}
.text-left{text-align:left}
.text-right{text-align:right}
.text-center{text-align:center}
h1,h2,h3,h4,h5,h6{margin:10px 0;font-family:inherit;font-weight:bold;line-height:20px;color:inherit;text-rendering:optimizelegibility}h1 small,h2 small,h3 small,h4 small,h5 small,h6 small{font-weight:normal;line-height:1;color:#999}
h1,h2,h3{line-height:40px}
h1{font-size:35.75px}
h2{font-size:29.25px}
h3{font-size:22.75px}
h4{font-size:16.25px}
h5{font-size:13px}
h6{font-size:11.049999999999999px}
h1 small{font-size:22.75px}
h2 small{font-size:16.25px}
h3 small{font-size:13px}
h4 small{font-size:13px}
.page-header{padding-bottom:9px;margin:20px 0 30px;border-bottom:1px solid #eee}
ul,ol{padding:0;margin:0 0 10px 25px}
ul ul,ul ol,ol ol,ol ul{margin-bottom:0}
li{line-height:20px}
ul.unstyled,ol.unstyled{margin-left:0;list-style:none}
ul.inline,ol.inline{margin-left:0;list-style:none}ul.inline>li,ol.inline>li{display:inline-block;*display:inline;*zoom:1;padding-left:5px;padding-right:5px}
dl{margin-bottom:20px}
dt,dd{line-height:20px}
dt{font-weight:bold}
dd{margin-left:10px}
.dl-horizontal{*zoom:1}.dl-horizontal:before,.dl-horizontal:after{display:table;content:"";line-height:0}
.dl-horizontal:after{clear:both}
.dl-horizontal dt{float:left;width:160px;clear:left;text-align:right;overflow:hidden;text-overflow:ellipsis;white-space:nowrap}
.dl-horizontal dd{margin-left:180px}
hr{margin:20px 0;border:0;border-top:1px solid #eee;border-bottom:1px solid #fff}
abbr[title],abbr[data-original-title]{cursor:help;border-bottom:1px dotted #999}
abbr.initialism{font-size:90%;text-transform:uppercase}
blockquote{padding:0 0 0 15px;margin:0 0 20px;border-left:5px solid #eee}blockquote p{margin-bottom:0;font-size:16.25px;font-weight:300;line-height:1.25}
blockquote small{display:block;line-height:20px;color:#999}blockquote small:before{content:'\2014 \00A0'}
blockquote.pull-right{float:right;padding-right:15px;padding-left:0;border-right:5px solid #eee;border-left:0}blockquote.pull-right p,blockquote.pull-right small{text-align:right}
blockquote.pull-right small:before{content:''}
blockquote.pull-right small:after{content:'\00A0 \2014'}
q:before,q:after,blockquote:before,blockquote:after{content:""}
address{display:block;margin-bottom:20px;font-style:normal;line-height:20px}
code,pre{padding:0 3px 2px;font-family:monospace;font-size:11px;color:#333;border-radius:3px;-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px}
code{padding:2px 4px;color:#d14;background-color:#f7f7f9;border:1px solid #e1e1e8;white-space:nowrap}
pre{display:block;padding:9.5px;margin:0 0 10px;font-size:12px;line-height:20px;word-break:break-all;word-wrap:break-word;white-space:pre;white-space:pre-wrap;background-color:#f5f5f5;border:1px solid #ccc;border:1px solid rgba(0,0,0,0.15);border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}pre.prettyprint{margin-bottom:20px}
pre code{padding:0;color:inherit;white-space:pre;white-space:pre-wrap;background-color:transparent;border:0}
.pre-scrollable{max-height:340px;overflow-y:scroll}
form{margin:0 0 20px}
fieldset{padding:0;margin:0;border:0}
legend{display:block;width:100%;padding:0;margin-bottom:20px;font-size:19.5px;line-height:40px;color:#333;border:0;border-bottom:1px solid #e5e5e5}legend small{font-size:15px;color:#999}
label,input,button,select,textarea{font-size:13px;font-weight:normal;line-height:20px}
input,button,select,textarea{font-family:"Helvetica Neue",Helvetica,Arial,sans-serif}
label{display:block;margin-bottom:5px}
select,textarea,input[type="text"],input[type="password"],input[type="datetime"],input[type="datetime-local"],input[type="date"],input[type="month"],input[type="time"],input[type="week"],input[type="number"],input[type="email"],input[type="url"],input[type="search"],input[type="tel"],input[type="color"],.uneditable-input{display:inline-block;height:20px;padding:4px 6px;margin-bottom:10px;font-size:13px;line-height:20px;color:#555;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;vertical-align:middle}
input,textarea,.uneditable-input{width:206px}
textarea{height:auto}
textarea,input[type="text"],input[type="password"],input[type="datetime"],input[type="datetime-local"],input[type="date"],input[type="month"],input[type="time"],input[type="week"],input[type="number"],input[type="email"],input[type="url"],input[type="search"],input[type="tel"],input[type="color"],.uneditable-input{background-color:#fff;border:1px solid #ccc;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);-moz-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);-webkit-transition:border linear .2s, box-shadow linear .2s;-moz-transition:border linear .2s, box-shadow linear .2s;-o-transition:border linear .2s, box-shadow linear .2s;transition:border linear .2s, box-shadow linear .2s}textarea:focus,input[type="text"]:focus,input[type="password"]:focus,input[type="datetime"]:focus,input[type="datetime-local"]:focus,input[type="date"]:focus,input[type="month"]:focus,input[type="time"]:focus,input[type="week"]:focus,input[type="number"]:focus,input[type="email"]:focus,input[type="url"]:focus,input[type="search"]:focus,input[type="tel"]:focus,input[type="color"]:focus,.uneditable-input:focus{border-color:rgba(82,168,236,0.8);outline:0;outline:thin dotted \9;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(82,168,236,.6);-moz-box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(82,168,236,.6);box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(82,168,236,.6)}
input[type="radio"],input[type="checkbox"]{margin:4px 0 0;*margin-top:0;margin-top:1px \9;line-height:normal}
input[type="file"],input[type="image"],input[type="submit"],input[type="reset"],input[type="button"],input[type="radio"],input[type="checkbox"]{width:auto}
select,input[type="file"]{height:30px;*margin-top:4px;line-height:30px}
select{width:220px;border:1px solid #ccc;background-color:#fff}
select[multiple],select[size]{height:auto}
select:focus,input[type="file"]:focus,input[type="radio"]:focus,input[type="checkbox"]:focus{outline:thin dotted #333;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}
.uneditable-input,.uneditable-textarea{color:#999;background-color:#fcfcfc;border-color:#ccc;-webkit-box-shadow:inset 0 1px 2px rgba(0,0,0,0.025);-moz-box-shadow:inset 0 1px 2px rgba(0,0,0,0.025);box-shadow:inset 0 1px 2px rgba(0,0,0,0.025);cursor:not-allowed}
.uneditable-input{overflow:hidden;white-space:nowrap}
.uneditable-textarea{width:auto;height:auto}
input:-moz-placeholder,textarea:-moz-placeholder{color:#999}
input:-ms-input-placeholder,textarea:-ms-input-placeholder{color:#999}
input::-webkit-input-placeholder,textarea::-webkit-input-placeholder{color:#999}
.radio,.checkbox{min-height:20px;padding-left:20px}
.radio input[type="radio"],.checkbox input[type="checkbox"]{float:left;margin-left:-20px}
.controls>.radio:first-child,.controls>.checkbox:first-child{padding-top:5px}
.radio.inline,.checkbox.inline{display:inline-block;padding-top:5px;margin-bottom:0;vertical-align:middle}
.radio.inline+.radio.inline,.checkbox.inline+.checkbox.inline{margin-left:10px}
.input-mini{width:60px}
.input-small{width:90px}
.input-medium{width:150px}
.input-large{width:210px}
.input-xlarge{width:270px}
.input-xxlarge{width:530px}
input[class*="span"],select[class*="span"],textarea[class*="span"],.uneditable-input[class*="span"],.row-fluid input[class*="span"],.row-fluid select[class*="span"],.row-fluid textarea[class*="span"],.row-fluid .uneditable-input[class*="span"]{float:none;margin-left:0}
.input-append input[class*="span"],.input-append .uneditable-input[class*="span"],.input-prepend input[class*="span"],.input-prepend .uneditable-input[class*="span"],.row-fluid input[class*="span"],.row-fluid select[class*="span"],.row-fluid textarea[class*="span"],.row-fluid .uneditable-input[class*="span"],.row-fluid .input-prepend [class*="span"],.row-fluid .input-append [class*="span"]{display:inline-block}
input,textarea,.uneditable-input{margin-left:0}
.controls-row [class*="span"]+[class*="span"]{margin-left:20px}
input.span12,textarea.span12,.uneditable-input.span12{width:926px}
input.span11,textarea.span11,.uneditable-input.span11{width:846px}
input.span10,textarea.span10,.uneditable-input.span10{width:766px}
input.span9,textarea.span9,.uneditable-input.span9{width:686px}
input.span8,textarea.span8,.uneditable-input.span8{width:606px}
input.span7,textarea.span7,.uneditable-input.span7{width:526px}
input.span6,textarea.span6,.uneditable-input.span6{width:446px}
input.span5,textarea.span5,.uneditable-input.span5{width:366px}
input.span4,textarea.span4,.uneditable-input.span4{width:286px}
input.span3,textarea.span3,.uneditable-input.span3{width:206px}
input.span2,textarea.span2,.uneditable-input.span2{width:126px}
input.span1,textarea.span1,.uneditable-input.span1{width:46px}
.controls-row{*zoom:1}.controls-row:before,.controls-row:after{display:table;content:"";line-height:0}
.controls-row:after{clear:both}
.controls-row [class*="span"],.row-fluid .controls-row [class*="span"]{float:left}
.controls-row .checkbox[class*="span"],.controls-row .radio[class*="span"]{padding-top:5px}
input[disabled],select[disabled],textarea[disabled],input[readonly],select[readonly],textarea[readonly]{cursor:not-allowed;background-color:#eee}
input[type="radio"][disabled],input[type="checkbox"][disabled],input[type="radio"][readonly],input[type="checkbox"][readonly]{background-color:transparent}
.control-group.warning .control-label,.control-group.warning .help-block,.control-group.warning .help-inline{color:#c09853}
.control-group.warning .checkbox,.control-group.warning .radio,.control-group.warning input,.control-group.warning select,.control-group.warning textarea{color:#c09853}
.control-group.warning input,.control-group.warning select,.control-group.warning textarea{border-color:#c09853;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);-moz-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);box-shadow:inset 0 1px 1px rgba(0,0,0,0.075)}.control-group.warning input:focus,.control-group.warning select:focus,.control-group.warning textarea:focus{border-color:#a47e3c;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #dbc59e;-moz-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #dbc59e;box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #dbc59e}
.control-group.warning .input-prepend .add-on,.control-group.warning .input-append .add-on{color:#c09853;background-color:#fcf8e3;border-color:#c09853}
.control-group.error .control-label,.control-group.error .help-block,.control-group.error .help-inline{color:#b94a48}
.control-group.error .checkbox,.control-group.error .radio,.control-group.error input,.control-group.error select,.control-group.error textarea{color:#b94a48}
.control-group.error input,.control-group.error select,.control-group.error textarea{border-color:#b94a48;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);-moz-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);box-shadow:inset 0 1px 1px rgba(0,0,0,0.075)}.control-group.error input:focus,.control-group.error select:focus,.control-group.error textarea:focus{border-color:#953b39;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #d59392;-moz-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #d59392;box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #d59392}
.control-group.error .input-prepend .add-on,.control-group.error .input-append .add-on{color:#b94a48;background-color:#f2dede;border-color:#b94a48}
.control-group.success .control-label,.control-group.success .help-block,.control-group.success .help-inline{color:#468847}
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.control-group.success .input-prepend .add-on,.control-group.success .input-append .add-on{color:#468847;background-color:#dff0d8;border-color:#468847}
.control-group.info .control-label,.control-group.info .help-block,.control-group.info .help-inline{color:#3a87ad}
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.form-actions{padding:19px 20px 20px;margin-top:20px;margin-bottom:20px;background-color:#f5f5f5;border-top:1px solid #e5e5e5;*zoom:1}.form-actions:before,.form-actions:after{display:table;content:"";line-height:0}
.form-actions:after{clear:both}
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.input-append .active,.input-prepend .active{background-color:#a9dba9;border-color:#46a546}
.input-prepend .add-on,.input-prepend .btn{margin-right:-1px}
.input-prepend .add-on:first-child,.input-prepend .btn:first-child{border-radius:4px 0 0 4px;-webkit-border-radius:4px 0 0 4px;-moz-border-radius:4px 0 0 4px;border-radius:4px 0 0 4px}
.input-append input,.input-append select,.input-append .uneditable-input{border-radius:4px 0 0 4px;-webkit-border-radius:4px 0 0 4px;-moz-border-radius:4px 0 0 4px;border-radius:4px 0 0 4px}.input-append input+.btn-group .btn:last-child,.input-append select+.btn-group .btn:last-child,.input-append .uneditable-input+.btn-group .btn:last-child{border-radius:0 4px 4px 0;-webkit-border-radius:0 4px 4px 0;-moz-border-radius:0 4px 4px 0;border-radius:0 4px 4px 0}
.input-append .add-on,.input-append .btn,.input-append .btn-group{margin-left:-1px}
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.input-prepend.input-append .add-on:last-child,.input-prepend.input-append .btn:last-child{margin-left:-1px;border-radius:0 4px 4px 0;-webkit-border-radius:0 4px 4px 0;-moz-border-radius:0 4px 4px 0;border-radius:0 4px 4px 0}
.input-prepend.input-append .btn-group:first-child{margin-left:0}
input.search-query{padding-right:14px;padding-right:4px \9;padding-left:14px;padding-left:4px \9;margin-bottom:0;border-radius:15px;-webkit-border-radius:15px;-moz-border-radius:15px;border-radius:15px}
.form-search .input-append .search-query,.form-search .input-prepend .search-query{border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.form-search .input-append .search-query{border-radius:14px 0 0 14px;-webkit-border-radius:14px 0 0 14px;-moz-border-radius:14px 0 0 14px;border-radius:14px 0 0 14px}
.form-search .input-append .btn{border-radius:0 14px 14px 0;-webkit-border-radius:0 14px 14px 0;-moz-border-radius:0 14px 14px 0;border-radius:0 14px 14px 0}
.form-search .input-prepend .search-query{border-radius:0 14px 14px 0;-webkit-border-radius:0 14px 14px 0;-moz-border-radius:0 14px 14px 0;border-radius:0 14px 14px 0}
.form-search .input-prepend .btn{border-radius:14px 0 0 14px;-webkit-border-radius:14px 0 0 14px;-moz-border-radius:14px 0 0 14px;border-radius:14px 0 0 14px}
.form-search input,.form-inline input,.form-horizontal input,.form-search textarea,.form-inline textarea,.form-horizontal textarea,.form-search select,.form-inline select,.form-horizontal select,.form-search .help-inline,.form-inline .help-inline,.form-horizontal .help-inline,.form-search .uneditable-input,.form-inline .uneditable-input,.form-horizontal .uneditable-input,.form-search .input-prepend,.form-inline .input-prepend,.form-horizontal .input-prepend,.form-search .input-append,.form-inline .input-append,.form-horizontal .input-append{display:inline-block;*display:inline;*zoom:1;margin-bottom:0;vertical-align:middle}
.form-search .hide,.form-inline .hide,.form-horizontal .hide{display:none}
.form-search label,.form-inline label,.form-search .btn-group,.form-inline .btn-group{display:inline-block}
.form-search .input-append,.form-inline .input-append,.form-search .input-prepend,.form-inline .input-prepend{margin-bottom:0}
.form-search .radio,.form-search .checkbox,.form-inline .radio,.form-inline .checkbox{padding-left:0;margin-bottom:0;vertical-align:middle}
.form-search .radio input[type="radio"],.form-search .checkbox input[type="checkbox"],.form-inline .radio input[type="radio"],.form-inline .checkbox input[type="checkbox"]{float:left;margin-right:3px;margin-left:0}
.control-group{margin-bottom:10px}
legend+.control-group{margin-top:20px;-webkit-margin-top-collapse:separate}
.form-horizontal .control-group{margin-bottom:20px;*zoom:1}.form-horizontal .control-group:before,.form-horizontal .control-group:after{display:table;content:"";line-height:0}
.form-horizontal .control-group:after{clear:both}
.form-horizontal .control-label{float:left;width:160px;padding-top:5px;text-align:right}
.form-horizontal .controls{*display:inline-block;*padding-left:20px;margin-left:180px;*margin-left:0}.form-horizontal .controls:first-child{*padding-left:180px}
.form-horizontal .help-block{margin-bottom:0}
.form-horizontal input+.help-block,.form-horizontal select+.help-block,.form-horizontal textarea+.help-block,.form-horizontal .uneditable-input+.help-block,.form-horizontal .input-prepend+.help-block,.form-horizontal .input-append+.help-block{margin-top:10px}
.form-horizontal .form-actions{padding-left:180px}
table{max-width:100%;background-color:transparent;border-collapse:collapse;border-spacing:0}
.table{width:100%;margin-bottom:20px}.table th,.table td{padding:8px;line-height:20px;text-align:left;vertical-align:top;border-top:1px solid #ddd}
.table th{font-weight:bold}
.table thead th{vertical-align:bottom}
.table caption+thead tr:first-child th,.table caption+thead tr:first-child td,.table colgroup+thead tr:first-child th,.table colgroup+thead tr:first-child td,.table thead:first-child tr:first-child th,.table thead:first-child tr:first-child td{border-top:0}
.table tbody+tbody{border-top:2px solid #ddd}
.table .table{background-color:#fff}
.table-condensed th,.table-condensed td{padding:4px 5px}
.table-bordered{border:1px solid #ddd;border-collapse:separate;*border-collapse:collapse;border-left:0;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}.table-bordered th,.table-bordered td{border-left:1px solid #ddd}
.table-bordered caption+thead tr:first-child th,.table-bordered caption+tbody tr:first-child th,.table-bordered caption+tbody tr:first-child td,.table-bordered colgroup+thead tr:first-child th,.table-bordered colgroup+tbody tr:first-child th,.table-bordered colgroup+tbody tr:first-child td,.table-bordered thead:first-child tr:first-child th,.table-bordered tbody:first-child tr:first-child th,.table-bordered tbody:first-child tr:first-child td{border-top:0}
.table-bordered thead:first-child tr:first-child>th:first-child,.table-bordered tbody:first-child tr:first-child>td:first-child,.table-bordered tbody:first-child tr:first-child>th:first-child{-webkit-border-top-left-radius:4px;-moz-border-radius-topleft:4px;border-top-left-radius:4px}
.table-bordered thead:first-child tr:first-child>th:last-child,.table-bordered tbody:first-child tr:first-child>td:last-child,.table-bordered tbody:first-child tr:first-child>th:last-child{-webkit-border-top-right-radius:4px;-moz-border-radius-topright:4px;border-top-right-radius:4px}
.table-bordered thead:last-child tr:last-child>th:first-child,.table-bordered tbody:last-child tr:last-child>td:first-child,.table-bordered tbody:last-child tr:last-child>th:first-child,.table-bordered tfoot:last-child tr:last-child>td:first-child,.table-bordered tfoot:last-child tr:last-child>th:first-child{-webkit-border-bottom-left-radius:4px;-moz-border-radius-bottomleft:4px;border-bottom-left-radius:4px}
.table-bordered thead:last-child tr:last-child>th:last-child,.table-bordered tbody:last-child tr:last-child>td:last-child,.table-bordered tbody:last-child tr:last-child>th:last-child,.table-bordered tfoot:last-child tr:last-child>td:last-child,.table-bordered tfoot:last-child tr:last-child>th:last-child{-webkit-border-bottom-right-radius:4px;-moz-border-radius-bottomright:4px;border-bottom-right-radius:4px}
.table-bordered tfoot+tbody:last-child tr:last-child td:first-child{-webkit-border-bottom-left-radius:0;-moz-border-radius-bottomleft:0;border-bottom-left-radius:0}
.table-bordered tfoot+tbody:last-child tr:last-child td:last-child{-webkit-border-bottom-right-radius:0;-moz-border-radius-bottomright:0;border-bottom-right-radius:0}
.table-bordered caption+thead tr:first-child th:first-child,.table-bordered caption+tbody tr:first-child td:first-child,.table-bordered colgroup+thead tr:first-child th:first-child,.table-bordered colgroup+tbody tr:first-child td:first-child{-webkit-border-top-left-radius:4px;-moz-border-radius-topleft:4px;border-top-left-radius:4px}
.table-bordered caption+thead tr:first-child th:last-child,.table-bordered caption+tbody tr:first-child td:last-child,.table-bordered colgroup+thead tr:first-child th:last-child,.table-bordered colgroup+tbody tr:first-child td:last-child{-webkit-border-top-right-radius:4px;-moz-border-radius-topright:4px;border-top-right-radius:4px}
.table-striped tbody>tr:nth-child(odd)>td,.table-striped tbody>tr:nth-child(odd)>th{background-color:#f9f9f9}
.table-hover tbody tr:hover>td,.table-hover tbody tr:hover>th{background-color:#f5f5f5}
table td[class*="span"],table th[class*="span"],.row-fluid table td[class*="span"],.row-fluid table th[class*="span"]{display:table-cell;float:none;margin-left:0}
.table td.span1,.table th.span1{float:none;width:44px;margin-left:0}
.table td.span2,.table th.span2{float:none;width:124px;margin-left:0}
.table td.span3,.table th.span3{float:none;width:204px;margin-left:0}
.table td.span4,.table th.span4{float:none;width:284px;margin-left:0}
.table td.span5,.table th.span5{float:none;width:364px;margin-left:0}
.table td.span6,.table th.span6{float:none;width:444px;margin-left:0}
.table td.span7,.table th.span7{float:none;width:524px;margin-left:0}
.table td.span8,.table th.span8{float:none;width:604px;margin-left:0}
.table td.span9,.table th.span9{float:none;width:684px;margin-left:0}
.table td.span10,.table th.span10{float:none;width:764px;margin-left:0}
.table td.span11,.table th.span11{float:none;width:844px;margin-left:0}
.table td.span12,.table th.span12{float:none;width:924px;margin-left:0}
.table tbody tr.success>td{background-color:#dff0d8}
.table tbody tr.error>td{background-color:#f2dede}
.table tbody tr.warning>td{background-color:#fcf8e3}
.table tbody tr.info>td{background-color:#d9edf7}
.table-hover tbody tr.success:hover>td{background-color:#d0e9c6}
.table-hover tbody tr.error:hover>td{background-color:#ebcccc}
.table-hover tbody tr.warning:hover>td{background-color:#faf2cc}
.table-hover tbody tr.info:hover>td{background-color:#c4e3f3}
[class^="icon-"],[class*=" icon-"]{display:inline-block;width:14px;height:14px;*margin-right:.3em;line-height:14px;vertical-align:text-top;background-image:url("../img/glyphicons-halflings.png");background-position:14px 14px;background-repeat:no-repeat;margin-top:1px}
.icon-white,.nav-pills>.active>a>[class^="icon-"],.nav-pills>.active>a>[class*=" icon-"],.nav-list>.active>a>[class^="icon-"],.nav-list>.active>a>[class*=" icon-"],.navbar-inverse .nav>.active>a>[class^="icon-"],.navbar-inverse .nav>.active>a>[class*=" icon-"],.dropdown-menu>li>a:hover>[class^="icon-"],.dropdown-menu>li>a:focus>[class^="icon-"],.dropdown-menu>li>a:hover>[class*=" icon-"],.dropdown-menu>li>a:focus>[class*=" icon-"],.dropdown-menu>.active>a>[class^="icon-"],.dropdown-menu>.active>a>[class*=" icon-"],.dropdown-submenu:hover>a>[class^="icon-"],.dropdown-submenu:focus>a>[class^="icon-"],.dropdown-submenu:hover>a>[class*=" icon-"],.dropdown-submenu:focus>a>[class*=" icon-"]{background-image:url("../img/glyphicons-halflings-white.png")}
.icon-glass{background-position:0 0}
.icon-music{background-position:-24px 0}
.icon-search{background-position:-48px 0}
.icon-envelope{background-position:-72px 0}
.icon-heart{background-position:-96px 0}
.icon-star{background-position:-120px 0}
.icon-star-empty{background-position:-144px 0}
.icon-user{background-position:-168px 0}
.icon-film{background-position:-192px 0}
.icon-th-large{background-position:-216px 0}
.icon-th{background-position:-240px 0}
.icon-th-list{background-position:-264px 0}
.icon-ok{background-position:-288px 0}
.icon-remove{background-position:-312px 0}
.icon-zoom-in{background-position:-336px 0}
.icon-zoom-out{background-position:-360px 0}
.icon-off{background-position:-384px 0}
.icon-signal{background-position:-408px 0}
.icon-cog{background-position:-432px 0}
.icon-trash{background-position:-456px 0}
.icon-home{background-position:0 -24px}
.icon-file{background-position:-24px -24px}
.icon-time{background-position:-48px -24px}
.icon-road{background-position:-72px -24px}
.icon-download-alt{background-position:-96px -24px}
.icon-download{background-position:-120px -24px}
.icon-upload{background-position:-144px -24px}
.icon-inbox{background-position:-168px -24px}
.icon-play-circle{background-position:-192px -24px}
.icon-repeat{background-position:-216px -24px}
.icon-refresh{background-position:-240px -24px}
.icon-list-alt{background-position:-264px -24px}
.icon-lock{background-position:-287px -24px}
.icon-flag{background-position:-312px -24px}
.icon-headphones{background-position:-336px -24px}
.icon-volume-off{background-position:-360px -24px}
.icon-volume-down{background-position:-384px -24px}
.icon-volume-up{background-position:-408px -24px}
.icon-qrcode{background-position:-432px -24px}
.icon-barcode{background-position:-456px -24px}
.icon-tag{background-position:0 -48px}
.icon-tags{background-position:-25px -48px}
.icon-book{background-position:-48px -48px}
.icon-bookmark{background-position:-72px -48px}
.icon-print{background-position:-96px -48px}
.icon-camera{background-position:-120px -48px}
.icon-font{background-position:-144px -48px}
.icon-bold{background-position:-167px -48px}
.icon-italic{background-position:-192px -48px}
.icon-text-height{background-position:-216px -48px}
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.icon-indent-right{background-position:-408px -48px}
.icon-facetime-video{background-position:-432px -48px}
.icon-picture{background-position:-456px -48px}
.icon-pencil{background-position:0 -72px}
.icon-map-marker{background-position:-24px -72px}
.icon-adjust{background-position:-48px -72px}
.icon-tint{background-position:-72px -72px}
.icon-edit{background-position:-96px -72px}
.icon-share{background-position:-120px -72px}
.icon-check{background-position:-144px -72px}
.icon-move{background-position:-168px -72px}
.icon-step-backward{background-position:-192px -72px}
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.icon-forward{background-position:-336px -72px}
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.icon-question-sign{background-position:-96px -96px}
.icon-info-sign{background-position:-120px -96px}
.icon-screenshot{background-position:-144px -96px}
.icon-remove-circle{background-position:-168px -96px}
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.icon-arrow-up{background-position:-289px -96px}
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.icon-share-alt{background-position:-336px -96px}
.icon-resize-full{background-position:-360px -96px}
.icon-resize-small{background-position:-384px -96px}
.icon-plus{background-position:-408px -96px}
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.icon-asterisk{background-position:-456px -96px}
.icon-exclamation-sign{background-position:0 -120px}
.icon-gift{background-position:-24px -120px}
.icon-leaf{background-position:-48px -120px}
.icon-fire{background-position:-72px -120px}
.icon-eye-open{background-position:-96px -120px}
.icon-eye-close{background-position:-120px -120px}
.icon-warning-sign{background-position:-144px -120px}
.icon-plane{background-position:-168px -120px}
.icon-calendar{background-position:-192px -120px}
.icon-random{background-position:-216px -120px;width:16px}
.icon-comment{background-position:-240px -120px}
.icon-magnet{background-position:-264px -120px}
.icon-chevron-up{background-position:-288px -120px}
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.icon-retweet{background-position:-336px -120px}
.icon-shopping-cart{background-position:-360px -120px}
.icon-folder-close{background-position:-384px -120px;width:16px}
.icon-folder-open{background-position:-408px -120px;width:16px}
.icon-resize-vertical{background-position:-432px -119px}
.icon-resize-horizontal{background-position:-456px -118px}
.icon-hdd{background-position:0 -144px}
.icon-bullhorn{background-position:-24px -144px}
.icon-bell{background-position:-48px -144px}
.icon-certificate{background-position:-72px -144px}
.icon-thumbs-up{background-position:-96px -144px}
.icon-thumbs-down{background-position:-120px -144px}
.icon-hand-right{background-position:-144px -144px}
.icon-hand-left{background-position:-168px -144px}
.icon-hand-up{background-position:-192px -144px}
.icon-hand-down{background-position:-216px -144px}
.icon-circle-arrow-right{background-position:-240px -144px}
.icon-circle-arrow-left{background-position:-264px -144px}
.icon-circle-arrow-up{background-position:-288px -144px}
.icon-circle-arrow-down{background-position:-312px -144px}
.icon-globe{background-position:-336px -144px}
.icon-wrench{background-position:-360px -144px}
.icon-tasks{background-position:-384px -144px}
.icon-filter{background-position:-408px -144px}
.icon-briefcase{background-position:-432px -144px}
.icon-fullscreen{background-position:-456px -144px}
.dropup,.dropdown{position:relative}
.dropdown-toggle{*margin-bottom:-3px}
.dropdown-toggle:active,.open .dropdown-toggle{outline:0}
.caret{display:inline-block;width:0;height:0;vertical-align:top;border-top:4px solid #000;border-right:4px solid transparent;border-left:4px solid transparent;content:""}
.dropdown .caret{margin-top:8px;margin-left:2px}
.dropdown-menu{position:absolute;top:100%;left:0;z-index:1000;display:none;float:left;min-width:160px;padding:5px 0;margin:2px 0 0;list-style:none;background-color:#fff;border:1px solid #ccc;border:1px solid rgba(0,0,0,0.2);*border-right-width:2px;*border-bottom-width:2px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;-webkit-box-shadow:0 5px 10px rgba(0,0,0,0.2);-moz-box-shadow:0 5px 10px rgba(0,0,0,0.2);box-shadow:0 5px 10px rgba(0,0,0,0.2);-webkit-background-clip:padding-box;-moz-background-clip:padding;background-clip:padding-box}.dropdown-menu.pull-right{right:0;left:auto}
.dropdown-menu .divider{*width:100%;height:1px;margin:9px 1px;*margin:-5px 0 5px;overflow:hidden;background-color:#e5e5e5;border-bottom:1px solid #fff}
.dropdown-menu>li>a{display:block;padding:3px 20px;clear:both;font-weight:normal;line-height:20px;color:#333;white-space:nowrap}
.dropdown-menu>li>a:hover,.dropdown-menu>li>a:focus,.dropdown-submenu:hover>a,.dropdown-submenu:focus>a{text-decoration:none;color:#fff;background-color:#0081c2;background-image:-moz-linear-gradient(top, #08c, #0077b3);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#08c), to(#0077b3));background-image:-webkit-linear-gradient(top, #08c, #0077b3);background-image:-o-linear-gradient(top, #08c, #0077b3);background-image:linear-gradient(to bottom, #08c, #0077b3);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff0088cc', endColorstr='#ff0077b3', GradientType=0)}
.dropdown-menu>.active>a,.dropdown-menu>.active>a:hover,.dropdown-menu>.active>a:focus{color:#fff;text-decoration:none;outline:0;background-color:#0081c2;background-image:-moz-linear-gradient(top, #08c, #0077b3);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#08c), to(#0077b3));background-image:-webkit-linear-gradient(top, #08c, #0077b3);background-image:-o-linear-gradient(top, #08c, #0077b3);background-image:linear-gradient(to bottom, #08c, #0077b3);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff0088cc', endColorstr='#ff0077b3', GradientType=0)}
.dropdown-menu>.disabled>a,.dropdown-menu>.disabled>a:hover,.dropdown-menu>.disabled>a:focus{color:#999}
.dropdown-menu>.disabled>a:hover,.dropdown-menu>.disabled>a:focus{text-decoration:none;background-color:transparent;background-image:none;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false);cursor:default}
.open{*z-index:1000}.open>.dropdown-menu{display:block}
.dropdown-backdrop{position:fixed;left:0;right:0;bottom:0;top:0;z-index:990}
.pull-right>.dropdown-menu{right:0;left:auto}
.dropup .caret,.navbar-fixed-bottom .dropdown .caret{border-top:0;border-bottom:4px solid #000;content:""}
.dropup .dropdown-menu,.navbar-fixed-bottom .dropdown .dropdown-menu{top:auto;bottom:100%;margin-bottom:1px}
.dropdown-submenu{position:relative}
.dropdown-submenu>.dropdown-menu{top:0;left:100%;margin-top:-6px;margin-left:-1px;border-radius:0 6px 6px 6px;-webkit-border-radius:0 6px 6px 6px;-moz-border-radius:0 6px 6px 6px;border-radius:0 6px 6px 6px}
.dropdown-submenu:hover>.dropdown-menu{display:block}
.dropup .dropdown-submenu>.dropdown-menu{top:auto;bottom:0;margin-top:0;margin-bottom:-2px;border-radius:5px 5px 5px 0;-webkit-border-radius:5px 5px 5px 0;-moz-border-radius:5px 5px 5px 0;border-radius:5px 5px 5px 0}
.dropdown-submenu>a:after{display:block;content:" ";float:right;width:0;height:0;border-color:transparent;border-style:solid;border-width:5px 0 5px 5px;border-left-color:#ccc;margin-top:5px;margin-right:-10px}
.dropdown-submenu:hover>a:after{border-left-color:#fff}
.dropdown-submenu.pull-left{float:none}.dropdown-submenu.pull-left>.dropdown-menu{left:-100%;margin-left:10px;border-radius:6px 0 6px 6px;-webkit-border-radius:6px 0 6px 6px;-moz-border-radius:6px 0 6px 6px;border-radius:6px 0 6px 6px}
.dropdown .dropdown-menu .nav-header{padding-left:20px;padding-right:20px}
.typeahead{z-index:1051;margin-top:2px;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}
.well{min-height:20px;padding:19px;margin-bottom:20px;background-color:#f5f5f5;border:1px solid #e3e3e3;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.05);-moz-box-shadow:inset 0 1px 1px rgba(0,0,0,0.05);box-shadow:inset 0 1px 1px rgba(0,0,0,0.05)}.well blockquote{border-color:#ddd;border-color:rgba(0,0,0,0.15)}
.well-large{padding:24px;border-radius:6px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px}
.well-small{padding:9px;border-radius:3px;-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px}
.fade{opacity:0;-webkit-transition:opacity .15s linear;-moz-transition:opacity .15s linear;-o-transition:opacity .15s linear;transition:opacity .15s linear}.fade.in{opacity:1}
.collapse{position:relative;height:0;overflow:hidden;-webkit-transition:height .35s ease;-moz-transition:height .35s ease;-o-transition:height .35s ease;transition:height .35s ease}.collapse.in{height:auto}
.close{float:right;font-size:20px;font-weight:bold;line-height:20px;color:#000;text-shadow:0 1px 0 #fff;opacity:.2;filter:alpha(opacity=20)}.close:hover,.close:focus{color:#000;text-decoration:none;cursor:pointer;opacity:.4;filter:alpha(opacity=40)}
button.close{padding:0;cursor:pointer;background:transparent;border:0;-webkit-appearance:none}
.btn{display:inline-block;*display:inline;*zoom:1;padding:4px 12px;margin-bottom:0;font-size:13px;line-height:20px;text-align:center;vertical-align:middle;cursor:pointer;color:#333;text-shadow:0 1px 1px rgba(255,255,255,0.75);background-color:#f5f5f5;background-image:-moz-linear-gradient(top, #fff, #e6e6e6);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#fff), to(#e6e6e6));background-image:-webkit-linear-gradient(top, #fff, #e6e6e6);background-image:-o-linear-gradient(top, #fff, #e6e6e6);background-image:linear-gradient(to bottom, #fff, #e6e6e6);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffffffff', endColorstr='#ffe6e6e6', GradientType=0);border-color:#e6e6e6 #e6e6e6 #bfbfbf;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#e6e6e6;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false);border:1px solid #ccc;*border:0;border-bottom-color:#b3b3b3;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;*margin-left:.3em;-webkit-box-shadow:inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05)}.btn:hover,.btn:focus,.btn:active,.btn.active,.btn.disabled,.btn[disabled]{color:#333;background-color:#e6e6e6;*background-color:#d9d9d9}
.btn:active,.btn.active{background-color:#ccc \9}
.btn:first-child{*margin-left:0}
.btn:hover,.btn:focus{color:#333;text-decoration:none;background-position:0 -15px;-webkit-transition:background-position .1s linear;-moz-transition:background-position .1s linear;-o-transition:background-position .1s linear;transition:background-position .1s linear}
.btn:focus{outline:thin dotted #333;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}
.btn.active,.btn:active{background-image:none;outline:0;-webkit-box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05)}
.btn.disabled,.btn[disabled]{cursor:default;background-image:none;opacity:.65;filter:alpha(opacity=65);-webkit-box-shadow:none;-moz-box-shadow:none;box-shadow:none}
.btn-large{padding:11px 19px;font-size:16.25px;border-radius:6px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px}
.btn-large [class^="icon-"],.btn-large [class*=" icon-"]{margin-top:4px}
.btn-small{padding:2px 10px;font-size:11.049999999999999px;border-radius:3px;-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px}
.btn-small [class^="icon-"],.btn-small [class*=" icon-"]{margin-top:0}
.btn-mini [class^="icon-"],.btn-mini [class*=" icon-"]{margin-top:-1px}
.btn-mini{padding:0 6px;font-size:9.75px;border-radius:3px;-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px}
.btn-block{display:block;width:100%;padding-left:0;padding-right:0;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}
.btn-block+.btn-block{margin-top:5px}
input[type="submit"].btn-block,input[type="reset"].btn-block,input[type="button"].btn-block{width:100%}
.btn-primary.active,.btn-warning.active,.btn-danger.active,.btn-success.active,.btn-info.active,.btn-inverse.active{color:rgba(255,255,255,0.75)}
.btn-primary{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#006dcc;background-image:-moz-linear-gradient(top, #08c, #04c);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#08c), to(#04c));background-image:-webkit-linear-gradient(top, #08c, #04c);background-image:-o-linear-gradient(top, #08c, #04c);background-image:linear-gradient(to bottom, #08c, #04c);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff0088cc', endColorstr='#ff0044cc', GradientType=0);border-color:#04c #04c #002a80;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#04c;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-primary:hover,.btn-primary:focus,.btn-primary:active,.btn-primary.active,.btn-primary.disabled,.btn-primary[disabled]{color:#fff;background-color:#04c;*background-color:#003bb3}
.btn-primary:active,.btn-primary.active{background-color:#039 \9}
.btn-warning{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#faa732;background-image:-moz-linear-gradient(top, #fbb450, #f89406);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#fbb450), to(#f89406));background-image:-webkit-linear-gradient(top, #fbb450, #f89406);background-image:-o-linear-gradient(top, #fbb450, #f89406);background-image:linear-gradient(to bottom, #fbb450, #f89406);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#fffbb450', endColorstr='#fff89406', GradientType=0);border-color:#f89406 #f89406 #ad6704;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#f89406;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-warning:hover,.btn-warning:focus,.btn-warning:active,.btn-warning.active,.btn-warning.disabled,.btn-warning[disabled]{color:#fff;background-color:#f89406;*background-color:#df8505}
.btn-warning:active,.btn-warning.active{background-color:#c67605 \9}
.btn-danger{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#da4f49;background-image:-moz-linear-gradient(top, #ee5f5b, #bd362f);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#ee5f5b), to(#bd362f));background-image:-webkit-linear-gradient(top, #ee5f5b, #bd362f);background-image:-o-linear-gradient(top, #ee5f5b, #bd362f);background-image:linear-gradient(to bottom, #ee5f5b, #bd362f);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffee5f5b', endColorstr='#ffbd362f', GradientType=0);border-color:#bd362f #bd362f #802420;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#bd362f;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-danger:hover,.btn-danger:focus,.btn-danger:active,.btn-danger.active,.btn-danger.disabled,.btn-danger[disabled]{color:#fff;background-color:#bd362f;*background-color:#a9302a}
.btn-danger:active,.btn-danger.active{background-color:#942a25 \9}
.btn-success{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#5bb75b;background-image:-moz-linear-gradient(top, #62c462, #51a351);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#62c462), to(#51a351));background-image:-webkit-linear-gradient(top, #62c462, #51a351);background-image:-o-linear-gradient(top, #62c462, #51a351);background-image:linear-gradient(to bottom, #62c462, #51a351);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff62c462', endColorstr='#ff51a351', GradientType=0);border-color:#51a351 #51a351 #387038;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#51a351;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-success:hover,.btn-success:focus,.btn-success:active,.btn-success.active,.btn-success.disabled,.btn-success[disabled]{color:#fff;background-color:#51a351;*background-color:#499249}
.btn-success:active,.btn-success.active{background-color:#408140 \9}
.btn-info{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#49afcd;background-image:-moz-linear-gradient(top, #5bc0de, #2f96b4);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#5bc0de), to(#2f96b4));background-image:-webkit-linear-gradient(top, #5bc0de, #2f96b4);background-image:-o-linear-gradient(top, #5bc0de, #2f96b4);background-image:linear-gradient(to bottom, #5bc0de, #2f96b4);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff5bc0de', endColorstr='#ff2f96b4', GradientType=0);border-color:#2f96b4 #2f96b4 #1f6377;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#2f96b4;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-info:hover,.btn-info:focus,.btn-info:active,.btn-info.active,.btn-info.disabled,.btn-info[disabled]{color:#fff;background-color:#2f96b4;*background-color:#2a85a0}
.btn-info:active,.btn-info.active{background-color:#24748c \9}
.btn-inverse{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#363636;background-image:-moz-linear-gradient(top, #444, #222);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#444), to(#222));background-image:-webkit-linear-gradient(top, #444, #222);background-image:-o-linear-gradient(top, #444, #222);background-image:linear-gradient(to bottom, #444, #222);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff444444', endColorstr='#ff222222', GradientType=0);border-color:#222 #222 #000;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#222;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-inverse:hover,.btn-inverse:focus,.btn-inverse:active,.btn-inverse.active,.btn-inverse.disabled,.btn-inverse[disabled]{color:#fff;background-color:#222;*background-color:#151515}
.btn-inverse:active,.btn-inverse.active{background-color:#080808 \9}
button.btn,input[type="submit"].btn{*padding-top:3px;*padding-bottom:3px}button.btn::-moz-focus-inner,input[type="submit"].btn::-moz-focus-inner{padding:0;border:0}
button.btn.btn-large,input[type="submit"].btn.btn-large{*padding-top:7px;*padding-bottom:7px}
button.btn.btn-small,input[type="submit"].btn.btn-small{*padding-top:3px;*padding-bottom:3px}
button.btn.btn-mini,input[type="submit"].btn.btn-mini{*padding-top:1px;*padding-bottom:1px}
.btn-link,.btn-link:active,.btn-link[disabled]{background-color:transparent;background-image:none;-webkit-box-shadow:none;-moz-box-shadow:none;box-shadow:none}
.btn-link{border-color:transparent;cursor:pointer;color:#08c;border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.btn-link:hover,.btn-link:focus{color:#005580;text-decoration:underline;background-color:transparent}
.btn-link[disabled]:hover,.btn-link[disabled]:focus{color:#333;text-decoration:none}
.btn-group{position:relative;display:inline-block;*display:inline;*zoom:1;font-size:0;vertical-align:middle;white-space:nowrap;*margin-left:.3em}.btn-group:first-child{*margin-left:0}
.btn-group+.btn-group{margin-left:5px}
.btn-toolbar{font-size:0;margin-top:10px;margin-bottom:10px}.btn-toolbar>.btn+.btn,.btn-toolbar>.btn-group+.btn,.btn-toolbar>.btn+.btn-group{margin-left:5px}
.btn-group>.btn{position:relative;border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.btn-group>.btn+.btn{margin-left:-1px}
.btn-group>.btn,.btn-group>.dropdown-menu,.btn-group>.popover{font-size:13px}
.btn-group>.btn-mini{font-size:9.75px}
.btn-group>.btn-small{font-size:11.049999999999999px}
.btn-group>.btn-large{font-size:16.25px}
.btn-group>.btn:first-child{margin-left:0;-webkit-border-top-left-radius:4px;-moz-border-radius-topleft:4px;border-top-left-radius:4px;-webkit-border-bottom-left-radius:4px;-moz-border-radius-bottomleft:4px;border-bottom-left-radius:4px}
.btn-group>.btn:last-child,.btn-group>.dropdown-toggle{-webkit-border-top-right-radius:4px;-moz-border-radius-topright:4px;border-top-right-radius:4px;-webkit-border-bottom-right-radius:4px;-moz-border-radius-bottomright:4px;border-bottom-right-radius:4px}
.btn-group>.btn.large:first-child{margin-left:0;-webkit-border-top-left-radius:6px;-moz-border-radius-topleft:6px;border-top-left-radius:6px;-webkit-border-bottom-left-radius:6px;-moz-border-radius-bottomleft:6px;border-bottom-left-radius:6px}
.btn-group>.btn.large:last-child,.btn-group>.large.dropdown-toggle{-webkit-border-top-right-radius:6px;-moz-border-radius-topright:6px;border-top-right-radius:6px;-webkit-border-bottom-right-radius:6px;-moz-border-radius-bottomright:6px;border-bottom-right-radius:6px}
.btn-group>.btn:hover,.btn-group>.btn:focus,.btn-group>.btn:active,.btn-group>.btn.active{z-index:2}
.btn-group .dropdown-toggle:active,.btn-group.open .dropdown-toggle{outline:0}
.btn-group>.btn+.dropdown-toggle{padding-left:8px;padding-right:8px;-webkit-box-shadow:inset 1px 0 0 rgba(255,255,255,.125), inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 1px 0 0 rgba(255,255,255,.125), inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 1px 0 0 rgba(255,255,255,.125), inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);*padding-top:5px;*padding-bottom:5px}
.btn-group>.btn-mini+.dropdown-toggle{padding-left:5px;padding-right:5px;*padding-top:2px;*padding-bottom:2px}
.btn-group>.btn-small+.dropdown-toggle{*padding-top:5px;*padding-bottom:4px}
.btn-group>.btn-large+.dropdown-toggle{padding-left:12px;padding-right:12px;*padding-top:7px;*padding-bottom:7px}
.btn-group.open .dropdown-toggle{background-image:none;-webkit-box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05)}
.btn-group.open .btn.dropdown-toggle{background-color:#e6e6e6}
.btn-group.open .btn-primary.dropdown-toggle{background-color:#04c}
.btn-group.open .btn-warning.dropdown-toggle{background-color:#f89406}
.btn-group.open .btn-danger.dropdown-toggle{background-color:#bd362f}
.btn-group.open .btn-success.dropdown-toggle{background-color:#51a351}
.btn-group.open .btn-info.dropdown-toggle{background-color:#2f96b4}
.btn-group.open .btn-inverse.dropdown-toggle{background-color:#222}
.btn .caret{margin-top:8px;margin-left:0}
.btn-large .caret{margin-top:6px}
.btn-large .caret{border-left-width:5px;border-right-width:5px;border-top-width:5px}
.btn-mini .caret,.btn-small .caret{margin-top:8px}
.dropup .btn-large .caret{border-bottom-width:5px}
.btn-primary .caret,.btn-warning .caret,.btn-danger .caret,.btn-info .caret,.btn-success .caret,.btn-inverse .caret{border-top-color:#fff;border-bottom-color:#fff}
.btn-group-vertical{display:inline-block;*display:inline;*zoom:1}
.btn-group-vertical>.btn{display:block;float:none;max-width:100%;border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.btn-group-vertical>.btn+.btn{margin-left:0;margin-top:-1px}
.btn-group-vertical>.btn:first-child{border-radius:4px 4px 0 0;-webkit-border-radius:4px 4px 0 0;-moz-border-radius:4px 4px 0 0;border-radius:4px 4px 0 0}
.btn-group-vertical>.btn:last-child{border-radius:0 0 4px 4px;-webkit-border-radius:0 0 4px 4px;-moz-border-radius:0 0 4px 4px;border-radius:0 0 4px 4px}
.btn-group-vertical>.btn-large:first-child{border-radius:6px 6px 0 0;-webkit-border-radius:6px 6px 0 0;-moz-border-radius:6px 6px 0 0;border-radius:6px 6px 0 0}
.btn-group-vertical>.btn-large:last-child{border-radius:0 0 6px 6px;-webkit-border-radius:0 0 6px 6px;-moz-border-radius:0 0 6px 6px;border-radius:0 0 6px 6px}
.alert{padding:8px 35px 8px 14px;margin-bottom:20px;text-shadow:0 1px 0 rgba(255,255,255,0.5);background-color:#fcf8e3;border:1px solid #fbeed5;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}
.alert,.alert h4{color:#c09853}
.alert h4{margin:0}
.alert .close{position:relative;top:-2px;right:-21px;line-height:20px}
.alert-success{background-color:#dff0d8;border-color:#d6e9c6;color:#468847}
.alert-success h4{color:#468847}
.alert-danger,.alert-error{background-color:#f2dede;border-color:#eed3d7;color:#b94a48}
.alert-danger h4,.alert-error h4{color:#b94a48}
.alert-info{background-color:#d9edf7;border-color:#bce8f1;color:#3a87ad}
.alert-info h4{color:#3a87ad}
.alert-block{padding-top:14px;padding-bottom:14px}
.alert-block>p,.alert-block>ul{margin-bottom:0}
.alert-block p+p{margin-top:5px}
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.nav>li>a>img{max-width:none}
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.nav-header{display:block;padding:3px 15px;font-size:11px;font-weight:bold;line-height:20px;color:#999;text-shadow:0 1px 0 rgba(255,255,255,0.5);text-transform:uppercase}
.nav li+.nav-header{margin-top:9px}
.nav-list{padding-left:15px;padding-right:15px;margin-bottom:0}
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.nav-list>li>a{padding:3px 15px}
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.nav-tabs{border-bottom:1px solid #ddd}
.nav-tabs>li{margin-bottom:-1px}
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.nav-stacked>li{float:none}
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.nav-pills.nav-stacked>li>a{margin-bottom:3px}
.nav-pills.nav-stacked>li:last-child>a{margin-bottom:1px}
.nav-tabs .dropdown-menu{border-radius:0 0 6px 6px;-webkit-border-radius:0 0 6px 6px;-moz-border-radius:0 0 6px 6px;border-radius:0 0 6px 6px}
.nav-pills .dropdown-menu{border-radius:6px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px}
.nav .dropdown-toggle .caret{border-top-color:#08c;border-bottom-color:#08c;margin-top:6px}
.nav .dropdown-toggle:hover .caret,.nav .dropdown-toggle:focus .caret{border-top-color:#005580;border-bottom-color:#005580}
.nav-tabs .dropdown-toggle .caret{margin-top:8px}
.nav .active .dropdown-toggle .caret{border-top-color:#fff;border-bottom-color:#fff}
.nav-tabs .active .dropdown-toggle .caret{border-top-color:#555;border-bottom-color:#555}
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.tabbable{*zoom:1}.tabbable:before,.tabbable:after{display:table;content:"";line-height:0}
.tabbable:after{clear:both}
.tab-content{overflow:auto}
.tabs-below>.nav-tabs,.tabs-right>.nav-tabs,.tabs-left>.nav-tabs{border-bottom:0}
.tab-content>.tab-pane,.pill-content>.pill-pane{display:none}
.tab-content>.active,.pill-content>.active{display:block}
.tabs-below>.nav-tabs{border-top:1px solid #ddd}
.tabs-below>.nav-tabs>li{margin-top:-1px;margin-bottom:0}
.tabs-below>.nav-tabs>li>a{border-radius:0 0 4px 4px;-webkit-border-radius:0 0 4px 4px;-moz-border-radius:0 0 4px 4px;border-radius:0 0 4px 4px}.tabs-below>.nav-tabs>li>a:hover,.tabs-below>.nav-tabs>li>a:focus{border-bottom-color:transparent;border-top-color:#ddd}
.tabs-below>.nav-tabs>.active>a,.tabs-below>.nav-tabs>.active>a:hover,.tabs-below>.nav-tabs>.active>a:focus{border-color:transparent #ddd #ddd #ddd}
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.tabs-left>.nav-tabs>li>a,.tabs-right>.nav-tabs>li>a{min-width:74px;margin-right:0;margin-bottom:3px}
.tabs-left>.nav-tabs{float:left;margin-right:19px;border-right:1px solid #ddd}
.tabs-left>.nav-tabs>li>a{margin-right:-1px;border-radius:4px 0 0 4px;-webkit-border-radius:4px 0 0 4px;-moz-border-radius:4px 0 0 4px;border-radius:4px 0 0 4px}
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.tabs-right>.nav-tabs>li>a{margin-left:-1px;border-radius:0 4px 4px 0;-webkit-border-radius:0 4px 4px 0;-moz-border-radius:0 4px 4px 0;border-radius:0 4px 4px 0}
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.nav>.disabled>a{color:#999}
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.navbar{overflow:visible;margin-bottom:20px;*position:relative;*z-index:2}
.navbar-inner{min-height:36px;padding-left:20px;padding-right:20px;background-color:#fafafa;background-image:-moz-linear-gradient(top, #fff, #f2f2f2);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#fff), to(#f2f2f2));background-image:-webkit-linear-gradient(top, #fff, #f2f2f2);background-image:-o-linear-gradient(top, #fff, #f2f2f2);background-image:linear-gradient(to bottom, #fff, #f2f2f2);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffffffff', endColorstr='#fff2f2f2', GradientType=0);border:1px solid #d4d4d4;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;-webkit-box-shadow:0 1px 4px rgba(0,0,0,0.065);-moz-box-shadow:0 1px 4px rgba(0,0,0,0.065);box-shadow:0 1px 4px rgba(0,0,0,0.065);*zoom:1}.navbar-inner:before,.navbar-inner:after{display:table;content:"";line-height:0}
.navbar-inner:after{clear:both}
.navbar .container{width:auto}
.nav-collapse.collapse{height:auto;overflow:visible}
.navbar .brand{float:left;display:block;padding:8px 20px 8px;margin-left:-20px;font-size:20px;font-weight:200;color:#777;text-shadow:0 1px 0 #fff}.navbar .brand:hover,.navbar .brand:focus{text-decoration:none}
.navbar-text{margin-bottom:0;line-height:36px;color:#777}
.navbar-link{color:#777}.navbar-link:hover,.navbar-link:focus{color:#333}
.navbar .divider-vertical{height:36px;margin:0 9px;border-left:1px solid #f2f2f2;border-right:1px solid #fff}
.navbar .btn,.navbar .btn-group{margin-top:3px}
.navbar .btn-group .btn,.navbar .input-prepend .btn,.navbar .input-append .btn,.navbar .input-prepend .btn-group,.navbar .input-append .btn-group{margin-top:0}
.navbar-form{margin-bottom:0;*zoom:1}.navbar-form:before,.navbar-form:after{display:table;content:"";line-height:0}
.navbar-form:after{clear:both}
.navbar-form input,.navbar-form select,.navbar-form .radio,.navbar-form .checkbox{margin-top:3px}
.navbar-form input,.navbar-form select,.navbar-form .btn{display:inline-block;margin-bottom:0}
.navbar-form input[type="image"],.navbar-form input[type="checkbox"],.navbar-form input[type="radio"]{margin-top:3px}
.navbar-form .input-append,.navbar-form .input-prepend{margin-top:5px;white-space:nowrap}.navbar-form .input-append input,.navbar-form .input-prepend input{margin-top:0}
.navbar-search{position:relative;float:left;margin-top:3px;margin-bottom:0}.navbar-search .search-query{margin-bottom:0;padding:4px 14px;font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;font-weight:normal;line-height:1;border-radius:15px;-webkit-border-radius:15px;-moz-border-radius:15px;border-radius:15px}
.navbar-static-top{position:static;margin-bottom:0}.navbar-static-top .navbar-inner{border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.navbar-fixed-top,.navbar-fixed-bottom{position:fixed;right:0;left:0;z-index:1030;margin-bottom:0}
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.navbar-fixed-top{top:0}
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.navbar .nav{position:relative;left:0;display:block;float:left;margin:0 10px 0 0}
.navbar .nav.pull-right{float:right;margin-right:0}
.navbar .nav>li{float:left}
.navbar .nav>li>a{float:none;padding:8px 15px 8px;color:#777;text-decoration:none;text-shadow:0 1px 0 #fff}
.navbar .nav .dropdown-toggle .caret{margin-top:8px}
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.navbar .nav>.active>a,.navbar .nav>.active>a:hover,.navbar .nav>.active>a:focus{color:#555;text-decoration:none;background-color:#e5e5e5;-webkit-box-shadow:inset 0 3px 8px rgba(0,0,0,0.125);-moz-box-shadow:inset 0 3px 8px rgba(0,0,0,0.125);box-shadow:inset 0 3px 8px rgba(0,0,0,0.125)}
.navbar .btn-navbar{display:none;float:right;padding:7px 10px;margin-left:5px;margin-right:5px;color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#ededed;background-image:-moz-linear-gradient(top, #f2f2f2, #e5e5e5);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#f2f2f2), to(#e5e5e5));background-image:-webkit-linear-gradient(top, #f2f2f2, #e5e5e5);background-image:-o-linear-gradient(top, #f2f2f2, #e5e5e5);background-image:linear-gradient(to bottom, #f2f2f2, #e5e5e5);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#fff2f2f2', endColorstr='#ffe5e5e5', GradientType=0);border-color:#e5e5e5 #e5e5e5 #bfbfbf;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#e5e5e5;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false);-webkit-box-shadow:inset 0 1px 0 rgba(255,255,255,.1), 0 1px 0 rgba(255,255,255,.075);-moz-box-shadow:inset 0 1px 0 rgba(255,255,255,.1), 0 1px 0 rgba(255,255,255,.075);box-shadow:inset 0 1px 0 rgba(255,255,255,.1), 0 1px 0 rgba(255,255,255,.075)}.navbar .btn-navbar:hover,.navbar .btn-navbar:focus,.navbar .btn-navbar:active,.navbar .btn-navbar.active,.navbar .btn-navbar.disabled,.navbar .btn-navbar[disabled]{color:#fff;background-color:#e5e5e5;*background-color:#d9d9d9}
.navbar .btn-navbar:active,.navbar .btn-navbar.active{background-color:#ccc \9}
.navbar .btn-navbar .icon-bar{display:block;width:18px;height:2px;background-color:#f5f5f5;-webkit-border-radius:1px;-moz-border-radius:1px;border-radius:1px;-webkit-box-shadow:0 1px 0 rgba(0,0,0,0.25);-moz-box-shadow:0 1px 0 rgba(0,0,0,0.25);box-shadow:0 1px 0 rgba(0,0,0,0.25)}
.btn-navbar .icon-bar+.icon-bar{margin-top:3px}
.navbar .nav>li>.dropdown-menu:before{content:'';display:inline-block;border-left:7px solid transparent;border-right:7px solid transparent;border-bottom:7px solid #ccc;border-bottom-color:rgba(0,0,0,0.2);position:absolute;top:-7px;left:9px}
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.navbar .nav li.dropdown.open>.dropdown-toggle,.navbar .nav li.dropdown.active>.dropdown-toggle,.navbar .nav li.dropdown.open.active>.dropdown-toggle{background-color:#e5e5e5;color:#555}
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.navbar .nav li.dropdown.open>.dropdown-toggle .caret,.navbar .nav li.dropdown.active>.dropdown-toggle .caret,.navbar .nav li.dropdown.open.active>.dropdown-toggle .caret{border-top-color:#555;border-bottom-color:#555}
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.navbar .pull-right>li>.dropdown-menu:after,.navbar .nav>li>.dropdown-menu.pull-right:after{left:auto;right:13px}
.navbar .pull-right>li>.dropdown-menu .dropdown-menu,.navbar .nav>li>.dropdown-menu.pull-right .dropdown-menu{left:auto;right:100%;margin-left:0;margin-right:-1px;border-radius:6px 0 6px 6px;-webkit-border-radius:6px 0 6px 6px;-moz-border-radius:6px 0 6px 6px;border-radius:6px 0 6px 6px}
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.navbar-inverse .brand{color:#999}
.navbar-inverse .navbar-text{color:#999}
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.navbar-inverse .nav .active>a,.navbar-inverse .nav .active>a:hover,.navbar-inverse .nav .active>a:focus{color:#fff;background-color:#111}
.navbar-inverse .navbar-link{color:#999}.navbar-inverse .navbar-link:hover,.navbar-inverse .navbar-link:focus{color:#fff}
.navbar-inverse .divider-vertical{border-left-color:#111;border-right-color:#222}
.navbar-inverse .nav li.dropdown.open>.dropdown-toggle,.navbar-inverse .nav li.dropdown.active>.dropdown-toggle,.navbar-inverse .nav li.dropdown.open.active>.dropdown-toggle{background-color:#111;color:#fff}
.navbar-inverse .nav li.dropdown>a:hover .caret,.navbar-inverse .nav li.dropdown>a:focus .caret{border-top-color:#fff;border-bottom-color:#fff}
.navbar-inverse .nav li.dropdown>.dropdown-toggle .caret{border-top-color:#999;border-bottom-color:#999}
.navbar-inverse .nav li.dropdown.open>.dropdown-toggle .caret,.navbar-inverse .nav li.dropdown.active>.dropdown-toggle .caret,.navbar-inverse .nav li.dropdown.open.active>.dropdown-toggle .caret{border-top-color:#fff;border-bottom-color:#fff}
.navbar-inverse .navbar-search .search-query{color:#fff;background-color:#515151;border-color:#111;-webkit-box-shadow:inset 0 1px 2px rgba(0,0,0,.1), 0 1px 0 rgba(255,255,255,.15);-moz-box-shadow:inset 0 1px 2px rgba(0,0,0,.1), 0 1px 0 rgba(255,255,255,.15);box-shadow:inset 0 1px 2px rgba(0,0,0,.1), 0 1px 0 rgba(255,255,255,.15);-webkit-transition:none;-moz-transition:none;-o-transition:none;transition:none}.navbar-inverse .navbar-search .search-query:-moz-placeholder{color:#ccc}
.navbar-inverse .navbar-search .search-query:-ms-input-placeholder{color:#ccc}
.navbar-inverse .navbar-search .search-query::-webkit-input-placeholder{color:#ccc}
.navbar-inverse .navbar-search .search-query:focus,.navbar-inverse .navbar-search .search-query.focused{padding:5px 15px;color:#333;text-shadow:0 1px 0 #fff;background-color:#fff;border:0;-webkit-box-shadow:0 0 3px rgba(0,0,0,0.15);-moz-box-shadow:0 0 3px rgba(0,0,0,0.15);box-shadow:0 0 3px rgba(0,0,0,0.15);outline:0}
.navbar-inverse .btn-navbar{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#0e0e0e;background-image:-moz-linear-gradient(top, #151515, #040404);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#151515), to(#040404));background-image:-webkit-linear-gradient(top, #151515, #040404);background-image:-o-linear-gradient(top, #151515, #040404);background-image:linear-gradient(to bottom, #151515, #040404);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff151515', endColorstr='#ff040404', GradientType=0);border-color:#040404 #040404 #000;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#040404;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.navbar-inverse .btn-navbar:hover,.navbar-inverse .btn-navbar:focus,.navbar-inverse .btn-navbar:active,.navbar-inverse .btn-navbar.active,.navbar-inverse .btn-navbar.disabled,.navbar-inverse .btn-navbar[disabled]{color:#fff;background-color:#040404;*background-color:#000}
.navbar-inverse .btn-navbar:active,.navbar-inverse .btn-navbar.active{background-color:#000 \9}
.breadcrumb{padding:8px 15px;margin:0 0 20px;list-style:none;background-color:#f5f5f5;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}.breadcrumb>li{display:inline-block;*display:inline;*zoom:1;text-shadow:0 1px 0 #fff}.breadcrumb>li>.divider{padding:0 5px;color:#ccc}
.breadcrumb>.active{color:#999}
.pagination{margin:20px 0}
.pagination ul{display:inline-block;*display:inline;*zoom:1;margin-left:0;margin-bottom:0;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;-webkit-box-shadow:0 1px 2px rgba(0,0,0,0.05);-moz-box-shadow:0 1px 2px rgba(0,0,0,0.05);box-shadow:0 1px 2px rgba(0,0,0,0.05)}
.pagination ul>li{display:inline}
.pagination ul>li>a,.pagination ul>li>span{float:left;padding:4px 12px;line-height:20px;text-decoration:none;background-color:#fff;border:1px solid #ddd;border-left-width:0}
.pagination ul>li>a:hover,.pagination ul>li>a:focus,.pagination ul>.active>a,.pagination ul>.active>span{background-color:#f5f5f5}
.pagination ul>.active>a,.pagination ul>.active>span{color:#999;cursor:default}
.pagination ul>.disabled>span,.pagination ul>.disabled>a,.pagination ul>.disabled>a:hover,.pagination ul>.disabled>a:focus{color:#999;background-color:transparent;cursor:default}
.pagination ul>li:first-child>a,.pagination ul>li:first-child>span{border-left-width:1px;-webkit-border-top-left-radius:4px;-moz-border-radius-topleft:4px;border-top-left-radius:4px;-webkit-border-bottom-left-radius:4px;-moz-border-radius-bottomleft:4px;border-bottom-left-radius:4px}
.pagination ul>li:last-child>a,.pagination ul>li:last-child>span{-webkit-border-top-right-radius:4px;-moz-border-radius-topright:4px;border-top-right-radius:4px;-webkit-border-bottom-right-radius:4px;-moz-border-radius-bottomright:4px;border-bottom-right-radius:4px}
.pagination-centered{text-align:center}
.pagination-right{text-align:right}
.pagination-large ul>li>a,.pagination-large ul>li>span{padding:11px 19px;font-size:16.25px}
.pagination-large ul>li:first-child>a,.pagination-large ul>li:first-child>span{-webkit-border-top-left-radius:6px;-moz-border-radius-topleft:6px;border-top-left-radius:6px;-webkit-border-bottom-left-radius:6px;-moz-border-radius-bottomleft:6px;border-bottom-left-radius:6px}
.pagination-large ul>li:last-child>a,.pagination-large ul>li:last-child>span{-webkit-border-top-right-radius:6px;-moz-border-radius-topright:6px;border-top-right-radius:6px;-webkit-border-bottom-right-radius:6px;-moz-border-radius-bottomright:6px;border-bottom-right-radius:6px}
.pagination-mini ul>li:first-child>a,.pagination-small ul>li:first-child>a,.pagination-mini ul>li:first-child>span,.pagination-small ul>li:first-child>span{-webkit-border-top-left-radius:3px;-moz-border-radius-topleft:3px;border-top-left-radius:3px;-webkit-border-bottom-left-radius:3px;-moz-border-radius-bottomleft:3px;border-bottom-left-radius:3px}
.pagination-mini ul>li:last-child>a,.pagination-small ul>li:last-child>a,.pagination-mini ul>li:last-child>span,.pagination-small ul>li:last-child>span{-webkit-border-top-right-radius:3px;-moz-border-radius-topright:3px;border-top-right-radius:3px;-webkit-border-bottom-right-radius:3px;-moz-border-radius-bottomright:3px;border-bottom-right-radius:3px}
.pagination-small ul>li>a,.pagination-small ul>li>span{padding:2px 10px;font-size:11.049999999999999px}
.pagination-mini ul>li>a,.pagination-mini ul>li>span{padding:0 6px;font-size:9.75px}
.pager{margin:20px 0;list-style:none;text-align:center;*zoom:1}.pager:before,.pager:after{display:table;content:"";line-height:0}
.pager:after{clear:both}
.pager li{display:inline}
.pager li>a,.pager li>span{display:inline-block;padding:5px 14px;background-color:#fff;border:1px solid #ddd;border-radius:15px;-webkit-border-radius:15px;-moz-border-radius:15px;border-radius:15px}
.pager li>a:hover,.pager li>a:focus{text-decoration:none;background-color:#f5f5f5}
.pager .next>a,.pager .next>span{float:right}
.pager .previous>a,.pager .previous>span{float:left}
.pager .disabled>a,.pager .disabled>a:hover,.pager .disabled>a:focus,.pager .disabled>span{color:#999;background-color:#fff;cursor:default}
.modal-backdrop{position:fixed;top:0;right:0;bottom:0;left:0;z-index:1040;background-color:#000}.modal-backdrop.fade{opacity:0}
.modal-backdrop,.modal-backdrop.fade.in{opacity:.8;filter:alpha(opacity=80)}
.modal{position:fixed;top:10%;left:50%;z-index:1050;width:560px;margin-left:-280px;background-color:#fff;border:1px solid #999;border:1px solid rgba(0,0,0,0.3);*border:1px solid #999;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;-webkit-box-shadow:0 3px 7px rgba(0,0,0,0.3);-moz-box-shadow:0 3px 7px rgba(0,0,0,0.3);box-shadow:0 3px 7px rgba(0,0,0,0.3);-webkit-background-clip:padding-box;-moz-background-clip:padding-box;background-clip:padding-box;outline:none}.modal.fade{-webkit-transition:opacity .3s linear, top .3s ease-out;-moz-transition:opacity .3s linear, top .3s ease-out;-o-transition:opacity .3s linear, top .3s ease-out;transition:opacity .3s linear, top .3s ease-out;top:-25%}
.modal.fade.in{top:10%}
.modal-header{padding:9px 15px;border-bottom:1px solid #eee}.modal-header .close{margin-top:2px}
.modal-header h3{margin:0;line-height:30px}
.modal-body{position:relative;overflow-y:auto;max-height:400px;padding:15px}
.modal-form{margin-bottom:0}
.modal-footer{padding:14px 15px 15px;margin-bottom:0;text-align:right;background-color:#f5f5f5;border-top:1px solid #ddd;-webkit-border-radius:0 0 6px 6px;-moz-border-radius:0 0 6px 6px;border-radius:0 0 6px 6px;-webkit-box-shadow:inset 0 1px 0 #fff;-moz-box-shadow:inset 0 1px 0 #fff;box-shadow:inset 0 1px 0 #fff;*zoom:1}.modal-footer:before,.modal-footer:after{display:table;content:"";line-height:0}
.modal-footer:after{clear:both}
.modal-footer .btn+.btn{margin-left:5px;margin-bottom:0}
.modal-footer .btn-group .btn+.btn{margin-left:-1px}
.modal-footer .btn-block+.btn-block{margin-left:0}
.tooltip{position:absolute;z-index:1030;display:block;visibility:visible;font-size:11px;line-height:1.4;opacity:0;filter:alpha(opacity=0)}.tooltip.in{opacity:.8;filter:alpha(opacity=80)}
.tooltip.top{margin-top:-3px;padding:5px 0}
.tooltip.right{margin-left:3px;padding:0 5px}
.tooltip.bottom{margin-top:3px;padding:5px 0}
.tooltip.left{margin-left:-3px;padding:0 5px}
.tooltip-inner{max-width:200px;padding:8px;color:#fff;text-align:center;text-decoration:none;background-color:#000;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}
.tooltip-arrow{position:absolute;width:0;height:0;border-color:transparent;border-style:solid}
.tooltip.top .tooltip-arrow{bottom:0;left:50%;margin-left:-5px;border-width:5px 5px 0;border-top-color:#000}
.tooltip.right .tooltip-arrow{top:50%;left:0;margin-top:-5px;border-width:5px 5px 5px 0;border-right-color:#000}
.tooltip.left .tooltip-arrow{top:50%;right:0;margin-top:-5px;border-width:5px 0 5px 5px;border-left-color:#000}
.tooltip.bottom .tooltip-arrow{top:0;left:50%;margin-left:-5px;border-width:0 5px 5px;border-bottom-color:#000}
.popover{position:absolute;top:0;left:0;z-index:1010;display:none;max-width:276px;padding:1px;text-align:left;background-color:#fff;-webkit-background-clip:padding-box;-moz-background-clip:padding;background-clip:padding-box;border:1px solid #ccc;border:1px solid rgba(0,0,0,0.2);-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;-webkit-box-shadow:0 5px 10px rgba(0,0,0,0.2);-moz-box-shadow:0 5px 10px rgba(0,0,0,0.2);box-shadow:0 5px 10px rgba(0,0,0,0.2);white-space:normal}.popover.top{margin-top:-10px}
.popover.right{margin-left:10px}
.popover.bottom{margin-top:10px}
.popover.left{margin-left:-10px}
.popover-title{margin:0;padding:8px 14px;font-size:14px;font-weight:normal;line-height:18px;background-color:#f7f7f7;border-bottom:1px solid #ebebeb;border-radius:5px 5px 0 0;-webkit-border-radius:5px 5px 0 0;-moz-border-radius:5px 5px 0 0;border-radius:5px 5px 0 0}.popover-title:empty{display:none}
.popover-content{padding:9px 14px}
.popover .arrow,.popover .arrow:after{position:absolute;display:block;width:0;height:0;border-color:transparent;border-style:solid}
.popover .arrow{border-width:11px}
.popover .arrow:after{border-width:10px;content:""}
.popover.top .arrow{left:50%;margin-left:-11px;border-bottom-width:0;border-top-color:#999;border-top-color:rgba(0,0,0,0.25);bottom:-11px}.popover.top .arrow:after{bottom:1px;margin-left:-10px;border-bottom-width:0;border-top-color:#fff}
.popover.right .arrow{top:50%;left:-11px;margin-top:-11px;border-left-width:0;border-right-color:#999;border-right-color:rgba(0,0,0,0.25)}.popover.right .arrow:after{left:1px;bottom:-10px;border-left-width:0;border-right-color:#fff}
.popover.bottom .arrow{left:50%;margin-left:-11px;border-top-width:0;border-bottom-color:#999;border-bottom-color:rgba(0,0,0,0.25);top:-11px}.popover.bottom .arrow:after{top:1px;margin-left:-10px;border-top-width:0;border-bottom-color:#fff}
.popover.left .arrow{top:50%;right:-11px;margin-top:-11px;border-right-width:0;border-left-color:#999;border-left-color:rgba(0,0,0,0.25)}.popover.left .arrow:after{right:1px;border-right-width:0;border-left-color:#fff;bottom:-10px}
.thumbnails{margin-left:-20px;list-style:none;*zoom:1}.thumbnails:before,.thumbnails:after{display:table;content:"";line-height:0}
.thumbnails:after{clear:both}
.row-fluid .thumbnails{margin-left:0}
.thumbnails>li{float:left;margin-bottom:20px;margin-left:20px}
.thumbnail{display:block;padding:4px;line-height:20px;border:1px solid #ddd;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;-webkit-box-shadow:0 1px 3px rgba(0,0,0,0.055);-moz-box-shadow:0 1px 3px rgba(0,0,0,0.055);box-shadow:0 1px 3px rgba(0,0,0,0.055);-webkit-transition:all .2s ease-in-out;-moz-transition:all .2s ease-in-out;-o-transition:all .2s ease-in-out;transition:all .2s ease-in-out}
a.thumbnail:hover,a.thumbnail:focus{border-color:#08c;-webkit-box-shadow:0 1px 4px rgba(0,105,214,0.25);-moz-box-shadow:0 1px 4px rgba(0,105,214,0.25);box-shadow:0 1px 4px rgba(0,105,214,0.25)}
.thumbnail>img{display:block;max-width:100%;margin-left:auto;margin-right:auto}
.thumbnail .caption{padding:9px;color:#555}
.media,.media-body{overflow:hidden;*overflow:visible;zoom:1}
.media,.media .media{margin-top:15px}
.media:first-child{margin-top:0}
.media-object{display:block}
.media-heading{margin:0 0 5px}
.media>.pull-left{margin-right:10px}
.media>.pull-right{margin-left:10px}
.media-list{margin-left:0;list-style:none}
.label,.badge{display:inline-block;padding:2px 4px;font-size:10.998px;font-weight:bold;line-height:14px;color:#fff;vertical-align:baseline;white-space:nowrap;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#999}
.label{border-radius:3px;-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px}
.badge{padding-left:9px;padding-right:9px;border-radius:9px;-webkit-border-radius:9px;-moz-border-radius:9px;border-radius:9px}
.label:empty,.badge:empty{display:none}
a.label:hover,a.label:focus,a.badge:hover,a.badge:focus{color:#fff;text-decoration:none;cursor:pointer}
.label-important,.badge-important{background-color:#b94a48}
.label-important[href],.badge-important[href]{background-color:#953b39}
.label-warning,.badge-warning{background-color:#f89406}
.label-warning[href],.badge-warning[href]{background-color:#c67605}
.label-success,.badge-success{background-color:#468847}
.label-success[href],.badge-success[href]{background-color:#356635}
.label-info,.badge-info{background-color:#3a87ad}
.label-info[href],.badge-info[href]{background-color:#2d6987}
.label-inverse,.badge-inverse{background-color:#333}
.label-inverse[href],.badge-inverse[href]{background-color:#1a1a1a}
.btn .label,.btn .badge{position:relative;top:-1px}
.btn-mini .label,.btn-mini .badge{top:0}
@-webkit-keyframes progress-bar-stripes{from{background-position:40px 0} to{background-position:0 0}}@-moz-keyframes progress-bar-stripes{from{background-position:40px 0} to{background-position:0 0}}@-ms-keyframes progress-bar-stripes{from{background-position:40px 0} to{background-position:0 0}}@-o-keyframes progress-bar-stripes{from{background-position:0 0} to{background-position:40px 0}}@keyframes progress-bar-stripes{from{background-position:40px 0} to{background-position:0 0}}.progress{overflow:hidden;height:20px;margin-bottom:20px;background-color:#f7f7f7;background-image:-moz-linear-gradient(top, #f5f5f5, #f9f9f9);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#f5f5f5), to(#f9f9f9));background-image:-webkit-linear-gradient(top, #f5f5f5, #f9f9f9);background-image:-o-linear-gradient(top, #f5f5f5, #f9f9f9);background-image:linear-gradient(to bottom, #f5f5f5, #f9f9f9);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#fff5f5f5', endColorstr='#fff9f9f9', GradientType=0);-webkit-box-shadow:inset 0 1px 2px rgba(0,0,0,0.1);-moz-box-shadow:inset 0 1px 2px rgba(0,0,0,0.1);box-shadow:inset 0 1px 2px rgba(0,0,0,0.1);border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}
.progress .bar{width:0;height:100%;color:#fff;float:left;font-size:12px;text-align:center;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#0e90d2;background-image:-moz-linear-gradient(top, #149bdf, #0480be);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#149bdf), to(#0480be));background-image:-webkit-linear-gradient(top, #149bdf, #0480be);background-image:-o-linear-gradient(top, #149bdf, #0480be);background-image:linear-gradient(to bottom, #149bdf, #0480be);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff149bdf', endColorstr='#ff0480be', GradientType=0);-webkit-box-shadow:inset 0 -1px 0 rgba(0,0,0,0.15);-moz-box-shadow:inset 0 -1px 0 rgba(0,0,0,0.15);box-shadow:inset 0 -1px 0 rgba(0,0,0,0.15);-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box;-webkit-transition:width .6s ease;-moz-transition:width .6s ease;-o-transition:width .6s ease;transition:width .6s ease}
.progress .bar+.bar{-webkit-box-shadow:inset 1px 0 0 rgba(0,0,0,.15), inset 0 -1px 0 rgba(0,0,0,.15);-moz-box-shadow:inset 1px 0 0 rgba(0,0,0,.15), inset 0 -1px 0 rgba(0,0,0,.15);box-shadow:inset 1px 0 0 rgba(0,0,0,.15), inset 0 -1px 0 rgba(0,0,0,.15)}
.progress-striped .bar{background-color:#149bdf;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(.25, rgba(255,255,255,0.15)), color-stop(.25, transparent), color-stop(.5, transparent), color-stop(.5, rgba(255,255,255,0.15)), color-stop(.75, rgba(255,255,255,0.15)), color-stop(.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);-webkit-background-size:40px 40px;-moz-background-size:40px 40px;-o-background-size:40px 40px;background-size:40px 40px}
.progress.active .bar{-webkit-animation:progress-bar-stripes 2s linear infinite;-moz-animation:progress-bar-stripes 2s linear infinite;-ms-animation:progress-bar-stripes 2s linear infinite;-o-animation:progress-bar-stripes 2s linear infinite;animation:progress-bar-stripes 2s linear infinite}
.progress-danger .bar,.progress .bar-danger{background-color:#dd514c;background-image:-moz-linear-gradient(top, #ee5f5b, #c43c35);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#ee5f5b), to(#c43c35));background-image:-webkit-linear-gradient(top, #ee5f5b, #c43c35);background-image:-o-linear-gradient(top, #ee5f5b, #c43c35);background-image:linear-gradient(to bottom, #ee5f5b, #c43c35);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffee5f5b', endColorstr='#ffc43c35', GradientType=0)}
.progress-danger.progress-striped .bar,.progress-striped .bar-danger{background-color:#ee5f5b;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(.25, rgba(255,255,255,0.15)), color-stop(.25, transparent), color-stop(.5, transparent), color-stop(.5, rgba(255,255,255,0.15)), color-stop(.75, rgba(255,255,255,0.15)), color-stop(.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}
.progress-success .bar,.progress .bar-success{background-color:#5eb95e;background-image:-moz-linear-gradient(top, #62c462, #57a957);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#62c462), to(#57a957));background-image:-webkit-linear-gradient(top, #62c462, #57a957);background-image:-o-linear-gradient(top, #62c462, #57a957);background-image:linear-gradient(to bottom, #62c462, #57a957);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff62c462', endColorstr='#ff57a957', GradientType=0)}
.progress-success.progress-striped .bar,.progress-striped .bar-success{background-color:#62c462;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(.25, rgba(255,255,255,0.15)), color-stop(.25, transparent), color-stop(.5, transparent), color-stop(.5, rgba(255,255,255,0.15)), color-stop(.75, rgba(255,255,255,0.15)), color-stop(.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}
.progress-info .bar,.progress .bar-info{background-color:#4bb1cf;background-image:-moz-linear-gradient(top, #5bc0de, #339bb9);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#5bc0de), to(#339bb9));background-image:-webkit-linear-gradient(top, #5bc0de, #339bb9);background-image:-o-linear-gradient(top, #5bc0de, #339bb9);background-image:linear-gradient(to bottom, #5bc0de, #339bb9);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff5bc0de', endColorstr='#ff339bb9', GradientType=0)}
.progress-info.progress-striped .bar,.progress-striped .bar-info{background-color:#5bc0de;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(.25, rgba(255,255,255,0.15)), color-stop(.25, transparent), color-stop(.5, transparent), color-stop(.5, rgba(255,255,255,0.15)), color-stop(.75, rgba(255,255,255,0.15)), color-stop(.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}
.progress-warning .bar,.progress .bar-warning{background-color:#faa732;background-image:-moz-linear-gradient(top, #fbb450, #f89406);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#fbb450), to(#f89406));background-image:-webkit-linear-gradient(top, #fbb450, #f89406);background-image:-o-linear-gradient(top, #fbb450, #f89406);background-image:linear-gradient(to bottom, #fbb450, #f89406);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#fffbb450', endColorstr='#fff89406', GradientType=0)}
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.carousel-caption h4,.carousel-caption p{color:#fff;line-height:20px}
.carousel-caption h4{margin:0 0 5px}
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.hero-unit li{line-height:30px}
.pull-right{float:right}
.pull-left{float:left}
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.show{display:block}
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.affix{position:fixed}
@-ms-viewport{width:device-width}.hidden{display:none;visibility:hidden}
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.visible-tablet{display:none !important}
.hidden-desktop{display:none !important}
.visible-desktop{display:inherit !important}
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<div class="highlight"><pre><span class="o">%</span><span class="k">pylab</span> <span class="n">inline</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
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<h1 id="using-finite-differences-to-approximate-derivatives">Using finite differences to approximate derivatives</h1>
<p>The material in this notebook is a supplement to chapter 1 of the text.</p>
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<p>Suppose that you&#39;re given a table of values of some &quot;secret&quot; function $f(x)$, but you are not given the function itself. For example:</p>
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<div class="highlight"><pre><span class="n">x_values</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span>
<span class="n">y_values</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">8</span><span class="p">,</span><span class="mi">27</span><span class="p">,</span><span class="mi">64</span><span class="p">)</span>
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<p>In order to understand the function that generated these values, we could plot them:</p>
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<div class="highlight"><pre><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span><span class="n">y_values</span><span class="p">,</span><span class="s">&#39;-o&#39;</span><span class="p">)</span>
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<p>In the plot, the points have been connected by a line, and you might use the slope of this line if you wanted to estimate the derivative of the function. For instance, to estimate the slope at $x=2$, you could use the slope of the line between $x=2$ and $x=3$:</p>
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<div class="highlight"><pre><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span><span class="n">y_values</span><span class="p">,</span><span class="s">&#39;-o&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">hold</span><span class="p">(</span><span class="bp">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_values</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">],</span><span class="n">y_values</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">],</span><span class="s">&#39;-r&#39;</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
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<p>$$\left. f'(x) \right|_{x=2} \approx \frac{f(3)-f(2)}{3-2} = 19.$$</p>
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<p>Alternatively, you might use the slope of the line between $x=1$ and $x=2$:</p>
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<div class="highlight"><pre><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span><span class="n">y_values</span><span class="p">,</span><span class="s">&#39;-o&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">hold</span><span class="p">(</span><span class="bp">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_values</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">],</span><span class="n">y_values</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">],</span><span class="s">&#39;-r&#39;</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
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<p>$$\left. f'(x) \right|_{x=2} \approx \frac{f(2)-f(1)}{2-1} = 7.$$</p>
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<p>Remember that the derivative is defined as the limit of a formula rather like our first approximation above (referred to as a <em>forward difference</em>):</p>
<p>$$ f'(x) = \lim_{h\to 0} \frac{f(x+h)-f(x)}{(x+h)-x} = \lim_{h\to 0} \frac{f(x+h)-f(x)}{h}.$$</p>
<p>Notice that the fraction in the definition is just the slope of the line connecting the values of $f$ at $x$ and $x+h$. We could equally well define the derivative in terms of a <em>backward difference</em>, similar to our second formula above:</p>
<p>$$ f'(x) = \lim_{h\to 0} \frac{f(x)-f(x-h)}{x-(x-h)} = \lim_{h\to 0} \frac{f(x)-f(x-h)}{h}.$$</p>
<p>Yet another way of defining the derivative would be to use the slope of the line connecting points $x+h$ and $x-h$, leading to</p>
<p>$$ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x-h)}{2h}.$$</p>
<p>Here the factor $2h$ in the denominator is just the length of the interval $(x-h,x+h)$. Using this formula with our values gives</p>
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<div class="highlight"><pre><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span><span class="n">y_values</span><span class="p">,</span><span class="s">&#39;-ok&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">hold</span><span class="p">(</span><span class="bp">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">((</span><span class="n">x_values</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="n">x_values</span><span class="p">[</span><span class="mi">3</span><span class="p">]),(</span><span class="n">y_values</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="n">y_values</span><span class="p">[</span><span class="mi">3</span><span class="p">]),</span><span class="s">&#39;-r&#39;</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
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<p>$$\left. f'(x) \right|_{x=2} \approx \frac{f(3)-f(1)}{3-1} = 13.$$</p>
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<p>When we only know the values of a function at a finite set of points, we can&#39;t compute these limits, so it makes sense to use a finite value of $h$ in order to approximate the derivative. This approach is known as the <em>finite difference method</em>. Soon we will use it to solve differential equations, but first let&#39;s examine its effectiveness in approximating derivatives.</p>
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<p>You may have guessed that the &quot;secret&quot; function that generated these values is $f(x)=x^3$. Let&#39;s compare our three estimates of the derivative with the true derivative: $f'(2) = 3\cdot 2^2 = 12$. Clearly the third formula (known as a <em>centered difference</em>) is the best approximation. We can also see this by plotting the approximations and the tangent line (whose slope is that of the true derivative):</p>
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<div class="highlight"><pre><span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span>
<span class="n">tangent</span> <span class="o">=</span> <span class="mi">8</span> <span class="o">+</span> <span class="mi">12</span><span class="o">*</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="s">&#39;k&#39;</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_values</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">],</span><span class="n">y_values</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">],</span><span class="s">&#39;-g&#39;</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_values</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">],</span><span class="n">y_values</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">],</span><span class="s">&#39;-b&#39;</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">((</span><span class="n">x_values</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="n">x_values</span><span class="p">[</span><span class="mi">3</span><span class="p">]),(</span><span class="n">y_values</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="n">y_values</span><span class="p">[</span><span class="mi">3</span><span class="p">]),</span><span class="s">&#39;-r&#39;</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">tangent</span><span class="p">,</span><span class="s">&#39;--k&#39;</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s">&#39;f(x)&#39;</span><span class="p">,</span><span class="s">&#39;Forward&#39;</span><span class="p">,</span><span class="s">&#39;Backward&#39;</span><span class="p">,</span><span class="s">&#39;Centered&#39;</span><span class="p">,</span><span class="s">&#39;Tangent&#39;</span><span class="p">],</span><span class="n">loc</span><span class="o">=</span><span class="s">&#39;best&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">((</span><span class="mf">0.5</span><span class="p">,</span><span class="mf">3.5</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">40</span><span class="p">))</span>
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<p>It&#39;s clear that the centered difference approximation (slope of the red line) is closest to the derivative (slope of the dotted line). Would this be true if we picked another function $f(x)$, or if we used function values at different points? Let&#39;s answer the second question with an experiment.</p>
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<div class="highlight"><pre><span class="n">x</span> <span class="o">=</span> <span class="mf">2.</span>
<span class="n">df</span> <span class="o">=</span> <span class="mf">12.</span>
<span class="k">for</span> <span class="n">h</span> <span class="ow">in</span> <span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.05</span><span class="p">,</span> <span class="mf">0.025</span><span class="p">):</span>
<span class="n">forward</span> <span class="o">=</span> <span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="o">+</span><span class="n">h</span><span class="p">)</span><span class="o">-</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">))</span><span class="o">/</span><span class="n">h</span>
<span class="n">forward_error</span> <span class="o">=</span> <span class="n">forward</span> <span class="o">-</span> <span class="n">df</span>
<span class="k">print</span> <span class="n">forward_error</span>
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<p>It seems clear from the results that reducing $h$ by a factor of two also reduces the error in the forward difference approximation by a factor of two.</p>
<p><strong>Now add backward and centered difference approximations to the code above and try to figure out what happens to their errors as $h$ decreases. Make a table like Table 1.1 on page 5 of the textbook.</strong> Is the centered difference always the most accurate? Do you think it will still be the most accurate if we continue reducing $h$?</p>
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<p><strong>Now redefine the function $f(x)$ to be $x^2$ and generate the same table. Do you see anything surprising? Can you explain it?</strong> If not, make a guess.</p>
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<h2 id="estimating-truncation-errors">Estimating truncation errors</h2>
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<p>The error made by a finite difference approximation is called <em>truncation error</em>. Why? Well, we can estimate the error by expanding each function value in a <em>Taylor series</em>:</p>
<p>$$f(x+h) = f(x) + h f'(x) + \frac{1}{2}h^2 f''(x) + \frac{1}{6} h^3 f'''(x) + {\mathcal O}(h^4)$$</p>
<p>Here ${\mathcal O}(h^4)$ indicates that the rest of the terms in the series vanish at least as quickly as $h^4$ when $h\to 0$ (see Appendix A of the text).
Substituting this series in our forward difference formula gives
\begin{align}
\frac{f(x+h) - f(x)}{h} &amp; = \frac{f(x) + h f'(x) + \frac{1}{2}h^2 f''(x) + \frac{1}{6} h^3 f'''(x) + {\mathcal O}(h^4) - f(x)}{h} \\
&amp; = f'(x) + \frac{1}{2}h f''(x) + \frac{1}{6} h^2 f'''(x) + {\mathcal O}(h^3) \\
&amp; = f'(x) + \frac{1}{2}h f''(x) + {\mathcal O}(h^2).
\end{align}</p>
<p>This analysis confirms our intuition that the forward difference approximates $f'(x)$, but it tells us much more. Most importantly, it shows that the largest term in the error in this approximation is proportional to $h$. That&#39;s why we saw that decreasing $h$ by a factor of two caused the error to decrease by the same amount.</p>
<p>Notice that if we truncated the Taylor series after the first term, we would get the forward difference formula exactly. That is why the error is referred to as <em>truncation error</em> -- it&#39;s the error we get from truncating an infinite series. The term $\frac{1}{2} h f''(x)$ is referred to as the <em>leading truncation error</em> because when $h$ is very small we expect that term to be much bigger than all the ones that come after it.</p>
<p>Since in our simple example we know the function $f(x)$, we could evaluate error terms in the series above to get a better approximation of the error. But typically we won&#39;t know what the function is (if we did, why would we need finite differences?), so we&#39;ll be most interested in knowing what power of $h$ multiplies the leading error term.</p>
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<p><strong>Write down the Taylor series for $f(x-h)$ about $x$. Use that (and the series above) to work out the leading truncation error terms for the backward and centered difference formulas.</strong> Does your result for the centered formula allow you to explain the results you found before when applying it to $f(x)=x^2$?</p>
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<h2 id="polynomial-interpolation-and-finite-difference-formulas">Polynomial interpolation and finite difference formulas</h2>
<p>In sections 1.2-1.5 of the text, a method for finding finite difference formulas is given, based on Taylor series. Here we will approach the same topic from a different route, using polynomial interpolation. The idea is this: to approximate the derivative of a function whose point values are known, we first find a polynomial that interpolates those values, then evaluate the derivative of that polynomial.</p>
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<p>To begin, suppose we are given three function values: $f(x_0-h), f(x_0), f(x_0+h)$, which we&#39;ll denote by $(f_1,f_2,f_3)$. We wish to find a polynomial that passes through these three points. As you may know, a set of $n$ values uniquely defines a polynomial of degree $n-1$, so we will look for a quadratic polynomial. To make the computation simpler, we&#39;ll write it this way: $p(x) = a + b (x-x_0) + c (x-x_0)^2$. We know that $p$ and $f$ must agree at the three given points, which means
\begin{align}
a + b(-h) + c (-h)^2 &amp; = f_1 \\
a + b(0) + c(0)^2 &amp; = f_2 \\
a + b (h) + c (h)^2 &amp; = f_3 \\
\end{align}</p>
<p>or simply</p>
<p>\begin{align}
a - hb + h^2c &amp; = f_1 \\
a &amp; = f_2 \\
a + hb + h^2c &amp; = f_3 \\
\end{align}</p>
<p>We can rewrite this system of equations in matrix form:</p>
<p>\begin{align}
\begin{pmatrix}
1 &amp; -h &amp; h^2 \\
1 &amp; 0 &amp; 0 \\
1 &amp; h &amp; h^2 \\
\end{pmatrix}
\begin{pmatrix} a \\ b \\ c \end{pmatrix}
&amp; = \begin{pmatrix} f_1 \\ f_2 \\ f_3 \end{pmatrix}
\end{align}</p>
<p>This is a linear system that we can solve for the coefficients $a,b,c$ in terms of $h$, and the values of $f$. The result is</p>
<p>\begin{align}
a &amp; = f_2, &amp; b &amp; = \frac{f_3-f_1}{2h}, &amp; c &amp; = \frac{f_1 -2 f_2 + f_3}{2h^2}.
\end{align}</p>
<p>Thus</p>
<p>\begin{align}
p(x) = f_2 + \frac{x-x_0}{2h}(f_3-f_1) + \frac{(x-x_0)^2}{2h^2}(f_1-2f_2+f_3).
\end{align}</p>
<p>Now suppose we wish to approximate the derivative of $f$. We have an easy approach: use the derivative of $p$:</p>
<p>\begin{align}
p'(x) = \frac{f_3-f_1}{2h} + \frac{x-x_0}{h^2}(f_1 -2 f_2 + f_3).
\end{align}</p>
<p>In particular, if want to approximate the derivative at $x=x_0$, we get simply</p>
<p>$$f'(x) \approx p'(x_0) = \frac{f_3-f_1}{2h} = \frac{f(x_0+h) - f(x_0-h)}{2h}.$$</p>
<p><strong>Do you recognize this approximation? Now use $p(x)$ to get an approximation for the second derivative of $f(x)$. Write down the resulting formula.</strong></p>
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Derive a formula for $f''(x)$ based on the values $f(x), f(x-h), f(x-3h)$ by determining the interpolating polynomial and differentiating it. How accurate is your formula?
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<p><strong>Can you think of a similar approach that would allow you to derive rules for numerical quadrature (integration)?</strong></p>
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