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| /* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ | |
| /* [ Created with wxMaxima version 0.8.3 ] */ | |
| /* [wxMaxima: title start ] | |
| 2301560 Comp Tools Math | |
| September 4, 2009 | |
| [wxMaxima: title end ] */ | |
| /* [wxMaxima: section start ] | |
| Graphics | |
| [wxMaxima: section end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: subsect start ] | |
| Simple 2D Plots | |
| [wxMaxima: subsect end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot2d(sin(x)/x,[x,-6*%pi,6*%pi]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot2d(sin(x)/x,[x,-6*%pi,6*%pi],[y,-1.2,1.2], | |
| [xlabel,"x label here"],[ylabel,"y label here"],[box,false]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot2d(sin(x)/x,[x,-6*%pi,6*%pi],[psfile,"fig1.ps"]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot2d([sin(x),cos(x)],[x,-2*%pi,2*%pi],[legend,"sine","cosine"]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| my_preamble: "set xtics ('-2{/Symbol p}' -6.283,\ | |
| '-3{/Symbol p}/2' -4.712, '-{/Symbol p}' -3.1415, \ | |
| '-{/Symbol p}/2' -1.5708, '0' 0,'{/Symbol p}/2' 1.5708, \ | |
| '{/Symbol p}' 3.1415,'3{/Symbol p}/2' 4.712, '2{/Symbol p}' 6.283)"$ | |
| plot2d ([cos(x), sin(x), tan(x)], [x, -2*%pi, 2*%pi], | |
| [y, -2, 2], [gnuplot_preamble, my_preamble],[psfile,"fig2.ps"]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: subsect start ] | |
| 2D List Plots | |
| [wxMaxima: subsect end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: input start ] */ | |
| data1:makelist([x/50,sin(x)],x,-500,500)$ | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot2d([discrete,data1],[style,[points,0.5,0,1]]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: subsect start ] | |
| 2D Parametric Plots | |
| [wxMaxima: subsect end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot2d([parametric,cos(t),sin(t),[t,0,2*%pi],[nticks,200]],[x,-4/3,4/3]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot2d([parametric,cos(t),sin(t),[t,0,2*%pi],[nticks,4]],[x,-4/3,4/3]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot2d([parametric,cos(3*t),sin(5*t),[t,0,2*%pi],[nticks,1000]],[x,-1.2,1.2],[y,-1.2,1.2]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: subsect start ] | |
| Implicit Plots | |
| [wxMaxima: subsect end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: input start ] */ | |
| load(implicit_plot); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| implicit_plot(x^2 - y^2 = 1, [x, -4, 4], [y, -4, 4]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| implicit_plot(makelist(x^2 - y^2 = i,i,1,5), [x, -4, 4], [y, -4, 4], | |
| [gnuplot_preamble,"unset key; set zeroaxis"]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: subsect start ] | |
| Contour Plots | |
| [wxMaxima: subsect end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: input start ] */ | |
| contour_plot(x^2-y^2,[x,-10,10],[y,-10,10]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| set_plot_option([gnuplot_preamble, | |
| "set cntrparam levels incremental -100,10,100;unset clabel;unset key"])$ | |
| contour_plot(x^2-y^2,[x,-10,10],[y,-10,10]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: subsect start ] | |
| Gradient Fields | |
| [wxMaxima: subsect end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: input start ] */ | |
| load(plotdf); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plotdf(y-0.1*x^2/10,[trajectory_at,2,0.9]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plotdf(a*y+b*x^2/10+c,[trajectory_at,2,0.9],[sliders,"a=-10:10,b=0.1:4,c=-5:5"]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: subsect start ] | |
| 3D Plots | |
| [wxMaxima: subsect end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot3d (2^(-u^2 + v^2), [u, -3, 3], [v, -2, 2]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot3d (2^(-u^2 + v^2), [u, -3, 3], [v, -2, 2],[plot_format, openmath]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: subsect start ] | |
| 3D Parametric Plots | |
| [wxMaxima: subsect end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot3d([sin(u)*cos(v),sin(u)*sin(v),cos(u)],[u,0,%pi],[v,0,2*%pi]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot3d([u*cos(v),u*sin(v),u^2],[u,0,3],[v,0,2*%pi]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: subsect start ] | |
| Draw | |
| [wxMaxima: subsect end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: input start ] */ | |
| load(draw); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| draw2d( | |
| ellipse(0,0,1,1,0,360), | |
| transparent=true, | |
| color = blue, | |
| line_width = 4, | |
| ellipse(0,0,2,1/2,0,360), | |
| proportional_axes = xy) $ | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| draw2d( | |
| explicit(sin(x),x,0,10), | |
| yaxis_secondary = true, | |
| ytics_secondary = true, | |
| yrange = [-3, 3], | |
| yrange_secondary = [-20, 20], | |
| color = blue, | |
| explicit(100*sin(x+0.1)+2,x,0,10)); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| draw3d(yrange = [-3,3], | |
| zrange = [-2,5], | |
| explicit(x^2+y^2,x,-1,1,y,-1,1), | |
| xrange = [-3,3])$ | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| draw3d ( | |
| enhanced3d = true, | |
| color = green, | |
| cbrange = [-3,10], | |
| explicit(x^2+y^2, x,-2,2,y,-2,2)); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| draw( | |
| delay = 100, | |
| file_name = "fig3", | |
| terminal = 'animated_gif, | |
| gr2d(explicit(x^2,x,-1,1)), | |
| gr2d(explicit(x^3,x,-1,1)), | |
| gr2d(explicit(x^4,x,-1,1))); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| draw2d(xrange = [0,10], | |
| yrange = [0,10], | |
| point_size = 3, | |
| point_type = diamant, | |
| points([[1,1],[5,1],[9,1]]), | |
| point_type = filled_down_triangle, | |
| points([[1,2],[5,2],[9,2]]), | |
| point_type = asterisk, | |
| points([[1,3],[5,3],[9,3]]), | |
| point_type = filled_diamant, | |
| points([[1,4],[5,4],[9,4]]), | |
| point_type = 5, | |
| points([[1,5],[5,5],[9,5]]), | |
| point_type = 6, | |
| points([[1,6],[5,6],[9,6]]), | |
| point_type = filled_circle, | |
| points([[1,7],[5,7],[9,7]]), | |
| point_type = 8, | |
| points([[1,8],[5,8],[9,8]]), | |
| point_type = filled_diamant, | |
| points([[1,9],[5,9],[9,9]]) ); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| x: make_array (fixnum, 10) $ | |
| y: make_array (fixnum, 10) $ | |
| z: make_array (fixnum, 10) $ | |
| for i:0 thru 9 do ( | |
| x[i]: random(10), | |
| y[i]: random(10), | |
| z[i]: random(10) ) $ | |
| draw3d(points(x,y,z)); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: section start ] | |
| Curve Fitting | |
| [wxMaxima: section end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: input start ] */ | |
| load(lsquares); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| data1_list:makelist([x,2*x+3+random(1.0)],x,-5,5)$ | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot2d([discrete,data1_list],[style,[points,2,2,1]]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| data1_matrix:apply('matrix,data1_list)$ | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| param1:lsquares_estimates(data1_matrix, [x,y], y = a*x+b, [a,b]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: input start ] */ | |
| plot2d([[discrete,data1_list],subst(param1[1],a*x+b)],[x,-5,5], | |
| [style, [points,2,2,1], [lines,1,1]], | |
| [legend,"data","least squares fit"]); | |
| /* [wxMaxima: input end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* [wxMaxima: section start ] | |
| Exercise | |
| [wxMaxima: section end ] */ | |
| /* [wxMaxima: fold start ] */ | |
| /* [wxMaxima: comment start ] | |
| Prob 1. Let Tn(x) be the Taylor polynomial of degree n of cos x about the point 0. | |
| Plot cos(x) along with T2(x), T4(x), T6(x), and T8(x). | |
| Set an appropriate range of the plot to reveal how well the Taylor polynomials | |
| approximate the function. The Taylor polynomials should be automatically generated. | |
| [wxMaxima: comment end ] */ | |
| /* [wxMaxima: comment start ] | |
| Prob 2. Plot the polar curve r = 1+4sin(theta/3). | |
| [wxMaxima: comment end ] */ | |
| /* [wxMaxima: comment start ] | |
| Prob 3. Plot the surface of revolution generated by y = x^2, 0 < x < 1 | |
| about each of the following axes. | |
| 3.1 The x axis. | |
| 3.2 The y axis. | |
| 3.3 The line y = x. | |
| [wxMaxima: comment end ] */ | |
| /* [wxMaxima: comment start ] | |
| Prob 4. Generate the following data | |
| [x, (1+random(1.0)) x^4 + random(1.0)x] | |
| where x = -1.00, -0.95, -0.90, ..., 1.00. | |
| Then fit each of the following models to the this set of data. | |
| You should make some plots to show how well the model fits to the data. | |
| 4.1 y = ax^4 + bx^3 + cx^2 + dx + e. | |
| 4.2 y = ax^4 + bx. | |
| [wxMaxima: comment end ] */ | |
| /* [wxMaxima: comment start ] | |
| Prob 5. Fit the following data with an appropriate model. | |
| [x, x + (4 + random(1.0))sin(x) + (1+random(1.0))sin(5x)] | |
| where x = 0.0, 0.1, 0.2, ..., 10.0 | |
| . | |
| [wxMaxima: comment end ] */ | |
| /* [wxMaxima: fold end ] */ | |
| /* Maxima can't load/batch files which end with a comment! */ | |
| "Created with wxMaxima"$ |
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