markusbuchholz

POSIX commands Cheatsheat

• admin - create and administer SCCS files (DEVELOPMENT)
• alias - define or display aliases
• ar - create and maintain library archives
• asa - interpret carriage-control characters
• at - execute commands at a later time
• awk - pattern scanning and processing language
• basename - return non-directory portion of a pathname
• batch - schedule commands to be executed in a batch queue

markusbuchholz

// g++ digital_filter_design.cpp -o t -I/usr/include/python3.8 -lpython3.8

#include <iostream>
#include <vector>
#include <tuple>
#include <complex>

#include "matplotlibcpp.h"

markusbuchholz

##############
$$\large B(t) = \sum_{i=0}^{n} \binom{n}{i}(1-t)^{n-i}t^{i}P_{i} $$

$$\large \text {where, parameter t:}$$

$$\large 0\leq t\leq 1 $$
#############
$$\large \binom{n}{k} = \frac{n!}{k!(n-k)!} = \prod_{i=1}^{k}\frac{n+1-i}{i} $$
#############
$$\large B(t) = (1-t)^3P_{0} + 3(1-t)^2tP_{1} + 3(1-t)^2t^2P_{2} + t^3P_{3} $$

markusbuchholz

//// g++ bezier_curve.cpp -o t -I/usr/include/python3.8 -lpython3.8

#include <iostream>
#include <vector>
#include <tuple>
#include <math.h>

#include "matplotlibcpp.h"

namespace plt = matplotlibcpp;

markusbuchholz

double computeBinominal(int n, int k)
{

    double value = 1.0;

    for (int i = 1; i <= k; i++)
    {

        value = value * ((n + 1 - i) / i);
    }

markusbuchholz

1	144.4
2	124.2
3	113.8
4	133.8
5	104.4
6	95
7	135.2
8	49.2
9	75.2
10	71.2

markusbuchholz

68–95–99.7 rule

$$\large P_{r}(\mu - 1\sigma \leq \mu + 1\sigma ) \approx 68.27%$$ $$\large P_{r}(\mu - 2\sigma \leq \mu + 3\sigma ) \approx 95.45%$$ $$\large P_{r}(\mu - 3\sigma \leq \mu + 3\sigma ) \approx 99.73%$$

Normal distribution

markusbuchholz

//g++ standard_deviation.cpp -I/usr/include/python3.8 -lpython3.8

#include <iostream>
#include <tuple>
#include <vector>
#include <math.h>

#include "matplotlibcpp.h"

namespace plt = matplotlibcpp;

markusbuchholz

//g++ cpp_smoothing.cpp -I/usr/include/python3.8 -lpython3.8
#include <iostream>
#include <fstream>
#include <sstream>
#include <string>
#include <algorithm> //for replace
#include <vector>
#include <tuple>
#include <math.h>
#include <list>

markusbuchholz

eq1--------------------------------------------

$$\large \frac{d^2}{dt^2}I(t) + \frac{R}{L}\frac{d}{dt}I(t)+ \frac{1}{LC}I(t)=0 $$

eq2--------------------------------------------

$$\large F\Bigg(t, x(t),\frac{dx(t)}{dt}, \frac{d^2x(t)}{dt^2}, \frac{d^nx(t)}{dt^n} \Bigg)=0 $$

eq3--------------------------------------------