## Wednesday, July 29, 2020

### Matlab - Move sinus function toward x axis direction

% The Script plot a Sinus Graph Functin and move it to the x axis direction.
x= 0:0.1:2*pi
y = sin(x);

for i1=0:630
y = sin(x- i1/100);
plot(x,y);
drawnow;
F(i1+1) = getframe;
end

% One can use the movie function to Play recorded movie frames
% To play the movie two times, use movie(F,2).

## Friday, July 24, 2020

### Matlab - Read data from Excel file and plot the data

This script use the matlab function readtable and table2array to read data from Excel file and plot the data.

Data in Excel file: Data in Excel file

The script:

% This script read data from Excel file
% and put the data in array and plot the data

% Read the data from Excel file Book1.xlsx
% and put the data in table variable t.
disp( "The data read from Book1.xlsx file")

% Put the data from table variable  t  to variable x, y.
% "x" and "y" are the titles of the data un xlsx file.
x = table2array(t(:, "x"));
y = table2array(t(:, "y"));

% plot thr data.
plot(x,y)

Script Output

The data read from Book1.xlsx file

t =

20×2 table

y     x
___    __

1     1
4     2
9     3
16     4
25     5
36     6
49     7
64     8
81     9
100    10
121    11
144    12
169    13
196    14
225    15
256    16
289    17
324    18
361    19
400    20

Data Graph

## Tuesday, July 7, 2020

### Octave - Symbolic calculation - Plot function and its derivetive

This symbilic script get input a function f(x), and the order n of the derivetive requsted.
The script plot the function f(x) and the order n derivetive.

% This script plot derivetive fd(x) of the function f(x).
% The script use the function_handle function to create numeric
% function ffd from dff(x).

setenv PYTHON C:\ProgramData\Anaconda3\pythonw.exe

disp('Order of derivetive:')
n = 2
% Declare symbolic variable x
syms x;

disp('The function f(x):')
% Input the function f(x) here:
f = sin(x) + cos(x)+ x^2*sin(x)

disp('The n order derivetive fd(x) of the function f(x):')
% The derivative of the function f:
% fd(x) = f'(x)
fd(1) = diff(f,x);
i1 = 2;
while i1<=n
fd(i1) = diff(fd(i1-1), x);
i1++;
endwhile
fd(n)
% Convert symbolic function fd(x) to numeric function dff(x):
dff = function_handle(fd(n));

x=-2*pi:0.1:2*pi;
y= dff(x);
plot(x,y)
grid
xlabel('x')
ylabel('fd order n(x)')

Output

## Monday, July 6, 2020

### Symbolic derive of function and plot it

% This script plot derivetive fd(x) of the function f(x).
% The script use the function_handle function to create numeric
% function ffd from dff(x).

setenv PYTHON C:\ProgramData\Anaconda3\pythonw.exe

% Declare symbolic variable x
syms x;

disp('The function f(x):')
% Input the function f(x) here:
f = sin(x) + cos(x)+ x*sin(x)

disp('The derivetive fd(x) of the function f(x):')
% The derivative of the function f:
% fd(x) = f'(x)
fd = diff(f, x)

% Convert symbolic function fd(x) to numeric function dff(x):
dff = function_handle(fd);

x=-2*pi:0.1:2*pi;
y= dff(x);
plot(x,y)
xlabel('x')
ylabel('fd(x)')

Output

>> plot_derive_sym
The function f(x):
f = (sym) x*sin(x) + sin(x) + cos(x)
The derivetive fd(x) of the function f(x):
fd = (sym) x*cos(x) + cos(x) הוסף כיתוב

### Octave - Use solve function to symbolic solution of equation whith one variable

% Script for solving equation with one variable using the solve function
% sytax :
% S = solve(eqn,var) solves the equation eqn for the variable var.

% load symbolic package, and initilize PYTHON variable. (Octave only).
setenv PYTHON C:\ProgramData\Anaconda3\pythonw.exe

% Declare symbolic and variables and parameters
syms a b c x

% Define the equation to solve:
eqn = a*x^2 + b*x + c == 0

% activate solve function for x
S = solve(eqn, x)

% Solve for b:
Sb = solve(eqn, b)

Output

### Octave - Create two Symbolic matrices and calculte thier product

The script declare symbolic variables: psi phi theta psidot phidot thetadot, and create 3 matrices RzPsi, RyTheta, RzPhiwith with the variables and print the matrices.
The script also calculate symbolic products of the matrices RzPhi * RyTheta,
and print the product.

% script demonstrate how to use Symbolic matice

% load symbolic package, and initilize PYTHON variable. (Octave only).
setenv PYTHON C:\ProgramData\Anaconda3\pythonw.exe

% Declare Symbolic variable
syms psi phi theta psidot phidot thetadot

% Define Symbolic matrices
RzPsi = [[cos(psi), -sin(psi), 0]; [sin(psi), cos(psi), 0]; [0,0,1]]
RyTheta = [[cos(theta), 0, sin(theta)];[0,1,0];[-sin(theta), 0, cos(theta)]]
RzPhi = [[cos(phi), -sin(phi), 0]; [sin(phi), cos(phi), 0]; [0,0,1]]

disp(' Calculate the symbolic products of: RzPhi * RyTheta')

% Multiply Symbolic Matrices
RzPhi * RyTheta

The script output:

## Thursday, July 2, 2020

### Matlab - Nonlinear Differential Equation with Initial Condition

Nonlinear Differential Equation with Initial Condition

Solve this nonlinear differential equation with an initial condition. The equation has multiple solutions.

syms y(t) t0 y0
ode = (diff(y,t)+y)^2 == 1;
cond = y(t0) == y0;
ySol(t) = dsolve(ode,cond)

The matlab output:
ySol(t) =

exp(-t)*exp(t0)*(y0 + 1) - 1
exp(-t)*exp(t0)*(y0 - 1) + 1