source codes for MATLAB crash course

.gitignore

+*.png
+*.asv
+*~

ex01_triArea/myfirstscript.m

+clear all; close all; clc; format longG;
+
+base = 5;   % m
+height = 10;    % m
+
+a = triArea(base, height);
+
+fprintf('Area of triangle is %f m^2\n', a);
\ No newline at end of file

ex01_triArea/triArea.m

+function a = triArea(b, h)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% a = triArea(b,h)
+% 
+% Calculate the area of a triangle
+% 
+% INPUT:
+% - b   base of triangle
+% - h   height of triangle
+% 
+% OUTPUT:
+% - a   area of triangle
+%
+% Author: N. Baresi
+% Date: Sep 2023
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+base = b;
+height = h;
+
+a = base*height/2;
+end
\ No newline at end of file

ex02_sinplot/sinplot.m

+clear all; close all; clc; format longG;
+
+x = linspace(0, 2*pi, 100);
+y = sin(x);
+
+figure()
+plot(x, y);
\ No newline at end of file

ex02_sinplot/sinplot_extended.m

+clear all; close all; clc; format longG;
+
+x = linspace(0, 2*pi, 100);
+y1 = sin(x);
+y2 = cos(x);
+
+figure(), hold on, grid on;
+plot(x, y1, 'b-o', 'LineWidth', 2);
+plot(x, y2, 'r-o', 'LineWidth', 2);
+xlabel('x [-]')
+ylabel('y [-]')
+title('Harmonic Functions')
+legend('Sine','Cosine')

ex03_loops/for_loop.m

+clear all; close all; clc; format longG;
+
+a = 10;
+
+for ii = 1:10
+    fprintf('Value of a is %d\n', a);
+    a = a + 5;
+end
+fprintf('For loop has finished\n')
+
+
+
+    
\ No newline at end of file

ex03_loops/for_loop_with_break.m

+clear all; close all; clc; format longG;
+
+b = 10;
+
+for ii = 1:10
+    fprintf('Value of b is %d\n', b);
+    b = b + 5;
+    if(b >= 50)
+        break;
+    end
+end
+fprintf('For loop has finished\n');
\ No newline at end of file

ex03_loops/if_statements.m

+clear all; close all; clc; format longG;
+
+
+a = 10;
+
+%% IF Statement
+if(a > 5)
+    fprintf('a is greater than 5!\n');
+end
+
+
+%% IF-ELSE statement
+if(a < 5)
+    fprintf('a is less than 5!\n');
+else
+    fprintf('a is greater than 5!\n');
+end
+
+
+%% IF-ELSEIF-...-ELSE Statement
+if(a < 5)
+    fprintf('a is less than 5!\n');
+elseif(a >=5 && a < 10)
+    fprintf('a is greater or equal than 5, but less then 10\n');
+else
+    fprintf('a is greater or equal than 10!\n');
+end
+

ex03_loops/nested_loops.m

+clear all; close all; clc; format longG;
+
+% create a 4x3 matrix with normally distributed elements
+A = [1.3, 1.2, 1.3; 
+     3.1, 2.4, 3.1; 
+     4.1, 4.2, 4.3; 
+     7.1, 8.4, 9.1];
+
+% loop over rows
+for ii = 1:4
+
+    % loop over columns
+    for jj = 1:3
+
+        fprintf('A(%d,%d) = %f\n',ii, jj, A(ii,jj));
+    end
+end
+

ex03_loops/while_loop.m

+clear all; close all; clc; format longG;
+
+a = 10;
+
+while(a < 50)
+    fprintf('Value of a is %d\n', a);
+    a = a + 5;
+end
+fprintf('while loop has finished\n');
\ No newline at end of file

ex04_odes/pendulum_ode.m

+function dXdt = pendulum_ode(t, X, l, g)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% dXdt = pendulum_ode(t, X, l, g)
+%
+% System of first-order ODEs for the pendulum problem
+% 
+% INPUTS:
+% - t   time
+% - X   state vetor [angular position, angular velocity]
+% - l   pendulum length [m]
+% - g   gravitational acceleration [m/s^2]
+%
+% OUTPUTS:
+% - dXdt    time derivative of state vector [angular vel., angular acc.]
+%
+% Author: N. Baresi
+% Date: Sep 2023
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Retrieve inputs
+theta = X(1);
+omega = X(2);
+
+% initialize output
+dXdt = zeros(2,1);
+
+% Differential equations
+dXdt(1) = omega;
+dXdt(2) = -g/l*sin(theta);
+
+end

ex04_odes/pendulum_script.m

+clear all; close all; clc; format longG;
+set(0, 'DefaultTextInterpreter', 'latex');
+set(0, 'DefaultAxesFontSize', 20);
+set(0, 'DefaultLineLineWidth', 2);
+
+l = 1.0;     % pendulum length (m)
+g = 9.81;    % gravitational acceleration (m/s^2)
+
+% Set initial conditions
+theta0 = pi/8;
+omega0 = 0.1;
+X0 = [theta0; omega0];
+
+% Set time vector
+tstart = 0;
+tend = 10*2*pi*sqrt(l/g);
+tspan = [tstart, tend];
+
+
+% Ode-options
+ode_opt = odeset('RelTol', 3e-12, 'AbsTol', 1e-14);
+
+
+% Call to ODE45 (replace with ODE113 if you prefer)
+[tout, Xout] = ode45(@pendulum_ode, tspan, X0, ode_opt, l, g);
+
+
+% Store output in new variables
+time = tout;
+thetat = Xout(:, 1);   % Recall: X = [theta, omega]
+omegat = Xout(:, 2);
+
+
+%% Plot outputs
+figure()
+yyaxis left;
+plot(time, thetat);
+xlabel('Time (s)');
+ylabel('$\theta$ (rad)');
+xlim([0, time(end)]);
+ylim([1.2*min(thetat), 1.2*max(thetat)]);
+box on; grid on;
+
+yyaxis right;
+plot(time, omegat);
+ylabel('$\omega$ (rad/s)');
+ylim([1.2*min(omegat), 1.2*max(omegat)]);
+box on; grid on;
+savefig('pendulum_plots.fig');
+print('pendulum_plots.png','-dpng');
+
+
+%% Computing the Energy and Speed Comparison
+disp('Energy Calculation: For Loop');
+tic
+E_vec = zeros(length(thetat), 1);
+for ii = 1:length(thetat)
+    E_vec(ii) = 0.5*omegat(ii)^2 - (g/l)*cos(thetat(ii));
+end
+toc
+
+disp('Energy Calculation: Vectorised code');
+tic
+E_vec = 0.5*(omegat.^2) - (g/l)*cos(thetat);
+toc
+

ex04_odes/springmass_ode.m

+function dXdt = springmass_ode()
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% dXdt = springmass_ode()
+% 
+% INPUTS
+% 
+% OUTPUTS
+% .dXdt
+% 
+% Author:
+% Date:
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+% Retrieve initial conditions
+x = 
+v = 
+
+
+% initialize output
+dXdt = zeros( , );
+
+
+% Differential equations
+dXdt(1) = 
+dXdt(2) = 
+end

ex04_odes/springmass_script.m

+clear all; close all; clc; format longG;
+set(0, 'DefaultTextInterpreter', 'latex');
+set(0, 'DefaultAxesFontSize', 20);
+set(0, 'DefaultLineLineWidth', 2);
+
+
+% Define problem parameters
+k = 
+m = 
+
+
+% Define initial conditions
+x = 
+v =
+X = 
+
+
+% Define time vector
+t0 =
+tf =
+tspan
+
+
+% Ode-options
+ode_opt = odeset('RelTol', ,'AbsTol', );
+
+
+% Call ode113
+[tout, Xout] = ode113();
+
+
+
+% store output in new variables
+time = tout;
+x =
+v = 
+
+
+% Plot output
+figure()
+savefig('springmass_plots.fig');
+print('springmass_plots.png', '-dpng');
+
+
+% Calculate Energy
+
+

ex05_newton/newton_example.m

+clear all; close all; clc; format longG;
+
+x0 = 20;
+tol = 1e-10;
+
+[x, no_of_iter] = newton_method_for_loop(x0, tol);
+fprintf('The final value of x after %d iterations is %f\n', no_of_iter, x);
\ No newline at end of file

ex05_newton/newton_method_for_loop.m

+function [xf, no_of_iterations] = newton_method_for_loop(x0, tol)
+
+% retrieve initial guess
+xn = x0;
+
+for ii = 1:10
+
+    fxn = sin(xn) + xn*cos(xn);             % evaluate function in xn
+    fpxn = cos(xn) + cos(xn) - xn*sin(xn);  % evaluate first derivative in xn
+
+    % Print output
+    fprintf('xn: %f, |f(xn)|: %e\n', xn, abs(fxn));
+
+    % check for convergence using IF statement
+    if(abs(fxn) < tol)
+        break;
+    else
+        % Newton's method
+        dxn = -fxn/fpxn;                        % delta x_n
+        xn = xn + dxn;                          % update value of xn
+    end
+end
+
+% output variables
+xf = xn;
+no_of_iterations = ii;
\ No newline at end of file