Add 3D-plot and differential equations to Matlab

Signed-off-by: Aaron Erhardt <aaron.erhardt@t-online.de>

Matlab/Matlab.md

@@ -519,6 +519,22 @@ handle = subplot(2, 3, 1);        % select first plot
 handle.Children(1).LineWidth = 2; % get line from handle and change width
 ```
 
+## 3-dimensional
+
+### 3D-plot
+
+```matlab
+plot3(x, y, z);
+```
+
+### Meshgrid
+
+```matlab
+% Grids are simply specified by matrices of coordinates
+[X Y] = meshgrid(x, y, z); % Generate grid
+mesh(X, Y)                 % Plot mesh
+mesh(X, Y, Z)              % Plot mesh with Z coordinate
+```
 
 # Functions
 
@@ -624,6 +640,42 @@ id = @(is,ud)is*exp(ud/0.05)  % diode current
 is = lsqcurvefit(id, 1e-10, u, i); % find ideal value for is to fit measured values u and i
 ```
 
+## Differential equations
+
+### First order
+
+```matlab
+% transform the equation so that u' is separated
+du = @(t,u) -u/0.1;           % u' = -u/0.1
+U0 = 3;                       % start value
+tspan = [0 0.5];              % time span
+[t u] = ode45(du, tspan, U0); % calculate values
+```
+
+### Higher order
+
+```matlab
+% transform the equation so that y' = y1' and y'' = y2' are separated
+%            y1' = y2     y2' = sin(100*t) - y1   - y2
+dy = @(t,y) [      y(2) ;       sin(100*t) - y(1) - y(2) ]; 
+% c)
+[t y] = ode45(dy, [0 1], [1; 0]); % start at y1 = 1 and y2 = 0
+```
+
+### Options
+
+```matlab
+opts = odeset('absTol', 0.05); % set absolute error tolerance
+[t y] = ode45(@pendfun, tspan, yNull, opts);
+```
+
+### Other solving algorithms
+
+```matlab
+ode23s % 
+```
+
+
 # Control structures
 
 ## for-loop