21261 selected matlab visualization

Selected matlab codes to give visualizations of some ODEs in 21261, Introduction to Ordinary Differential Equations.

I hope this repo contains most MATLAB commands a typical undergraduate ODE course will need to use for visualization. This should help students to understand the behaviors of ODE at a glance and give a head start with Matlab.

Week1 discussion:

Equation: y'=y^3-y. Plot curves from some points:

Homework1 Plot:

Week4 discussion:

Visualize solutions of x'(t) = x(1-x) - h * (1+sin(2pit)) with different h values and initial data x_0

Visualize solutions of the system: x'=-y; y'=x

Homework6 Plot:

Plot the first few terms of the Picard iteration and the exact solution for the following initial value problems, as a visual illustration that Picard Iteration works.
(a) x'= x + 2, x(0) = 2.
(b) x'= x^(4/3), x(0) = 1.
(c) x'= cosx, x(0) = 0.

Week7 discussion:

Visualize solutions of x'' + bx' + kx = cos(omega*t)

By writing the ODE with a system of first order ODE,

x' = 0*x + 1*x';x''= -k*x - b*x' + cos(omega*t)

Homework 8 P4

Sketch phase portrait for the following system:

x'=x^2−2xy;y'=y^2−2xy.

Midterm exam problem 1 illustration

Problem statement:

Visualization for different values of a: