Videos from Math 4D
Morten Nome, the lecturer for Math 4D (almost the same as Math 4N), made some interesting videos.
Fourier series approximation
Fourier series approximation of the sawtooth wave
Here are different animations of vibrating strings.
Fundamental mode Second mode Third mode Fourth mode
Initial conditions (no initial velocity)
Quadratic function Triangular wave
You can create animations for Newton's method easily on Maple.
> with(Student[Calculus1]): > NewtonsMethod(f, x_0, view = [a .. b, DEFAULT], iterations = n, output = animation);
We encourage you to play with different functions and initial values x_0 to build your intuition.
Here is one example:
> with(Student[Calculus1]): > NewtonsMethod(x^3-5x^2+x+2, -2.5, view = [-3 .. 5, DEFAULT], iterations = 5, output = animation);
Gauss integration nodes and coefficients
Since we have not seen how to obtain the nodes (=zeros of the Legendre polynomial) and the coefficients in Gauss integration formulas, here is a Matlab code that computes them.