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 Fourier approximation
Here are different animations of vibrating strings.
Initial conditions (no initial velocity)
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.