Additional material

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

Wave Equation

Here are different animations of vibrating strings.

Normal modes

Fundamental mode Second mode Third mode Fourth mode

Initial conditions (no initial velocity)

Quadratic function Triangular wave

Other videos

These are nice real-life experiments on YouTube:

video 1

video 2

video 3

Newton's method

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);

Newton's method.

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.

2017-10-18, Louis-Philippe Thibault