Numerical Methods

An HSSP Spring Course

Difficulty: High.

Required Knowledge:

• Middle school algebra.
• If you wish to do homework you should know Python. You would probably be fine with MATLAB, C++, or C#, but all code here will be written in Python with the packages numpy, scipy, matplotlib, and jupyter.

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Schedule

1. The derivative, fixed point iteration, Newton's method, Euler, Runge-Kutta, and multistep methods.
2. Quadrature a.k.a. numerical integration, finite difference methods and correctors.
3. Linear differential equations, matrix fundamentals, the QR algorithm, Newton-like methods, stiffness.
4. Finite element methods, various bases, Fourier/DCT transforms, Fourier analysis (faster solvers), Fourier analysis (stability).
5. Optimization: Binary and golden-section search, the simplex method, gradient descent, conjugate gradient descent, and Adam.
6. Stable diffusion.

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Lecture Notes

1. Week 1
2. Week 2
3. Week 3
4. Week 4
5. Week 5

Examples

1. Week 1
2. Week 2
3. Week 3
4. Week 4
5. Week 5
6. Week 6

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Installation

Open up the terminal (cmd line on Windows) and run

git clone https:/programjames/hssp-spring-numerical-methods
cd hssp-spring-numerical-methods/examples
pip install -r requirements.txt

To view a .ipynb file run jupyter notebook and open the corresponding file.