Introduction

Please sign up for the course on Piazza.

Demonstrations

Unit 1: Floating-Point Numbers

• IEEE Floating-Point
• Rounding Error Demo

Unit 2: Rootfinding

• Rootfinding

Unit 3: Ordinary Differential Equations

• Euler’s Method
• Local vs Global Error Demo (.py script)
• 3rd-Order Runge-Kutta (.py script)
• Python’s ODE Suite

Unit 4: Algebraic Methods for Linear Algebra

• Induced Matrix Norms
• LU and QR Factorization
• Least Squares
• Singular Value Decomposition (SVD)

Unit 5: Iterative Methods for Linear Systems

• Gershgorin Circle Theorem
• Jacobi Iteration

Unit 6: Fourier Theory

• Fourier Series
• Orthogonality, DFT Matrix
• Fourier Compression
• 2D Fourier Transforms
• Audio Filtering
• Aliasing Demo
• Demo of many Fourier properties

Unit 7: Eigenvectors and Eigenvalues

• Eigenvector Demos