Introduction

Please sign up for the course on Piazza.

Demonstrations

Unit 1: Floating-Point Numbers

• IEEE Floating-Point

Unit 2: Rootfinding

• Rootfinding

Unit 3: Ordinary Differential Equations

• Quiver Plot
• Euler’s Method
• Local vs Global Error Demo
• 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

Unit 6: Fourier Theory

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

Unit 7: Neural Networks

• Universal Approximation Theorem
• Classification Demo
• PyTorch Demo