A geometric introduction to complex variables, complex integration, and Laplace transforms. Materials below include lecture notes and resources from previous semesters.
Course outline
Before the midterm
- The relationship between the vector spaces $\mathbb{R}^2$ and $\mathbb{C}$, and what makes the complex plane different
- Complex variables and functions
- Limits and continuity
- Complex differentiability, harmonic functions, and analytic functions
After the midterm
- Line integrals and complex integration
- Laplace transforms
Lecture notes
Lecture slides
Complex variables
Lecture 1 · Lecture 2 · Lecture 3 · Lecture 4 · Lecture 6 · Lecture 7 · Lecture 8 · Lecture 9
Integration
Laplace transforms
Lecture 1 · Lecture 2 · Lecture 5
Fall 2025 materials
| Assessment | Material |
|---|---|
| Before the midterm | Assignment 1 · Quiz 1 |
| Midterm preparation | Practice problems with solutions |
| After the midterm | Assignment 2 · Quiz 2 · Quiz 3 · Quiz 4 |
Course communities
Fall 2024 Discord · Spring 2026 Discord
For access to other course communities, please email me.