Welcome to APMA 1941G, an exciting asymptotics adventure awaits you! On this website, you can find the syllabus, homework assignments, and study materials.
Syllabus
Homework Extension Request Form
Lecture Schedule
Lecture Notes: Lecture Notes (courtesy Will Kwon)
| Chapter | |||
|---|---|---|---|
| 1 | Jan 25 | 1 | What is an asymptotic expansion? (Notes) |
| 2 | Jan 30 | 1 | Perturbation of eigenvalues |
| 3 | Feb 1 | 1 | Derivation of the KdV equation |
| 4 | Feb 6 | 1 | Theoretical Aspects |
| 5 | Feb 8 | 2 | Laplace’s Method (I) |
| 6 | Feb 13 | 2 | Laplace’s Method (II) (Notes) |
| 7 | Feb 15 | 2 | Stationary Phase |
| 8 | Feb 22 | 3 | Rapidly Oscillating Coefficients |
| 9 | Feb 27 | 3 | An Oscillator with Damping |
| 10 | Feb 29 | 3 | WKB Method |
| 11 | Mar 5 | 3 | Nonlinear Oscillator with Damping |
| 12 | Mar 7 | 3 | Nonlinear Wave Equation |
| 13 | Mar 12 | 3 | Diffusion-Transport PDE |
| 14 | Mar 14 | No class (Midterm) | |
| 15 | Mar 19 | 3 | Calculus of Variations |
| 16 | Mar 21 | 3 | Homogenization |
| 17 | Apr 2 | 4 | Matched Asymptotic Expansions |
| 18 | Apr 4 | 4 | Higher Order Equations |
| 19 | Apr 9 | 4 | Internal Layers |
| 20 | Apr 11 | 4 | Earth-Moon Spacecraft Problem |
| 21 | Apr 16 | 4 | Singular Variational Problem |
| 22 | Apr 18 | 4 | Singular Reaction-Diffusion PDE |
| 23 | Apr 23 | 4 | Singular Perturbation of Eigenvalues |
| 24 | Apr 25 | 4 | The Crushed Ice Problem |
| 25 | May 17 | Final Exam |
Assignments
Note: The solutions are written by Lulabel Seitz
| Homework 1 | Feb 2 | Solutions |
| Homework 2 | Feb 9 | Solutions |
| Homework 3 | Feb 16 | Solutions |
| Homework 4 | Feb 23 | Solutions |
| Homework 5 | Mar 1 | Solutions |
| Homework 6 | Mar 8 | Solutions |
| Homework 7 | Mar 22 | Solutions |
| Homework 8 | Apr 5 | Solutions |
| Homework 9 | Apr 12 | Solutions |
| Homework 10 | Apr 19 | Solutions |
| Homework 11 | Apr 26 | Solutions |
| Mini Project | May 3 |
Exams
Midterm: Monday, March 11 (12 pm) until Friday, March 15 (4 pm), covers Lectures 1-11
- Study Guide: Study Guide
Final Exam: Friday, April 26 until Friday, May 17 (4 pm), covers Lectures 1-24
- Study Guide: Study Guide
Calendar