APMA 1941G

Welcome to APMA 1941G, an exciting asymptotics adventure awaits you! On this website, you can find the syllabus, homework assignments, and study materials.

Syllabus 

APMA 1941G Syllabus

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Lecture Schedule

Lecture Notes: Lecture Notes (courtesy Will Kwon)

#
Date
 Chapter
Lecture Title
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
Due Date
Solutions
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

Final Exam: Friday, April 26 until Friday, May 17 (4 pm), covers Lectures 1-24

Calendar