APMA 0360

Welcome to APMA 0360 – partial differential equations, but a whole lot of fun! On this website, you can find the syllabus, lecture notes, homework assignments, and study materials.


Syllabus

APMA 0360 – Syllabus (Spring 2025)

Homework Extension Request Form 


Lecture Notes

Note: The lecture notes will be frequently updated. Please refresh your webpage so that you have the most up-to-date version of the notes

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Date
Lecture Title
YouTube Videos
1 Jan 22 What is a PDE? What is a PDE?
2 Jan 24 Classification of PDE Simple PDE
3 Jan 27 First-Order Linear PDE Constant-Coefficient PDE
Variable-Coefficient PDE
First-Order Example
4 Jan 29 Transport Equation Coordinate Method
Transport Equation Derivation
Transport Equation Solution
Transport Equation Demo (demo)
Coordinate Method (practice)
5 Jan 31 Wave Equation Derivation
6 Feb 3 Wave Equation Solution Undetermined Coefficients Review
Wave Equation Solution
Wave Equation Demo (demo)
7 Feb 5 D’Alembert’s Formula D’Alembert’s Formula
8 Feb 7 (Continuation)
9 Feb 10 Heat Equation Derivation
10  Feb 12 Fourier Transform
11 Feb 14 Fourier and Heat PDE (I)
12 Feb 19 Fourier and Heat PDE (II)
13 Feb 21 Inverse Fourier Transform
14 Feb 24 Heat Equation Properties
15 Feb 26 Energy Methods (I)
16 Feb 28 Energy Methods (II)
Feb 28 Summary: Heat vs Wave
17 Mar 3 Midterm 1 – Review
Mar 5 Midterm 1
18 Mar 7 Separation of Variables (I)
19 Mar 10 Separation of Variables (II)
20 Mar 12 Fourier Sine Series
21 Mar 14 Fourier Cosine Series
22 Mar 17 Complex Fourier Series
23 Mar 19 Parseval’s Formula
24 Mar 21 Laplace Equation
25 Mar 31 Separation of Variables (III)
26 Apr 2 Rotation Invariance
27 Apr 4 Fundamental Solution
28 Apr 7 Laplace Properties
29 Apr 9 Method of Characteristics
30 Apr 11 Ecology Application
31 Apr 14 Midterm 2 – Review
Apr 16 Midterm 2
32 Apr 18 Epidemiology: COVID Model
33 Apr 21 Wealth and Income Distributions
34 Apr 23 The PDE that got me the PhD
35 Apr 25 Final Exam – Review
Never Fluid Flow Application (optional)
Never Calculus of Variations (optional)
May 13 Final Exam

 


Assignments

Homework
Due Date
Solutions
Videos
Homework 1 Jan 31 Solutions
Homework 2 Feb 7 Transform Method
Homework 3 Feb 14
Homework 4 Feb 21
Homework 5 Feb 28
Homework 6 Mar 14
Homework 7 Mar 21
Homework 8 Apr 4
Homework 9 Apr 11
Homework 10 Apr 25
Homework 11 May 2 Optional
Mini Project May 2

 


Exams

Midterm 1: Wednesday, March 5, 12-12:50 pm covers Lec 1-13

Practice Exam Solutions Comments
Study Guide
Mock Midterm 1 Solutions
Mock Midterm 2 Solutions Ignore 4
Mock Midterm 3 Solutions Ignore 3 and 4
Mock Midterm 4 Solutions Spring 2023 Midterm 1
Mock Midterm 5 Solutions Fall 2024 Midterm 1
Midterm 1 – Review

Midterm 2: Wednesday, April 16, 12-12:50 pm, covers Lec 14-25

Practice Exam Solutions Comments
Study Guide
Mock Midterm 1 Solutions Only do 1, 6, 7
Mock Midterm 2 Solutions Ignore 3, 4, 8
Mock Midterm 3 Solutions Only do 4
Mock Midterm 4 Solutions Spring 2023 Midterm 2
Mock Midterm 5 Solutions Fall 2024 Midterm 2
Midterm 2 – Review
PDE Handout
Peyam 1 Solutions Only do 5, 7, Bonus
Peyam 2 Solutions Only do 4, 5a
Peyam 3 Solutions Only do 6
Peyam 4 Solutions
Canez Solutions Only do 16-20
Nadler Solutions Only 6, 7
Vojta 1 Solutions Only do 9a, 10
Vojta 2 Solutions Only do 12, 13
Ribet 1 Solutions Only do 5, 9
Ribet 2 Solutions Only do 5, 6
Holtz Solutions Only do 8, 9
Tarr Solutions Only do 1e, 5, 6
Poonen Solutions Only do 18, 20
Lenstra Solutions Only do 4c, 5
Bergman Solutions Only do 3ab, 6

Final Exam: Tuesday, May 13, 9 am to 12 pm, covers the entire course

Note: Please also check out the practice midterms above for more study material

Practice Exam Solutions Comments
Study Guide
Mock Final 1 Solutions Updated, Ignore 7
Mock Final 2 Solutions Ignore 3, 4
Mock Final 3 Solutions Ignore 4, 8
Mock Final 4 Solutions Spring 2023 Final, ignore 7
Final Exam – Review

 


Calendar