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 (Fall 2024)

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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
1 Sep 4 What is a PDE?
2 Sep 6 Classification of PDE
3 Sep 9 First-Order Linear PDE
4 Sep 11 Transport Equation
5 Sep 13 Wave Equation Derivation
6 Sep 16 Wave Equation Solution
7 Sep 18 D’Alembert’s Formula
8 Sep 20 (Continuation)
9 Sep 23 Heat Equation Derivation
10  Sep 25 Fourier Transform
11 Sep 27 Fourier and Heat PDE (I)
12 Sep 30 Fourier and Heat PDE (II)
13 Oct 2 Inverse Fourier Transform
14 Oct 4 Heat Equation Properties
15 Oct 7 Midterm 1 – Review
Oct 9 Midterm 1
16 Oct 11 Energy Methods (I)
17 Oct 16 Energy Methods (II)
Summary: Heat vs Wave
18 Oct 18 Separation of Variables (I)
19 Oct 21 Separation of Variables (II)
20 Oct 23 Fourier Sine Series
21 Oct 25 Fourier Cosine Series
22 Oct 28 Complex Fourier Series
23 Oct 30 Parseval’s Formula
24 Nov 1 Laplace Equation
25 Nov 4 Separation of Variables (III)
26 Nov 6 Rotation Invariance
27 Nov 8 Fundamental Solution
28 Nov 11 Midterm 2 – Review
Nov 13 Midterm 2
29 Nov 15 Laplace Properties
30 Nov 18 Ecology Application
31 Nov 20 Epidemiology: COVID Model
32 Nov 22 (Continuation)
33 Nov 25 Method of Characteristics
34 Dec 2 Wealth and Income Distributions
35 Dec 4 The PDE that got me the PhD
36 Dec 6 Final Exam – Review
Fluid Flow Application (optional)
Calculus of Variations (optional)
Dec 14 Final Exam

 


Assignments

Homework
Due Date
Solutions
Homework 1 Sep 13 Solutions
Homework 2 Sep 20 Solutions
Homework 3 Sep 27 Solutions
Homework 4 Oct 4 Solutions
Homework 5 Oct 18 Solutions
Homework 6 Oct 25 Solutions
Homework 7 Nov 1 Solutions
Homework 8 Nov 8 Solutions
Homework 9 Nov 22
Homework 10 Dec 6
Mini Project Dec 13

 


Exams

Midterm 1: Wednesday, October 9, 12-12:50 pm in 117 Macmillan Hall, 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
Midterm 1 Solutions Fall 2024 Midterm
Midterm 1 – Review

Midterm 2: Wednesday, November 13, 12-12:50 pm in 117 Macmillan Hall, 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
Midterm 2 Solutions Fall 2024 Midterm
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: Saturday, December 14, 9 am to 12 pm in 106 Smith Buonanno Hall (last names A-F) and Alumnae Hall Aud (last names G-Z) 

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

Practice Exam Solutions Comments
Study Guide (TBA)
Mock Final 1 Solutions Ignore 6
Mock Final 2 Solutions Ignore 3, 4
Mock Final 3 Solutions Ignore 4, 8
Mock Final 4 Solutions Ignore 7
Final Exam – Review

 


Calendar