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 Catch-up
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
17 Oct 16 Heat vs Wave
18 Oct 18 Separation of Variables (I)
19 Oct 21 Separation of Variables (II)
20 Oct 23 Fourier Series (I)
21 Oct 25 Fourier Series (II)
22 Oct 28 Fourier Series (III)
23 Oct 30 Laplace Equation (I)
24 Nov 1 Laplace Equation (II)
25 Nov 4 Laplace’s Equation (III)
26 Nov 6 Laplace’s Equation (IV)
27 Nov 8 Laplace’s Equation (V)
28 Nov 11 Midterm 2 – Review
Nov 13 Midterm 2
29 Nov 15 Ecology Application
30 Nov 18 Epidemiology Application (I)
31 Nov 20 Epidemiology Application (II)
32 Nov 22 Method of Characteristics
33 Nov 25 Wealth and Income Distributions
34 Dec 2 The PDE that got me the PhD
35 Dec 4 Catch-up
36 Dec 6 Final Exam – Review
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
Homework 5 Oct 18
Homework 6 Oct 25
Homework 7 Nov 1
Homework 8 Nov 8
Homework 9 Nov 22
Homework 10 Dec 6
Mini Project Dec 13

 


Exams

Midterm 1: Wednesday, October 9, 12-12:50 pm, covers Lec 1-13

Practice Exam Solutions Comments
Study Guide (TBA)
Mock Midterm 1 Solutions
Mock Midterm 2 Solutions Ignore 4
Mock Midterm 3 Solutions Only do 1
Mock Midterm 4 Solutions Spring 2023 Midterm
Midterm 1 – Review

Midterm 2: Wednesday, November 13, 12-12:50 pm, covers Lec 14-26

Practice Exam Solutions Comments
Study Guide (TBA)
Mock Midterm 1 Solutions Ignore 3, 4, 5, 7b
Mock Midterm 2 Solutions Ignore 4, 8
Mock Midterm 3 Solutions Ignore 1, 3
Mock Midterm 4 Solutions Spring 2023 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, 7
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

Practice Exam Solutions Comments
Study Guide (TBA)
Mock Final 1 Solutions
Mock Final 2 Solutions Mock Midterm
Mock Final 3 Solutions
Mock Final 4 Solutions Ignore 3
Mock Final 5 Solutions Ignore 3, 4
Mock Final 6 Solutions Ignore 4, 8
Mock Final 7 Solutions Spring 2023 Midterm 1
Mock Final 8 Solutions Spring 2023 Midterm 2
Mock Final 9 Solutions Spring 2023 Final
Midterm 1 – Review
Midterm 2 – Review
Final Exam – Review

 


Calendar