Math 112A – Partial Differential Equations

Welcome to Math 112A – Partial Differential fun! In this course, we will explore the beauty of Partial Differential Equations by studying three fundamental PDE: The Wave Equation, the Heat/Diffusion Equation, and Laplace’s Equation. Along the way, we’ll also have fun with Fourier series. Enjoy!


Syllabus

Here is the syllabus of the course: Syllabus


Lecture Notes and Videos

Lecture Notes Title YouTube Videos
Lecture 1 1.1 What is a PDE? What is a PDE?
Simple PDE
Lecture 2 1.2 First-order Linear Equations (I) Homogeneous Solution
Constant Coefficient PDE
Lecture 3 1.2 First-order Linear Equations (II) Variable Coefficient PDE
Coordinate Method
Transform Method
Lecture 4 1.3, 1.4 The Transport Equation; Boundary Conditions (I)
Lecture 5 1.4, 1.5, 1.6 Boundary Conditions (II); Well-posed Problems; Types of Second-Order Equations
Lecture 6 2.1 The Wave Equation (I) Wave Equation
Factoring Method
Lecture 7 2.1 The Wave Equation (II) D’Alembert’s Formula
Lecture 8 2.2 Energy Method Energy Method (Wave)
Lecture 9 2.4 Diffusion on the Whole Line (I) Fundamental Solution
Gaussian Integral
Lecture 10 2.4 Diffusion on the Whole Line (II) Heat Equation Example
Convolution Intuition
Lecture 11 2.3 The Diffusion Equation (I) Energy Method (Heat)
Lecture 12 2.3 The Diffusion Equation (II) Maximum Principle
Lecture 13 2.5 Comparison of Waves and Diffusions
Lecture 14 Review
Lecture 15 Midterm
Lecture 16 3.1 Diffusion on the Half Line Half Heat Equation
Half Heat Example
Lecture 17 3.2 Reflections of Waves Reflection of Waves
Lecture 18 4.1 Separation of Variables (I) PDE Handout
Separation of Variables
Lecture 19 4.1 Separation of Variables (II)
Lecture 20 4.2 The Neumann Condition Sep of Var Neumann
Lecture 21 5.1 Fourier Coefficients (I) Fourier Series
Fourier Sine and Cosine Series
DI Method
Lecture 22 5.1 Fourier Coefficients (II) Complex Fourier Series
Lecture 23 5.4 Completeness Parseval’s Identity
Lecture 24 6.2 Rectangles and Cubes
Lecture 25 6.1 Laplace’s Equation (I) Rotation Invariance
Polar Laplace
Lecture 26 6.1 Laplace’s Equation (II)
Lecture 27 6.1 Laplace’s Equation (III)
Lecture 28 Review
Lecture 29 The PDE that got me the PhD Chemical Reactions

Homework

Homework will be posted here. Homework is due on Thursdays during discussion. The lowest homework assignment is dropped. There is also a quiz whenever a homework is due, written by your TA Yang Yang.

Homework Due Date Virtual OH Quiz Solutions
Homework 1 Thursday, October 3 OH 1 Quiz 1
Homework 2 Thursday, October 10 OH 2 Quiz 2
Homework 3 Thursday, October 17 OH 3 Quiz 3
Homework 4 Thursday, October 24 OH 4 Quiz 4
Homework 5 Thursday, November 7 OH 5 Quiz 5
Homework 6 Thursday, November 14 OH 6 Quiz 6
Homework 7 Thursday, November 21 OH 7 Quiz 7
Homework 8 Thursday, December 5 OH 8 Quiz 8

 


Useful links

Canvas Course Site (to check your quiz and exam scores)

My Youtube Channel

PDE Playlist (official playlist for our class)

Advanced PDE Playlist (same topics, but more advanced)

PDE Handout (covers the material from Chapters 4, 5, and 6.2)


Exams

Here you can find information about the exams, as well as other goodies such as practice exams.

 

Midterm Exam: Wednesday, October 30, 4-4:50 PM in 1600 DBH

Covers sections 1.1 – 1.2, 1.6, 2.1 – 2.4

Study Guide: Study Guide

Mock Midterm: Mock Midterm (Solutions)

Midterm: Midterm (Solutions)

Midterm Virtual Office Hours: Midterm OH

YouTube Playlist: PDE Playlist

 

Final Exam: Wednesday, December 11, 4-6 PM in 1600 DBH

Covers 1.1 – 1.6, 2.1 – 2.4, 3.1 – 3.2, 4.1 – 4.2, 5.1, 5.4, 6.1 – 6.2

Also check out the Quizzes and the OH Transcripts in the Homework section

Study Guide: Study Guide

Practice Exam: Mock Final (Solutions)

Final Exam: Final (Solutions)

Final Virtual Office Hours: Final OH

YouTube Playlist: PDE Playlist

PDE Handout: PDE Handout (covers the material from Chapters 4, 5, and 6.2)

More practice problems from Chapters 4 and 5, and 6.2:

Exam Comments Solutions
Peyam 1 Only do 5, 6, 7, Bonus Solutions
Peyam 2 Only do 4, 5 Solutions
Peyam 3 Only do 6, 7 Solutions
Peyam 4 Solutions
Canez Only do 16 – 20 Solutions
Nadler Only do 6, 7 Solutions
Vojta 1 Only do 9ab Solutions
Vojta 2 Only do 12, 13 Solutions
Ribet 1 Only do 5, 9 Solutions
Ribet 2 Only do 5, 6 Solutions
Holtz Only do 8, 9 Solutions
Tarr Only do 1e, 5, 6 Solutions
Poonen Only do 18, 20 Solutions
Lenstra Only do 4, 5 Solutions
Bergman Only do 3ab, 6 Solutions