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)
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 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 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 |