Welcome to Partial Differential Equations! For course info and policies, please see the syllabus. For grades, log into Moodle. If you need help or have questions, please contact Prof. Wright
Prof. Wright's drop-in hours: typically Mon. 1–2pm, Tues. 1:30–2:30pm, Wed. 11am–noon, Thurs. 10–11am, and Fri. 9–10am in RMS 405. Check Google Calendar for up-to-date availability, or email to schedule an appointment.
Homework help sessions: Tuesdays 7:00–8:30pm in Tomson 188
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Today
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Thursday
September 7
September 7
Introduction and ODE review
Do the following before next class:
- Complete the Introductory Survey.
- Read the Course Syllabus and Chapter 1 in our text (pages 1–13). Complete the Reading Questions and bring them to class on Tuesday.
- Watch But what is a partial differential equation? by 3Blue1Brown. Optionally, also watch Differential equations, a tourist's guide.
- Begin Homework 1, due next Thursday.
Tuesday
September 12
September 12
Uniform transport equation
Bonus video: Paths to Math: John Urschel
Do the following before next class:
- Read Sections 2.1 and 2.2 in the text. Complete the Reading Questions and bring them to class on Thursday.
- Finish Homework 1 (due 5pm Thursday). You may want to use the Homework 1 LaTeX template on Overleaf.
Do the following before next class:
- Read Section 2.4 in the text. There is a lot in this section, but focus on grasping the big ideas. Complete the Reading Questions and bring them to class on Tuesday.
- Begin Homework 2, due next Thursday.
Tuesday
September 19
September 19
Wave equation: d'Alembert's solution
Bonus video: Eugenia Cheng on The Late Show
Do the following before next class:
- Read Section 3.1 in the text. Complete the Reading Questions and bring them to class on Thursday.
- Finish Homework 2 (due 5pm Thursday). You may want to use the Homework 2 LaTeX template on Overleaf.
Do the following before next class:
- Watch the video But what is a Fourier series? From heat flow to drawing with circles by 3Blue1Brown.
- Begin Homework 3, due next Thursday.
Tuesday
September 26
September 26
Eigenvalues and Eigenfunctions
Bonus: Why is Mathematics Useful — Robert Ghrist, and Applied Dynamical Systems Vol. 1
Do the following before next class:
- Read pages 72–78 from Section 3.2 in the text. Complete the Reading Questions and bring them to class on Thursday.
- Finish Homework 3 (due 5pm Thursday). You may want to use the Homework 3 LaTeX template on Overleaf.
Do the following before next class:
- Read pages 79–91 from Section 3.2 in the text. Complete the Reading Questions and bring them to class on Tuesday.
- Begin Homework 4, due next Thursday.
Tuesday
October 3
October 3
Fourier series
Bonus video: Moon Duchin: "Political Geometry" and DistrictR
Do the following before next class:
- Read Sections 3.3 and 3.4 in the text. Complete the Reading Questions and bring them to class on Thursday.
- Finish Homework 4, due Thursday. You may want to use the Homework 4 LaTeX template on Overleaf.
Do the following before next class:
- Read Pages 121–126 in the text. Complete the Reading Questions and bring them to class on Tuesday.
- Begin work on Tutorial 1 (the first midterm exam), which is due next Thursday.
Tuesday
October 10
October 10
Separation of variables: heat equation
Bonus: Federico Ardila on Math, Music and the Space of Possibilities
Do the following before next class:
- Finish Tutorial 1 (the first midterm exam), which is due
Thursdaynow due Friday. Upload your files to the Tutorial 1 assignment on Moodle.
Fall break! No class Tuesday, October 17.
Do the following before next class:
- Review the separation of variables problems and solutions from class.
- Read Pages 126–132 in the text. Complete the Reading Questions and bring them to class on Thursday.
Thursday
October 19
October 19
Separation of variables: heat equation
Do the following before next class:
- Review the separation of variables problems and solutions from class.
- Read Pages 133–138 in the text. Complete the Reading Questions and bring them to class on Tuesday.
- Work on Homework 5, due next Thursday.
Tuesday
October 24
October 24
Separation of variables: wave equation
Do the following before next class:
- Review the wave equation problems and solutions from class.
- Read Pages 140–149 in the text. Complete the Reading Questions and bring them to class on Thursday.
- Finish Homework 5, due Thursday. You may want to use the Homework 5 LaTeX template on Overleaf.
- Optionally, revise Tutorial 1. Revisions are due Tuesday. If you have questions about how to revise, talk with the professor.
Thursday
October 26
October 26
Separation of variables: wave equation
Hyperbolic sine and cosine functions
Hyperbolic sine and cosine functions
Homework 5
due today
due today
Bonus: video How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg
Do the following before next class:
- Review the problems and solutions from class.
- Read Pages 152–159 in the text. Complete the Reading Questions and bring them to class on Thursday.
- Begin Homework 6, due next Thursday.
- Optionally, revise Tutorial 1. Revisions are due Tuesday. If you have questions about how to revise, talk with the professor. You may submit your revisions to the Tutorial 1 assignment on Moodle.
Bonus video: Yitang Zhang: An Unlikely Math Star Rises
Do the following before next class:
- Review the problems and solutions from class.
- Read the rest of Chapter 4 (pages 160–179) in the text.
- Finish Homework 6, due Thursday. You may want to use the Homework 6 LaTeX template on Overleaf.
Do the following before next class:
- Review the problems and solutions from class.
- Read Pages 182–188 in the text. Complete the Reading Questions and bring them to class on Tuesday.
- Begin Homework 7, due next Thursday.
Tuesday
November 7
November 7
Finite differences and the heat equation
Bonus video: MEET a Mathematician! - Trachette Jackson
Do the following before next class:
- Review the problems and solutions from class.
- Read pages 186–190 from Chapter 5 in the text. There are no reading questions for Thursday.
- Finish Homework 7, due Thursday. You may want to use the Homework 7 LaTeX template on Overleaf.
- Read the Final Project Information. Start thinking about what topic you would like to study and who you would like to work with.
Do the following before next class:
- Re-read Sections 5.1 and 5.2 in the text.
- Begin work on Tutorial 2 (the second midterm exam), which is due next Thursday.
- Read the Final Project Information. Thinking about what topic you would like to study and who you would like to work with. Complete the Final Project Planning Survey on Moodle.
Tuesday
November 14
November 14
Finite differences for first-order PDEs
Bonus videos: Satyan Devadoss — Blue Collar Mathematics and Mage Merlin's Unsolved Mathematical Mysteries
Do the following before next class:
- Review the problems and solutions from class.
- Read pages 195–200 in the text. Complete the Reading Questions and bring them to class on Thursday.
- Finish Tutorial 2, which is due Thursday. Upload your files to the Tutorial 2 assignment on Moodle.
Do the following before next class:
- Read Section 5.4 in the text. There are no reading questions for Tuesday.
- Start collecting resources for your final project and reading about your final project topic.
- Take a look at Homework 8, which is due on Nov. 30.
Tuesday
November 21
November 21
Generalized functions
Thanksgiving break! No class Thursday, Nov. 23.
Do the following before next class:
- Read Section 6.1 in the text. There are no reading questions for next Tuesday.
- Begin work on Homework 8, which is due on Nov. 30.
- Continue collecting resources for your final project and reading about your final project topic.
Tuesday
November 28
November 28
Green's functions
Bonus video: Francis Su — Mathematics for Human Flourishing short version and long version
Do the following before next class:
- Read Section 6.2 in the text. Note the important properties of Green's functions. There are no reading questions for Thursday.
- Finish Homework 8, which is due on Thursday. You may want to use the Homework 8 LaTeX template on Overleaf.
- Optionally, revise Tutorial 2.
- Continue planning your final project with your group.
Do the following before next class:
- Read as much (or as little) of Chapter 6 as you would like to read.
- Optionally, revise Tutorial 2.
- Continue planning your final project with your group. Prepare an outline of your paper. One person in your group should submit your outline to the Final Project assignment on Moodle.
- Browse two sample papers from past final projects: tumor growth and the Navier-Stokes equations (on Moodle).
Tuesday
December 5
December 5
Bessel's equation (???)
Final project:
Outline of paper due
Outline of paper due
Do the following before next class:
- to be announced...
Do the following before next class:
- to be announced...
Tuesday
December 12
December 12
Final Projects
Finish your final project.
Saturday
December 16
December 16
Project presentations
1:00 – 3:00pm
1:00 – 3:00pm
