Matthew L. Wright
Assistant Professor, St. Olaf College

Partial Differential Equations

Math 330 ⋅ Fall 2018

Prof. Wright's office hours: Mon. 1–2, Tues. 10–11, Wed. 2–3, Thurs 10–11, Fri. 1–2, whenever the door is open, or by appointment in RMS 405

Help sessions: Tuesdays 7–8pm in Tomson 186

Thursday
Sep. 6
Introduction
ODE review
Do the following before next class:
Tuesday
Sep. 11
Heat equation
Do the following before next class:
• Read §1.3 and §1.4. Note three possible boundary conditions discussed in §1.3. Then note how the heat equation, with certain boundary conditions, can be solved for equilibrium solutions in §1.4.
• Finish Homework 1 (due 4pm Thursday). You may want to use the LaTeX template on Overleaf.
Thursday
Sep. 13
Heat equation
Homework 1
due today
Do the following before next class:
Tuesday
Sep. 18
Multidimensional heat equation
Do the following before next class:
• Read §2.1 and §2.2. Note the definition of a linear operator and the principle of superposition.
• Finish Homework 2 (due 4pm Thursday).
Thursday
Sep. 20
Separation of variables
Homework 2
due today
Do the following before next class:
• Read §2.3. This is a long section, but the the first half (or so) should be somewhat familiar from class. Answer the reading questions (TeX source), and bring your answer to class on Tuesday.
• Begin Homework 3.
Tuesday
Sep. 25
Separation of variables, continued
Do the following before next class:
• Read the §2.3 Appendix (pages 54–55). Also read §2.4, and make sure you understand the two examples in this section.
• Finish Homework 3 (due 4pm Thursday).
Thursday
Sep. 27
Orthogonality and initial conditions
Time-dependent solutions to the heat equation
Homework 3
due today
Do the following before next class:
• Re-read §2.4. Note how orthogonality of sine and cosine functions is used to find the coefficients of the series solutions in this section.
• Begin Homework 4.
Tuesday
Oct. 2
Laplace's equation and separation of variables
Do the following before next class:
• Read §3.1 and §3.2. Note the convergence theorem for Fourier series.
• Finish Homework 4 (due 4pm Thursday).
Thursday
Oct. 4
Fourier series
Take-home exam assigned
Homework 4
due today
Do the following before next class:
Tuesday
Oct. 9
Fourier series
Take-home exam
due today
Do the following before next class:
• Read §3.3. Pay close attention to the definitions, examples, and convergence properties of Fourier sine and cosine series.
• Read §3.4. Note the conditions under which a Fourier (cosine/sine) series can be differentiated term by term.
• Take a look at Homework 5.
Thursday
Oct. 11
Differentiation of Fourier series
Fall break! No class Tuesday, October 16.
Do the following before next class:
• Re-read §3.4. Make sure you understand the conditions under which a Fourier (cosine/sine) series can be differentiated term by term. Also note the method of eigenfunction expansion.
• Read §3.5 (it's short!). Note what happens when you integrate Fourier series.
• Finish Homework 5.
Thursday
Oct. 18
Eigenfunction expansion
Homework 5
due today
Do the following before next class:
Tuesday
Oct. 23
Wave equation
Do the following before next class:
Thursday
Oct. 25
Wave equation
Intro to Sturm-Liouville problems
Homework 6
due today
Do the following before next class:
Tuesday
Oct. 30
Sturm-Liouville problems
Do the following before next class:
Thursday
Nov. 1
Sturm-Liouville problems
Homework 7
due today
Do the following before next class:
Tuesday
Nov. 6
Sturm-Liouville problems
Rayleigh quotient and eigenvalue bounds
Do the following before next class:
Thursday
Nov. 8
Finite difference methods
Homework 8
due today
Do the following before next class:
Tuesday
Nov. 13
Finite difference methods
Do the following before next class:
Thursday
Nov. 15
Finite difference methods
Take-home exam assigned
Homework 9
due today
Do the following before next class:
Tuesday
Nov. 20
Higher-dimensional PDEs
Take-home exam
due today
Thanksgiving break! No class Thursday, Nov. 22
Tuesday
Nov. 27
Guest presentation
Work on your project. Identify sources, gather information, and make an outline for what you will include in your paper.
Thursday
Nov. 29
To be determined
Tuesday
Dec. 4
Work on projects