Matthew L. Wright
Assistant Professor, St. Olaf College

Partial Differential Equations

Math 330 ⋅ Fall 2019

Prof. Wright's office hours in RMS 405: Mon. 9:00–10:00, Tues. 9:30–10:30, Wed. 2:00–3:00, Thurs 1:00–2:00, Fri. 9:00–10:00, whenever the door is open, or by appointment

Help sessions: Mondays 7:30–8:30 in RNS 204

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Thursday
September 5
Introduction
ODE review
Do the following before next class:

Optionally, watch the following video: But what is a partial differential equation? (3Blue1Brown).

Tuesday
September 10
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
September 12
Heat equation
Homework 1
due today
Do the following before next class:
Tuesday
September 17
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). You may want to use the LaTeX template on Overleaf.
Thursday
September 19
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, and bring your answer to class on Tuesday.
  • Begin Homework 3.
Tuesday
September 24
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
September 26
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.
  • Read §2.5.1 and §2.5.2. Answer the reading questions, and bring your answer to class on Tuesday.
  • Begin Homework 4.
Tuesday
October 1
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
October 3
Fourier series
Take-home exam assigned
Homework 4
due today
Do the following before next class:
  • Complete the take-home exam.
Tuesday
October 8
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
October 10
Differentiation of Fourier series
Fall break! No class Tuesday, October 15.
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
October 17
Eigenfunction expansion
Homework 5
due today
Do the following before next class:
  • Read §4.1–4.4. Answer the reading questions and bring your answers to class on Tuesday.
  • Begin Homework 6.
Tuesday
October 22
Eigenfunction expansion
Wave equation
Do the following before next class:
  • Finish Homework 6 (due 4pm Thursday).
Thursday
October 24
Wave equation
Homework 6
due today
Do the following before next class:
  • Begin Homework 7.
Tuesday
October 29
Intro to Sturm-Liouville problems
Do the following before next class:
  • Read §5.1–§5.3. Answer the reading questions, and bring your answers to class on Thursday.
  • Finish Homework 7 (due 4pm Thursday).
  • Read the Final Project Information sheet and start thinking about what topic you might want to study.
Thursday
October 31
Sturm-Liouville problems
Homework 7
due today
Do the following before next class:
  • Read §5.4 and §5.5. To better understand connections between differential equations and linear algebra, read the Appendix to 5.5.
  • Continue thinking about what you might want to work on for the Final Project.
  • Begin Homework 8.
Tuesday
November 5
Sturm-Liouville problems
Operators, orthogonality, and self-adjointness
Do the following before next class:
  • Re-read §5.5. Note the role of Lagrange's identity and Green's formula in the proofs presented in this section.
  • Read §5.6. Observe how the Rayleigh quotient can provide a bound on the lowest eigenvalue.
  • Finish Homework 8 (due 4pm Thursday).
  • Continue thinking about what you might want to work on for the Final Project.
Thursday
November 7
Sturm-Liouville problems
Rayleigh quotient and eigenvalue bounds
Homework 8
due today
Do the following before next class:
  • Read §5.7. This example should look familiar now!
Tuesday
November 12
Finite difference methods
Do the following before next class:
Thursday
November 14
Finite difference methods
Homework 9
due today
Do the following before next class:
Tuesday
November 19
Finite difference methods
Do the following before next class:
Thursday
November 21
Finite difference methods
Take-home exam assigned
Homework 10
due today
Complete the take-home exam before next class.
Tuesday
November 26
To be determined
Thanksgiving break! No class Thursday, Nov. 22
Do the following before next class:
Tuesday
December 3
Final projects
Work on your final project.
Thursday
December 5
Final projects
Work on your final project.
Tuesday
December 10
Final projects
Work on your final project.
Wednesday
December 18
Project presentations
9:00 – 11:00am