Matthew L. Wright
Assistant Professor, St. Olaf College

Partial Differential Equations

Math 330 ⋅ Fall 2017

Prof. Wright's office hours: Mon. 2–3, Tues. 9:45–10:45, Wed. 9–10, Thurs 1–2, Fri. 10:30–11:30, or by appointment in RMS 405

Help sessions: Tues. 7–9pm RNS 204 (Oct. 24 through Nov. 14)

Jump to today
Thursday
Sep. 7
Introduction
Heat equation
Do the following before next class:
  • Complete the Syllabus Quiz.
  • Read §1.1 through §1.4 in the textbook. Be sure you understand the derivations of Equations (1.2.4), (1.2.5), (1.2.9), and (1.2.10).
  • Begin Homework 1.
Tuesday
Sep. 12
Heat equation: equilibrium solutions
Do the following before next class:
  • Read §1.5. Note similarities between the derivation of the heat equation in one dimension and in multiple dimensions.
  • Finish Homework 1 (due 4pm Thursday).
Thursday
Sep. 14
Multidimensional heat equation
Homework 1
due today
Do the following before next class:
  • Finish deriving Laplace's equation in polar coordinates (solution in the notes from Thursday).
  • Read §2.1 and §2.2. Come to class knowing the definition of a linear operator and the principle of superposition.
  • Begin Homework 2.
Tuesday
Sep. 19
Separation of variables
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. Note what it means for functions to be orthogonal. Also note how infinite series are used in the solutions toward the end of this section.
  • Finish Homework 2 (due 4pm Thursday).
Thursday
Sep. 21
Orthogonality and initial conditions
Homework 2
due today
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.
  • Begin Homework 3.
Tuesday
Sep. 26
Time-dependent solutions to the heat equation
Do the following before next class:
  • Read §2.5.1 and §2.5.2. Observe how separation of variables can be used to find equilibrium temperature distributions on a 2-dimensional region.
  • Finish Homework 3 (due 4pm Thursday).
Thursday
Sep. 28
Laplace's equation and separation of variables
Homework 3
due today
Do the following before next class:
  • Read §3.1, §3.2, and §3.3 up to page 100.
  • Begin Homework 4.
Tuesday
Oct. 3
Fourier series
Do the following before next class:
  • Read the rest of §3.3. Pay careful attention to the convergence of Fourier (sine/cosine) series.
  • Finish Homework 4 (due 4pm Thursday).
Thursday
Oct. 5
Differentiation of Fourier series
Take-home exam assigned
Homework 4
due today
Do the following before next class:
Tuesday
Oct. 10
Fourier series and Eigenfunction expansion
Take-home exam
due today
Do the following before next class:
  • Read §3.4. Make sure you understand the conditions under which Fourier series may be differentiated term by term.
Thursday
Oct. 12
Eigenfunction expansion
Fall break! No class Tuesday, October 17.
Do the following before next class:
  • Read §3.5 (it's short!). Note what happens when you integrate Fourier series.
  • Do the problems on Homework 5. Typing solutions and turning them in for a grade is optional.
Thursday
Oct. 19
Wave equation
Homework 5
due today (optional)
Do the following before next class:
  • Read §4.1–4.4. Make sure you understand the derivation of the wave equation and the solution of the wave equation by separation of variables.
  • Begin Homework 6.
Tuesday
Oct. 24
Wave equation
Intro to Sturm-Liouville problems
Do the following before next class:
  • Reading TBA...
  • Finish Homework 6 (due 4pm Thursday).
Thursday
Oct. 26
Sturm-Liouville problems
Homework 6
due today
Do the following before next class:
  • TBA...
Tuesday
Oct. 31
Sturm-Liouville problems
Do the following before next class:
  • TBA...
Thursday
Nov. 2
TBA...
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Tuesday
Nov. 7
TBA...
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Thursday
Nov. 9
TBA...
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Tuesday
Nov. 14
TBA...
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  • TBA...
Thursday
Nov. 16
TBA...
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Tuesday
Nov. 21
TBA...
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Thanksgiving break! No class Thursday, Nov. 23
Do the following before next class:
  • TBA...
Tuesday
Nov. 28
TBA...
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  • TBA...
Thursday
Nov. 30
Work on projects
Do the following before next class:
  • TBA...
Tuesday
Dec. 5
Work on projects
Do the following before next class:
  • TBA...
Thursday
Dec. 7
Work on projects
Do the following before next class:
  • TBA...
Tuesday
Dec. 12
Work on projects
Finish projects
Tuesday
Dec. 19
Project presentations
9:00 – 11:00am