Here is a list of topics covered and all written assignments for the course as well as a dynamic listing of what was actually planned and covered in the lecture. Remember: Your work on assignments should be neatly presented---if you can't write legibly, then figure out a way to type it---and submitted on Canvas.
Date Chapter.Section/Topics or Page/Problems
T Aug 22 Lecture 1 1-D Heat Equation
Assignment 1 Due Tuesday September 12, 2023
Th 24 Lecture 2 1-D Heat Equation (continued)
Assignment 2 Due Tuesday September 19, 2023
T 29 Lecture 3 2-D and 3-D Heat Equation, boundary values etc.
Assignment 3 Due Tuesday September 26, 2023
Th 31 Lecture 4 Derivation of the heat equation in higher dimensions
Integration and the Divergence Theorem
T Sept 5
Th 7 Lecture 6 Integration and the Divergence Theorem (continued)
To do list: separation of variables
T 12 Lecture 7 Integration and the divergence
Assignment 1 due
Th 14 Lecture 6 divergence theorem
separation of variables and Fourier series
Assignment 4 Due Tuesday October 17, 2023 (due date canged from October 10)
T 19 Lecture 9 review of derivation
Th 21 Lecture 10 separated variables solutions and Sturm-Liouville Problems
T 26 Lecture 11 separated variables solutions and superposition
Th 28 Lecture 12 Projection in Hilbert space
T Oct 3 Lecture 13 Fourier series solution
Assignment 5 Due Tuesday October 24, 2023
Th 5 Lecture 14 Fourier series solution of the 1D heat equation
T Oct 10 Fall Break
Th 12 Lecture 15 spatially forced 1-D heat equation (general approach)
T 17 Lecture 16 spatially forced 1-D heat equation: examples and
related topics
Assignment 6 Due Tuesday November 7, 2023
Th 19 Lecture 17 long time behavior and the Poincar'e inequality
T 24 Lecture 18 trading between forcing and initial conditions
Th 26 Lecture 19 weak solutions of ODEs
T 31 Lecture 20 application of weak solutions to the heat equation
Th Nov 2 Lecture 21 Weak C^1 solutions of the heat equation
T 7 Lecture 22 Laplace's equation
Assignment 7 Due Tuesday November 21, 2023
Th 9
T 14
Th 16
T 21
Th Nov 23 Thanksgiving Holiday
T 28
Th 30
T Dec 5 Last class meeting
Final Assignment Due Wednesday December 14, 2023
Th 7
T 12
Th Dec 14 Final Exam (11:20-2:10)
Date Chapter.Section/Topics or Page/Problems
T Aug 24 ODEs and PDEs
Didn't cover:
Introduction: Partial Differential Equations; The Heat Equation
See Lecture 2 notes (typed on main course page)
Assignment 1 (corrected version) Due Tuesday September 14, 2021
Assignment 1 (original version with errors in problems 9 and 10)
Th 26 Power Series and Fourier Series
Still haven't covered:
Derivation of the 1-D heat equation (see lecture 2 notes)
T 31 NOTE: On this day office hours start at 11:30 AM.
1-D heat conduction
Assignment 2 Due Tuesday September 28, 2021
Th Sept 2 higher spatial dimension
Separation of Variables (Chapter 2).
T 7 Separation of Variables
Separation of Variables (continued)
Assignment 3 = Exam 1 Due Tuesday October 12, 2021
Note that this assignment is being posted over a month in advance of the due date,
and we have covered almost all the material needed for completion of this assignment
in lecture already. Suggestion: Assignment 1 is due in a week. After you get that
one done, pick up the pace and get Assignment 2 done a little early, so you have
plenty of time to get Assignment 3 done before Fall Break. Of course, if you
procrastinate, you can spend the first four or so days of Fall Break doing Assignment 3.
Th 9 See the mathematica notebook posted on the main page concerning graphical representation
of solutions
Lecture 6 (?)
Transport equations
The divergence and the divergence theorem
T 14 Lecture 7 Intrinsic Mathematics
Lecture 7 Intrinsic Mathematics
Th 16 Lecture 8 Heat conduction on a ring
T 21 Lecture 9 Calculus of Variations
Th 23 Lecture 10 Calculus of Variations (continued) last page
Assignment 4 Due October 26, 2021
T 28 Lecture 11 Calculus of Variations: Dirichlet energy
Assignment 2 Problem 5: Polar coordinates and the chain rule
Th 30 Lecture 12 Directional derivatives, Laplace's PDE on a disk last page
T Oct 5 Lecture 13 The mean value property and the maximum principle(s)
Assignment 5 Due November 9, 2021
Th 7 Lecture 14 Open sets and other mathematical sounding words (topology)
T Oct 12 Fall Break
Th 14 Lecture 15 Chapter 3 (of Haberman) Fourier series
T 19 Lecture 16 Fourier's theorem (pointwise convergence) last page
and eigenfunction expansion
Th 21 Lecture 17 Riesz-Fischer theorem (L^2 convergence)
and clean up of various topics:
(a) Lecture 16/Chapter 3
(b) Initial condition in eigenfunction expansion
(c) Weak maximum principle (to do list)
T 26 Lecture 18 Wave equation: separation of variables/superposition
Th 28 Lecture 19 Wave equation: derivation
T Nov 2 Lecture 20 Hanging slinky and river crossing
Assignment 6 = Exam 2 Due November 23, 2021
Th 4 Lecture 21
Trig identity/induction for Gibb's phenomenon
river crossing problem (calculus of variations)
d'Alembert's solution/method of characteristics
T 9 Lecture 22 d'Alembert's solution and Streamlines last page
Th 11 Lecture 23 Streamlines contined
Assignment 7 Due December 7, 2021
Assignment 8 = Final Exam Due December 13, 2021
T 16 Lecture 24 Transverse Oscillations and Sturm-Liouville Theory
Th 18 Lecture 25 Sturm-Liouville Theory and Bessel Functions
T 23 Lecture 26 Transverse Vibrations
1-D
2-D rectangle
2-D disk
Th Nov 25 Holiday
T 30 Lecture 27 Transverse Oscillations of a Hanging Chain
Th Dec 2 Lecture 28 Free Day
Assignment 7 Problem 1
Problem 2
1-D Internal Oscillations
(motion of a hanging slinky/spring in gravity)
T 7 Last class meeting
Lecture 29
M 13 Final Exam (11:20-2:10)