proton.me
proton.me
Text:
Elementary Applied Partial Differential Equations, Fourth Ed.
by Richard Haberman, Prentice-Hall
Purchasing of the text is recommended but not strictly required; any edition
should do, but the fourth edition is
the one I will use. According to my recollection, some
earlier editions were a bit better, so if you can find
one of those you might
get it...also for some diversity. I will type up and post assignments, so
you should be able to get precise problem statements without the text.
If you need additional reading or review, I will mostly tell
you to obtain and look at a copy of Haberman. I may type up some notes of
my own from time to time. I will certainly do that for the introductory
material of the first week or so. Of course, you are also
encouraged to listen to the lectures and discuss any questions you have
(with me) during the lectures or during office hours. I really like for
students to ask good questions. Beyond that, any decent
calculus text (Salas, Hille, and Etgen, Thomas, Schwarz, Stewart, Anton,...)
should provide adequate prerequisite reading, assuming of course you know
stuff like algebra and trigonometry (maybe a little arithmetic). Above all
don't worry. You don't have to be a math whiz when you start my course...just
when you finish it.
Supplemental Texts:
Fourier Series and Orthogonal Functions
by Harry Davis, Dover
Also, most any decent text with a title like
Advanced Engineering Math should cover all the material in
this course (more or less). Some recommended authors in this category
might be Peter O'Neill, Erwin Kreyszig, Erich Zauderer, and David Zill.
This course is an introduction to the basic partial differential equations of nineteenth century physics and engineering: The heat equation, the wave equation, and Laplace's equation. In the process of understanding the basic properties of solutions of these equations, we will study series methods (eigenfunction expansion) and transform methods. Fourier series are interesting by themselves, so just that topic should be worth the cover price for an engineer.
Course activities:
There will be approximately 10 assignments over the course of the semester. Their weights and names will be approximately as follows:
Assignment 1 10% (ODE)
Assignment 2 10% (Fourier series)
Assignment 3 10% (linearity and norms)
Assignment 4 10% (ODE Review/Exam 1)
Assignment 5 10% (Heat Equation)
Assignment 6 10% (Laplace's Equation)
Assignment 7 10% (Elliptic and Parabolic PDE Review/Exam 2)
Assignment 8 10% (Wave Equation)
Assignment 9 10% (hyperbolic PDE Review/Exam 3)
Assignment 10 (Final Exam) 10%
No special note or distinction need be made concerning assignments designated as "exams." This is purely administrative. There are no in-class exams. You may work on an assignment any time after it is made available on the schedule page. You may turn in your work on an assignment at any time after an upload link for that assignment has appeared on canvas until the end of the semester. If you want an assignment graded, turn in your work on canvas before the due date.
(Below 60% C; 60-85% B; 86-100% A)
Additional Materials:
Notes (Lectures 1 and 2)
Solutions for Problems 4 and 8 of
Assignment 1 (2024)
(old) notes on mollification
(old) notes on the volume of balls
Mathematica notebook related to Problem 9 of Assignment 4
Laplace Transform
Administrative Details
Including grading policy.