Classical Mathematical Methods in Engineering

MATH 4581 (sections AU, AG, and Q) Fall 2021

TTh Lecture 12:30-1:45, Cluck Commons Room 423
INSTRUCTOR: John McCuan
Office hours TTh 11:00-12:00 or by appointment
email:   gtfall21 pm.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 what I just happened to grab off my shelf, so that 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 tell you to obtain and look at a copy of Haberman. 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).

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.

Additional Materials:
Lecture 2 notes
Best fitting circle
Orthogonality
Plotting and Animating Graphs (Mathematica notebook) exported in pdf
A brief introduction to transport equations
Intrinsic Mathematics
Calculating Fourier Coefficients
Assignment 1 Problems 1 and 5 (solutions)
Assignment 2 Problem 2 (solution)
Stokes' flow around a cylinder

Administrative Details
Including grading policy.

Syllabus

(Important) Announcements

Lecture Schedule and Homework

Exam 1 Tuesday October 12, 2021



If you have suggestions for improvements to this course site or you did not find/could not access something that you should have been able to, send mail to mccuan@math.gatech.edu