Math 241: Calculus IV |
Spring 2015 |
---|

Faculty: Jerry L. Kazdan

Telephone: (215) 898-5109

email:kazdan AT math.upenn.edu

Office Hours: Wed. 10:30-11:30 (and also by appointment) in DRL 4E15TA: Joseph Hoisington

Telephone: (215) 898-5973

email:jhois AT math.upenn.edu

Office Hours: ??? (and by appointment) in DRL 4C11

## Calculus IV, Spring 2015

Primary Math 241 Web PageHandout (to Math Instructors)

Prerequisite(s):MATH 114 and 240.

Syllabus:The heart of this course is to cover some basic techniques and ideas that arise in applications, particularly to partial differential equations.

Some topics include Sturm-Liouville problems, orthogonal functions, Fourier series, and partial differential equations including solutions of the wave, heat and Laplace equations, Fourier transforms.

Text:Haberman, Richard,Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th Edition 2012, Pearson/Prentice Hall, Publishers, ISBN-13: 978-0321797063

Note:check online for alternate less expensive sources of the text.Prerequisites & Review Material

Some References:books, articles, web pages

Exams:- Exam 1: Tues, Feb. 17: PDF , condensed, + Extra problems
- Exam 2: Tues, Mar. 24 PDF, condensed
- Final Exam: Monday, May 11 PDF, condensed, solutions
- Exam Scores
You may always use one 3"x5" card withhandwrittennotes on both sides

Notes:

LaTeX: If you will be writing many documents that contain equations, it is wise to learn (and use) LaTeX. It is available on Windows, Macs, and Linux -- and isfree. See TeX Stuff. For some students, this might be the most useful item you learn in this course.

Some Classical PDEs

Striking a Match: Turbulence

Tacoma Narrows Bridge http://www.math.upenn.edu/~kazdan/425S11/math21-2011.pdf

Some notes (1965!) from a course like our Math 240 (there are typos.)

ODE's: Generalities on Linear ODE's DeTurck Notes

DeTurck's Math 425 for 2010

DeTurck notes on first order PDE's

Derivation of the heat equation

Inner Product: print version (display version)

Examples Using Orthogonal Vectors and Fourier Series Fourier Series Examples

Remarks on hw3-2.5.9b

Physics of Music Music

Gibbs Phenomenon

Nodal Lines

Sines and Cosines using ODE

circular drumhead (Bessel)

Lorentz Transformations

Wave Eq in R^2 and R^3

Light-cones in R^2 and R^3

Hear the Shape of a Drum (also, Google search on: Gordon "Shape of a drum")

Homework Assignments:

- Set 0: Rust Remover (LaTeX source ) Due: Never (this will not be collected).
- Set 1 (LaTeX source ) Due: Thurs., Jan. 22 in class [Late papers accepted until 1:00 PM Friday.]
- Set 2 (LaTeX source ) Due: Thurs., Jan. 29 in class [Late papers accepted until 1:00 PM Friday.]
- Set 3 (LaTeX source ) Due: Thurs., Feb. 5 in class [Late papers accepted until 1:00 PM Friday.]
- Set 4 (LaTeX source ) Due: Thurs., Feb. 12 in class [Late papers accepted until 1:00 PM Friday.]
- Set 5 (LaTeX source ) Due: Thurs., Feb. 26 in class [Late papers accepted until 1:00 PM Friday.]
- Set 6 (LaTeX source ) Due: Thurs., Mar. 5 in class [Late papers accepted until 1:00 PM Friday.]
- Set 7 (LaTeX source ) Due: Thurs., Mar. 19 in class [Late papers accepted until 1:00 PM Friday.]
- Set 8 (LaTeX source ) Due: Thurs., April 2 in class [Late papers accepted until 1:00 PM Friday.]
- Set 9 (LaTeX source ) Due: Thurs., April 9 in class [Late papers accepted until 1:00 PM Friday.]

Notes on Problem 1- Set 10 (LaTeX source ) Due: Thurs., April 16 in class [Late papers accepted until 1:00 PM Friday.]
- Set 11 (LaTeX source ) Due: Thurs., April 23 in class [Late papers accepted until 1:00 PM Friday.]

Math 241 Old Final Exams

Note:The curriculum changed beginning Fall 2012. Thus the old final exams (through Spring 2012) will not accurately reflect the content of subsequent exams.