Math 241: Calculus IV | Spring 2015 |
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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 Page Handout (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:
You may always use one 3"x5" card with handwritten notes on both sides- 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
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 is free. 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.