Penn Math Math 241: Calculus IV Spring 2015

Faculty: Jerry L. Kazdan
    Telephone: (215) 898-5109
    email: kazdan AT
    Office Hours: Wed. 10:30-11:30   (and also by appointment) in DRL 4E15
TA: Joseph Hoisington
    Telephone: (215) 898-5973
    email: jhois AT
    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

Course and Homework Grading

Some References: books, articles, web pages

You may always use one 3"x5" card with handwritten notes on both sides

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
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:

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.