Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Prerequisites
Differential Equations (18.03 or 18.034). Complex Variables with Applications (18.04) or Functions of a Complex Variable (18.112) are useful, as well as previous acquaintance with the equations as they arise in scientific applications.
Textbook
Either one of the following textbooks will do.
Guenther, R. B., and J. W. Lee. Partial Differential Equations of Mathematical Physics and Integral Equations. New York, NY: Dover Publications, 1996. ISBN: 0486688895.
Myint-U, Tyn, and Lokenath Debnath. Linear Partial Differential Equations for Scientists and Engineers. 4th ed. Boston, MA: Birkhauser, 2006. ISBN: 0817643931.
Assignments and Exams
There will be 6 problem sets given throughout the term. There will be two in-class tests and a final exam.
Grading
| ACTIVITIES | PERCENTAGES |
|---|---|
| Assignments | 20% |
| In-class Tests (2 tests each worth 20%) | 40% |
| Final Exam | 40% |
Outline
I. The Heat Equation in One Space Variable
- Separation of Variables, Fourier Series, Sturm-Liouville Eigenvalue Problems
II. The Wave Equation in One Space Variable
- Method of Characteristics
III. Method of Characteristics Solution to Quasilinear PDEs
IV. The Heat and Wave Equations with Two or Three Space Variables
- Bessel Functions, Laplace's Equation
V. The Heat Equation and Laplace's Equation on Unbounded Spacial Domains
- Fourier Transform
VI. Green's Function Method for Solving ODEs, PDEs