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
Haberman, R. Applied Partial Differential Equations. 4th ed. Upper Saddle River, NJ: Prentice Hall, March 24, 2003. ISBN: 0130652431.
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
Course 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
VI. Green's Function Method for Solving ODEs, PDEs