Partial Differential Equations Preliminary Exam Syllabus
(Spring 1997)
Texts:
(1) R.B. Guenther & J.W. Lee,
Partial Differential Equations of Mathematical Physics,
Chapters 1-6 and 8
(2) H.F. Weinberger,
A first course in Partial Differential Equations,
Chapters 1-4, 7, and 10
Syllabus
- Heat, Wave and Laplace equations
- Existence and Uniqueness theorems
- Minimum and Maximum theorems
- Solution techniques
- Green's Function methods
- Separation of variables
- Rectangular coordinates
- Polar coordinates
- Spherical coordinates
- Fourier series and integrals
- Approximation theorems
- Convergence properties
- Method of Characteristics for quasilinear first order equations
- Existence and uniqueness theorems
- Solution techniques