## Applied Differential Equations

**Basic Topics**

Course material- Mathematics 266AB; additional sources are Mathematics 135AB, 136, and 146. Topics- Spectrum theory of regular boundary value problems and examples of singular Sturm-Liouville problems, related integral equations, special functions; Fourier series, Fourier and Laplace transforms; phase plane analysis of nonlinear equations; asymptotic methods for obtaining approximate solutions of ordinary differential equations; solution of simple initial and boundary value problems for potential, heat and wave equations, Green’s functions, separation of variables.

**More Advanced Topics**

Course material- Mathematics 266ABC.

Topics- All M.A. level topics as well as: first order partial differential equations; classification and theory of linear and nonlinear higher order partial differential equations; well-posed problems; classical potential theory, Dirichlet and Neumann problems; fundamental solutions; wave equations, Cauchy problem, initial-boundary value problems, energy estimates, method of characteristics, principle of linearization; variational problems; maximum principles; equations of fluid mechanics.

**References**

- Bender C. M. & Orszag, S. A. (1978). Advanced Mathematical Methods for Scientists and Engineers, New York: McGraw-Hill.
- Boyce, W. E. & Diprima, R. C. (1986). Elementary Differential Equations and Boundary Value Problem (4th edition), New York: Wiley.
- Courant and Hilbert, Methods of Mathematical Physics, Vols. I, II.
- Garabedian, Partial Differential Equations.
- Haberman, Elementary Applied Partial Differential Equations.
- John, Partial Differential Equations.
- Stakgold, Boundary Value Problems of Mathematical Physics, Vols. I, II.
- Zauderer, Partial Differential Equations of Applied Mathematics.
- Haberman, Elementary Applied Partial Differential Equations