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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