Teaching Information: Office: Rm721, General III building. Tel: ext 3115.

1998-99

Calculus E&E department

1999-2000

Advanced Calculus

Text Book: J. E. Marsden: Elementary Classical Analysis

Introduction to PDE

Ref: L. C. Evans: Partial Differential Equations ; F. John: Partial Differential Equations. (Evans will be the prime reference, our course outline)

Part I: Difinition of PDE; Notation; Linear PDE's; Four impotatant linear PDE's: linear transport equation, Wave equation, Laplace equation and heat equation.

Part II: General techniques for solving linear PDE's: exact formula, reduction to ODE (method of characteristics), Fourier transform and Laplace transform. Separation of variables (Eigenfunction expansions), ...

Part III: Theory of Linear PDE: Generalized functions (distributions); Weak dereivatives, Weak solutions (distribution-valued solutions), Well posedness, Initial value problem, boundary value problem, Initial boundary value problem, Hilbert space method, Maximum princeple, Energy method, Smooth approximations, Fourier analysis revisited, ...

Part IV, Nonlinear PDE's ...

Contact: Office 721, General III building. Tel: ext 3115.