I.Contents：
(1) Numerical approach to elliptic problems and the related error estimate.
(2) Numerical method for large linear system resulting from discretization.
(3) Numerical approach to parabolic problems and the related time integration.
(4) Computer programming for solving above introduced problems.
II.Course prerequisite：
Basic knowledge about advanced calculus, numerical linear algebra, elementary real or functional analysis is required.
III.Reference material ( textbook(s) )：
We will focus on finite element approaches, and courseware may be adapted to fit one semester program more or less from the following standard references:
(1) P.G.. Ciarlet, Finite element methods for elliptic problems.
(2) O.C. Zienkiewicz & R.L. Taylor, The finite element methods Vol. I.
(3) G. Strang & G. Fix, An analysis of the finite element method.
IV.Grading scheme：
attendance 30%, mid-exam 30%, final 40%