**Instructor:**Dmitriy Leykekhman

**Office Hour:**3:15-4:15 p.m. Tuesday, at MSB 318

**Prerequisites:**Basic Linear Algebra. Some knowledge in MATLAB programming helps.

**Textbook:**"Partial Differential Equations with Numerical Methods" by Stig Larsson and Vidar Thomee.

Available at Amazon.com

**Course workload:**Homework will be assigned roughly once a week, mostly with MATLAB programming assignments and one final take-home project.

**Credits:**3 credit hours.

**Grading Policy :**The final grade will be determined from the homework assignments and the final project.

You may organize study groups to discuss material and assignments, but you must write your own solutions.

**Scope:**This course is appropriate for graduate students majoring in mathematics as well as mathematically inclined graduate engineering students. I will try to make the course self contained. Familiarity with basic real analysis, partial differential equations, and functional analytical tools for Hilbert spaces is required. Basic knowledge of MATLAB is required. The material can be split into several part:

**Topics covered:**

Two-point boundary value problem.

Elliptic problems.

Finite Difference method for elliptic equations.

Finite Element method for elliptic equations.

Parabolic problems.

Finite Difference method for parabolic equations.

Finite Element method for parabolic equations.

Hyperbolic problems.

Finite Difference method for hyperbolic equations.

Finite Element method for hyperbolic equations.