### Math 275: Topics in Applied Mathematics, Fall 2005

**Lecture:** MWF 12:10-1:00 pm, 75 Evans

**Instructor:** Jon Wilkening,
wilken@math.berkeley.edu

**Course webpage:**
http://math.berkeley.edu/~wilken/275.F05

**Office:** 1091 Evans, (510) 643-7990 or (510) 486-7006.

**Office hours:** Monday 1:00-2:00, Thursday 3:00-4:00

**Course Description**

**Prerequisites:** Advanced Calculus

**Texts:**

Dietrich Braess, * Finite Elements: Theory, fast solvers, and
applications in solid mechanics.*

C. Pozrikidis, * Boundary integral and singularity methods for linearized
viscous flow.*

**Grading:**

I will assign 5 straightforward programming
projects during the semester. Students are expected to complete 3 of
them according to their interests. They may work in groups of one,
two or three and use any convenient programming language (Matlab, C,
C++, Fortran, Java...).

**Content:**

In this course, we will study fundamental aspects
of the finite element and boundary integral methods for solving
elliptic equations, especially the Poisson equation, the equations of
elasticity, and the Stokes equations. I will also cover more advanced
topics including mixed finite element methods, corner singularities,
least squares finite elements, the calculus of variations, shape
optimization, the Navier-Stokes equations (in the velocity-pressure
and vorticity-stream formulations), fast linear solvers, elliptic grid
generation, and various competing methods such as the immersed
interface and immersed boundary methods. My goal is to present a wide
array of interesting numerical methods for solving partial
differential equations which aren't normally covered in Math 228b.