Mathematics 128a, Spring 2013, Numerical analysis

Instructor: Alexandre Chorin, 911 Evans Hall, chorin@math.berkeley.edu

Class: MWF 8-9, 4 LeConte. Office hours: MF 9.10-10.10 (after class), W 1-2, 911 Evans Hall.

Textbook: Greenberg and Chartier, Numerical Methods, Princeton.

TAs: Jed Duersch, 810 Evans, office hours M 3.30-5.30; Daniel Greengard, 853 Evans, office hours W 2-4; Thanh Vu, 1040 Evans, office hours MT 11-12.

Grading: 10% theory homework, 20% computer homework, 25% midterm, 45% final, an F in the computer homework is an F in the course.

I have covered: Floating point arithmetic (pp. 112-117, skipping the IEEE standard), Newton's method (pp.83-89), fixed point iterations (pp. 93-96), constant slope method, secant method (pp. 90-93), interpolation (pp. 181-191), norms of functions (there is a discussion of norms for vectors on p. 154, but I could not find where the norms of functions are discussed in detail), orthogonal polynomials and the Gram-Schmidt process (p. 236), best approximation in the 2-norm (see additional reading), best approximation in the infinity norm (pp. 192-197), numerical differentiation (pp.213-218); Newton-Cotes for numerical integration (pp. 227-234 and 243-245); Gaussian integration (pp. 234-240); Euler's scheme for ordinary differential equations (pp. 257-262); linear difference equations (pp. 280-282); Runge-Kutta methods (pp. 265-267); extrapolation and adaptivity; multistep methods (pp. 275-279); systems of equations; stiff systems (pp. 284-288); solution of linear systems (pp. 133-143); matrix norms (pp. 154-156); the condition number (pp. 158-164).