The course will cover continuous and discrete Fourier transforms, the Fast Fourier Transform (FFT), truncation and aliasing, orthogonal polynomials including Chebyshev, interpolation, quadrature, numerical differentiation, analysis of initial-value and boundary-value ordinary differential equations (ODE), numerical methods for ODE. If time permits, finite elements and spectral elements.

This material covers notions of numerical analysis central for modern scientific computing, i.e., the kind of computing related to phenomena governed by continuous mathematics (functions, derivatives, integrals, differential equations), like in physics and finance. The course will also contain notions of analysis of ODE not covered in Math 53, and some harmonic analysis.

While the course is clearly geared towards applications, the style of the lecture and the homework will be theoretical, like in other mathematics classes. There will be no programming homework assigments.

There are two required textbooks. The first one is An Introduction to Numerical Analysis by Endre Suli and David F. Mayers. It should be available at the bookstore. Math 118 is a new class; if the bookstore runs out of copies, please let the teaching staff know immediately about it.

The second textbook is Spectral Methods in MATLAB by L. N. Trefethen, ed. SIAM (2001). It will NOT be available at the bookstore. Instead, the plan is to order it online with a decent discount from the editor. I recommend going through the following steps:

Become a student member of the Society for Industrial and Applied Mathematics (SIAM) by signing up here. It's free and as a perk you will receive the 8-page newsjournal "SIAM news" once every 2 months. (If you are already a member of SIAM skip the membership application.)

With student membership you have a 30 percent discount on all SIAM books, including the class textbook. Order the book here and don't forget to scroll down choose "SIAM member price" over "List price" at the bottom of the page. Make sure you specify "Member price Math 118 Stanford" in the Special Instruction box before submitting your order. If one of the steps of ordering online poses an insurmountable difficulty to you, contact the teaching staff for help.

If you wish to purchase the books elsewhere, or if you wish to group orders among yourselves, that is fine. One copy of each book will be on reserve at the Math/CS library.

The lecture may occasionally be inspired by material not included in either book, but typeset notes will be provided everytime this happens.

PDF notes: February 11 version, March 17 version, March 18 version.

Math 51 and Math 53. Alternatively, familiarity with the following notions:

Vector and matrix operations;

Partial derivatives and the chain rule of vector calculus;

Solutions of linear ordinary differential equations.

No knowledge of computer programming is necessary. Notions of matrix theory (Math 104) can be helpful, but are not necessary.

Instructor Laurent Demanet Contact info Lecture: MW 3:15p - 4:30p Room 380-381U Office hours: MW 1:30p - 3:00p or by appointment Room 380-382J

Course assistant Kaiyuan Zhang Office hours: Th 2:30p - 4:30p or by appointment Room 380-380G