San Francisco State University
Math 400, Spring 2018

Numerical Analysis

Tu Th 12:35 - 1:50 (TH 211)


Instructor: Dr. Shidong Li
Office: TH 929,    Phone: x81481, email: shidong@sfsu.edu
Office Hours:  Tu 3:30 - 5:00, or by appointment.
Prerequisite:  C or better in Math 228 (Calculus III), Math 325 (Linear Algebra), and CSC210 or Math 309 (basic programing).

Text: Numerical Methods ,   by Faires/Burden, 4th edition.

Suggested Reference: Numerical Analysis,  by Faires/Burden, 6th (or earlier) edition.

Numerical analysis is about the study of algorithms for mathematical calculations using computers. It contains algorithms for solving equations, interpolation and approximations, algorithms for numerical integrations and differentiations, and error estimate and analysis as well as convergence studies, etc.. In today's work place, either in engineering/scientific applications or in scientific and mathematical research, efficient numerical implementations are part of critical steps.

Topics to be covered (tentative):
Chapter 1:  Mathematical preliminaries and error analysis
Chapter 2:  Solutions of equations of one variable (2.4 ~ 2.5)
Chapter 3:  Interpolation and polynomial Approximation
Chapter 4:  Numerical Integration (4.1 ~ 4.6)
Chapter 7:  Iterative methods for solving linear systems
Chapter 8:  Approximation Theory( 8.1 ~ 8.4, 8.6, 8.7)
Chapter 9:  Topics on Eigenvalue Approximations (should time permits)

MATLAB  programming will be the main platform for the class. Matlab is by far the most popular numerical package used in scientific and engineering research and implementations. It is the software preferred by most of the professional numerical analysts. It contains the most advanced numerical algorithms. A brief introduction of Matlab programming will be given in the class. Many homework assignments may need programming implementations. There will be also projects integrated with the course.

Grading Percentage:
Homework and projects :                  40%
Mid-term:                                          30% (Tentatively scheduled on 3/15)
Final:                                                  30%

Homework are assigned on each lecture.  Students are expected to spend at least 2-3 hours on each assignment.   Doing homework and projects in time is clearly the most important part of the class.