**Numerical Analysis**

**Instructor**: Dr. Shidong Li

Office: TH 929, **Phone:** x81481,
**email:**
*shidong@sfsu.edu*

Office Hours: Tu Th 2:00 -3:00, or by appointment.

Prerequisite: C or better in Math 228 (Calculus III), CSC210
or Math 309 (basic programing) , and in Math 325 (Linear Algebra).

**Text**: *Numerical Methods* , by Faires/Burden,
3rd 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.. Evidently, it is a single class that every math and science/engineering student should take. 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,
2.6)

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)

**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. The software is available for use in the Mathematics
Lab TH404. 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%

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.