Course Introduction

• Prerequisite：Calculus, Linear Algebra, Introduction to Computer Science, Numerical Analysis
• Recommended for： Graduate
• Introduction：

Many problems in science and engineering can’t be solved analytically or empirically. Problems such as weather forecasting, financial and economic forecasting and big data processing etc., can only be studied using computer simulations. Moreover, with advance computer technologies, industry also relies on a lot of simulations for product design and manufacturing. Scientific computing as one of the core element inside every computer simulation plays an important role in the development of science and technology nowadays. The emphasis of this course is on understanding and using numerical methods that are foundations of scientific computation. Students who finished this course are expected to be able to solve the following types of problems: solutions of linear equations, nonlinear root finding, optimization, curve fitting, numerical integration and the solution of differential equations by using computer simulations.

• Syllabus：

1. This course is an introduction to the basic theories and algorithms on the topic of Scientific Calculate.
2. Scientific Computing
3. Systems of Linear Equations
4. Linear Least Squares
5. Eigenvalue Problems
6. Nonlinear Equations
7. Optimization
8. Interpolation
9. Numerical Integration and Differentiation
10. Initial Value Problems for ODEs
11. Boundary Value Problems for ODEs
12. Partial Differential Equations
13. Fast Fourier Transform

• Reference：

1. Michael T. Heath, Scientific Computing: An Introductory Survey, 2nd ed., McGraw Hill, Boston, 2002