Course Introduction

• Prerequisite：Calculus、Linear Algebra
• Recommended for： Junior
• Introduction：

Computational mathematics is the study of algorithms use to solve mathematical problems. In this course, we introduce numerical methods for solving systems of linear equations and nonlinear equations. Approximation theory including polynomial interpolation, numerical differentiation and numerical integration will also be covered. Numerical errors arisen from various approximations in some of the above mentioned topics will be analyzed. Moreover, round-off errors from computations under floating point arithmetic will be discussed. Finally, students will learn methods for solving ordinary differential equations numerically and understand the stability/consistency of the numerical methods they use.

• Syllabus：

1. Errors in numerical computations on floating point arithmetic
2. Methods for solving linear systems
3. Iterative methods for solving nonlinear equations
4. Polynomial approximation and interpolation
5. Numerical differentiation and integration
6. Numerical methods for solving initial value problems of the ordinary differential equations

• Reference：

1. Endre Suli and David Mayers, An introduction to numerical analysis. Cambridge University Press, 2003.
2. David Kincaid and Ward Cheney, Numerical Analysis: Mathematics of scientific computing, 3rd. ed. Brooks&Cole, 2012.
3. Richard Burden and Douglas Faires, Numerical Analysis, 10th ed. Brooks&Cole, 2018.