1
课程详述
COURSE SPECIFICATION
以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问，请联
系授课教师。
The course information as follows may be subject to change, either during the session because of unforeseen
circumstances, or following review of the course at the end of the session. Queries about the course should be
directed to the course instructor.
1.
课程名称 Course Title
科学计算 Scientific Computing
2.
授课院系
Originating Department
数学系 Department of Mathematics
3.
课程编号
Course Code
MAT8006
4.
课程学分 Credit Value
3
5.
课程类别
Course Type
专业选修课 Major Elective Courses
6.
授课学期
Semester
春季 Spring
7.
授课语言
Teaching Language
英文 English
8.
授课教师、所属学系、联系方
式（如属团队授课，请列明其
他授课教师）
Instructor(s), Affiliation&
Contact
（For team teaching, please list
all instructors）
Alexander Kurganov, 教授, 数学系, alexander@sustc.edu.cn
Alexander Kurganov, Professor, Department of Mathematics, alexander@sustc.edu.cn
9.
实验员/助教、所属学系、联系
方式
Tutor/TA(s), Contact
待公布 To be announced
10.
选课人数限额(可不填)
Maximum Enrolment
（Optional）
授课方式
Delivery Method
讲授
Lectures
习题/辅导/讨论
Tutorials
实验/实习
Lab/Practical
其它(请具体注明)
Other（Please specify）
总学时
Total
11.
学时数
Credit Hours
48
48
2
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
常微分方程 A（MA201a）
Ordinary Differential Equations A（MA201a）
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
14.
其它要求修读本课程的学系
Cross-listing Dept.
教学大纲及教学日历 SYLLABUS
15.
教学目标 Course Objectives
教授基本数值方法，理论及其在现代科学计算中的应用。
Teaching basic numerical methods, theory and their applications in modern scientific computing.
16.
预达学习成果 Learning Outcomes
After completing this course, students should master the basic concepts and methods in modern scientific computing, in both theory
and programming.
完成本课程后,学生应掌握现代科学计算的基本概念和方法，包括理论以及编程实现。
17.
课程内容及教学日历 （如授课语言以英文为主，则课程内容介绍可以用英文；如团队教学或模块教学，教学日历须注明
主讲人）
Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if
this is a team teaching or module course.)
Section 1, Principles of Numerical Mathematics（2H）
Well-posedness
Stability and convergence of numerical methods
A-priori and a-posteriori analysis
Sources of error in computational models
Machine representation of numbers
Section 2, Polynomial Interpolation （4H）
Lagrange polynomial interpolation and their Newton forms
Hermite polynomial interpolation
Piecewise polynomial interpolation
Approximation by splines, B-splines
Section 3, Numerical Differentiation and Integration （4H）
Finite-difference approximations of derivatives
Newton-Cote formulae
Section 4, Solutions of Linear Systems of Equations （8H）
Linear Operators on Normed Spaces, vector and matrix norms
Direct methods - LU factorization; Cholesky factorization
Iterative methods - Jacobi, Gauss-Seidel, SOR, Conjugate Gradient
Conditioning and condition number
Multi-grid methods
Domain decomposition techniques
Section 5, Eigenvalue Problem（4H）
Power method
Householder’s reflection, Given’s rotation, and QR factorization
The singular value decomposition (SVD)
Lanczos’ method
Section 6, Least Squares Problems and Orthogonal Polynomials in Approximation Theory（13H）
Least-squares approximation and normal equations
3
Orthogonal polynomials
Gaussian quadrature with orthogonal polynomials
Rational function approximation
Approximation by Fourier trigonometric polynomials
Fast Fourier transforms
Gaussian quadrature over unbounded intervals
Approximation of function derivatives (classical finite differences, compact finite differences, pseudo-spectral derivative)
Section 7, Solutions of Nonlinear Systems of Equations （5H）
Fixed-point iterations (the banach fixed-point theorem and convergence results)
Newton's methods and quasi-Newton’s methods
Steepest descent methods
Stopping criteria
Post-processing techniques for iterative methods
Section 8, Numerical Methods for Ordinary Differential Equations（8H）
Initial value problems
One-step methods
Linear multistep methods
Runge-Kutta methods
Stability and stiffness
Finite-difference method for boundary value problems
Local truncation error, global error
Stability, consistence, and convergence
18.
教材及其它参考资料 Textbook and Supplementary Readings
参考教材 Textbook：
1、A first course in Numerical Analysis, 2nd edition, by Anthony Ralston and Philip Rabinowitz, Dover Publications INC, 2001.
2、Iterative Methods for Sparse Linear Systems, 2nd edition, by Yousef Saad, Society for Industrial and Applied Mathematics 2003.
3、Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, by
Randall J. LeVeque, SIAM, 2007.
4、Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, by L. N. Trefethen, Cornell University,
1996.
5、数值分析，张平文，李铁军 编著，北京大学出版社, 2007
课程评估 ASSESSMENT
19.
评估形式
Type of
Assessment
评估时间
Time
占考试总成绩百分比
% of final
score
违纪处罚
Penalty
备注
Notes
出勤 Attendance
10%
课堂表现
Class
Performance
小测验
Quiz
课程项目 Projects
平时作业
Assignments
20%
期中考试
Mid-Term Test
30%
期末考试
Final Exam
40%
4
期末报告
Final
Presentation
其它（可根据需要
改写以上评估方
式）
Others (The
above may be
modified as
necessary)
20.
记分方式 GRADING SYSTEM
A. 十三级等级制 Letter Grading
B. 二级记分制（通过/不通过） Pass/Fail Grading
课程审批 REVIEW AND APPROVAL
21.
本课程设置已经过以下责任人/委员会审议通过
This Course has been approved by the following person or committee of authority
