课程大纲

COURSE SYLLABUS

1.

课程代码/名称

Course Code/Title

MAE5003 高等应用数学

Advanced Methods in Applied Mathematics

2.

课程性质

Compulsory/Elective

专业核心课 Graduate core course

3.

课程学分/学时

Course Credit/Hours

3/48

4.

授课语言

Teaching Language

英文 English

5.

授课教师

Instructor(s)

杨东 助理教授

力学与航空航天工程系

yangd3@sustech.edu.cn

YANG Dong, Assistant Professor

Department of Mechanics and Aerospace Engineering

yangd3@sustech.edu.cn

6.

是否面向本科生开放

Open to undergraduates

or not

否

NO

7.

先修要求

Pre-requisites

（如面向本科生开放，请注明区分内容。 If the course is open to

undergraduates, please indicate the difference.）

8.

教学目标

Course Objectives

This class teaches advanced methods in applied mathematics, with emphasis on practical applications in

science and engineering. Thus, while mathematical derivations will be given when appropriate, most methods

will be introduced and taught by practical examples in fluid mechanics, vibrations, and acoustics. It covers the

following topics: generalized functions, convolution algebra, complex variables, Fourier transform, evaluation

of integrals, Green ’ s function, and integral equation. The class includes regular lectures and a research

project, with the former teaching the basic skills in applied mathematics, and the latter applying these skills to

research.

9.

教学方法

Teaching Methods

讲授 Lectures

10.

教学内容

Course Contents

Section 1

Generalized functions (6)

Section 2

Convolution algebra (8)

Section 3

Complex variables (8)

Section 4

Fourier transform (4)

Section 5

Evaluation of integrals (8)

Section 6

Greens function (6)

Section 7

Integral equation (4)

Section 8

Research project (4)

11.

课程考核

Course Assessment

（

○

1 考核形式 Form of examination；

○

2 .分数构成 grading policy；

○

3 如面向本科生开放，请注明

区分内容。 If the course is open to undergraduates, please indicate the difference.）

1.final exam

2.分数构成 grading policy

Homework (30%)

Homework will be assigned for each topic, and will be due at the end of each month.Homework grading will

be based on both completeness and correctness.

Research project (30%)

The research project will be an application of the methods covered in the lectures to a practical problem.

The problem will be assigned with instructions in November.

The report will be presented in the format of a technical paper.

Final exam (40%)

The final exam will be a two-hour, close-book test.

The exam will be scheduled at the completion of the lectures.

The final grades may be subject to curving.

12.

教材及其它参考资料

Textbook and Supplementary Readings

This course will provide a complete set of lecture notes. The following can be used as additional reading

material. M. J. Lighthill “Fourier Analysis and Generalized Functions” Cambridge University Press,

1958

D. G. Crighton, A. P. Dowling, J. E. Ffowcs Williams, M. Heckl & F. G. Leppington “Modern Methods

in Analytical Acoustics” Spring-Verlag 1992

A. P. Dowling & J. E. Ffowcs Williams “Sound and Sources of Sound” Ellis Horwood Limited 1983

G. R. Carrier, M. Krook & C. E. Pearson “Functions of a Complex Variable: Theory and Techniques”

McGrawHill 1966