工程數學 Engineering Mathematics II

 

  Instructor:  Professor Wu-ting Tsai,  wttsai@ntu.edu.tw

 Textbook: Advanced Engineering Mathematics by Erwin Kreyszig. John Wiley, 10th edition, 2011

 Grading: Based on the grades of six quizzes

 Syllabus:

 

 

Lecture

Reading

1

Fourier series: Euler formulas, Orthogonality of trigonometric system, Fourier theorem

11.1

2

Fourier series: Example (rectangular wave)

11.1

3

Periodic function with arbitrary period. Even and odd fuctions

11.2

4

Half-range expansion

11.2

5

Forced Oscillation: applications of Fourier series to non-homogeneous ordinary differential equations

11.3

6

First quiz

7

Fourier integral

11.7, Try out Fourier integral Java applets listed below

8

Fourier cosine and sine integrals

11.7

9

Fourier cosine and sine transforms

11.8

10

Fourier transform

11.9

11

Fourier transform of derivatives, convolution theorem

11.9

12

Second quiz

13

Basic concepts of partial differential equation;
Modeling: vibrating string (wave equation)

12.1
12.2

14

Solution of wave equation by method of separation of variables

12.3

15

D'Alembert's solution of the wave equation

12.4

16

Third quiz

17

Modeling: heat conduction along a rod (1-d heat equation)

12.5

18

Solution of heat equation with isothermal boundaries by method of separation of variables

12.6

19

Solution of heat equation with adiabatic boundaries by method of separation of variables;  Physical meanings of Dirichlet and Neumann boundary conditions

12.6

20

Sturm-Liouville problem; Orthogonal functions

11.5

21

Fourth quiz

22

Heat equation in an infinite bar (Fourier integral & Fourier transform)

12.7

23

Heat equation for semi-infinite bars (Fourier cosine or sine transform)

12.7 & lecture notes

24

Wave equation in an infinite-long string (Fourier transform)

12.7 & lecture notes

25

Steady 2-D heat equation in semi-infinite domain (Fourier transform)

12.7 & lecture notes

26

Fifth quiz

27

Approximation by trigonometric polynomials

11.4

28

Fourier series in complex form

lecture notes

29

Discrete Fourier transform

11.4

30

Double Fourier series: wave equation on rectangular membrane

12.9

31

Sixth quiz

 

 Lecture Notes: 

 


 Java applets: (You need Java software for these webpages. Get it free from java.sun.com.)

 


 Materials related to the course: