Engineering Mathematics chapter 11,

1

Lecture One:Fourier Series, Integrals, and

Transforms (Ch. 11) School of Science and Engineering

Sharif University of Technology International Campus

Dr. A. Selk GhafariEmail: a_selkghafari@sharif.edu

Homepage: http://kish.sharif.edu/~a_selkghafari

2

11.1 Fourier Series

Engineering Mathematics, Dr. A. Selk Ghafari

3

11.1 Fourier Series

Engineering Mathematics, Dr. A. Selk Ghafari 4

11.1 Fourier Series

Engineering Mathematics, Dr. A. Selk Ghafari

5

11.1 Fourier Series

Engineering Mathematics, Dr. A. Selk Ghafari 6

11.1 Fourier Series

Engineering Mathematics, Dr. A. Selk Ghafari

7

11.1 Fourier Series

Engineering Mathematics, Dr. A. Selk Ghafari 8

11.1 Fourier Series

Engineering Mathematics, Dr. A. Selk Ghafari

9

11.1 Fourier Series

Engineering Mathematics, Dr. A. Selk Ghafari 10

11.1 Fourier Series

Engineering Mathematics, Dr. A. Selk Ghafari

11

11.2 Fourier Series for Functions of Period 2L

Engineering Mathematics, Dr. A. Selk Ghafari 12

11.2 Fourier Series for Functions of Period 2L

Note: See examples 2, and 3 in section 11.2 of your text book (pp. 488-489).Engineering Mathematics, Dr. A. Selk Ghafari

13

11.3 Even and Odd Functions

Engineering Mathematics, Dr. A. Selk Ghafari 14

11.3 Even and Odd Functions

Engineering Mathematics, Dr. A. Selk Ghafari

15

11.3 Even and Odd Functions

Note: See examples 1, and 2 in section 11.3 of your text book (p. 492)

Engineering Mathematics, Dr. A. Selk Ghafari 16

11.3 Even and Odd Functions

Engineering Mathematics, Dr. A. Selk Ghafari

17

11.3 Even and Odd Functions

Engineering Mathematics, Dr. A. Selk Ghafari 18

11.3.1 Half Range Expansion

Engineering Mathematics, Dr. A. Selk Ghafari

19

11.3.1 Half Range Expansion

Engineering Mathematics, Dr. A. Selk Ghafari 20

11.3.1 Half Range Expansion

Engineering Mathematics, Dr. A. Selk Ghafari

21

11.3.1 Half Range Expansion

Engineering Mathematics, Dr. A. Selk Ghafari 22

11.4 Complex Fourier Series

Engineering Mathematics, Dr. A. Selk Ghafari

23

11.5 Application: Forced Oscillation

Engineering Mathematics, Dr. A. Selk Ghafari 24

11.5 Application: Forced Oscillation

(**)

(*)

Engineering Mathematics, Dr. A. Selk Ghafari

25

11.5 Application: Forced Oscillation

Engineering Mathematics, Dr. A. Selk Ghafari 26

11.6 Approximation by Trigonometric Polynomials

Engineering Mathematics, Dr. A. Selk Ghafari

27

11.6 Approximation by Trigonometric Polynomials

Engineering Mathematics, Dr. A. Selk Ghafari 28

11.6 Approximation by Trigonometric Polynomials

Engineering Mathematics, Dr. A. Selk Ghafari

29

11.7 Fourier Integral

Engineering Mathematics, Dr. A. Selk Ghafari 30

11.7 Fourier Integral

Note: See examples 1 in section 11.7 of your text book (p. 506)

Engineering Mathematics, Dr. A. Selk Ghafari

31

11.7 Fourier Integral

Engineering Mathematics, Dr. A. Selk Ghafari 32

11.7 Fourier Integral

Engineering Mathematics, Dr. A. Selk Ghafari

33

11.7.1 FourierCosine & Sine Integral

Engineering Mathematics, Dr. A. Selk Ghafari 34

11.8 Fourier Transform

Engineering Mathematics, Dr. A. Selk Ghafari

35

11.8.1 Fourier Cosine & Sine Transform

Engineering Mathematics, Dr. A. Selk Ghafari 36

11.8.1 Fourier Sine & Cosine Transform

Note: See examples 2 in section 11.8 of your text book (p. 515)

Engineering Mathematics, Dr. A. Selk Ghafari

37

11.8.4 Fourier Sine and Cosine Transform Linear Operation

Engineering Mathematics, Dr. A. Selk Ghafari 38

11.8.5 Transforms of Derivatives

Engineering Mathematics, Dr. A. Selk Ghafari

39

11.8.5 Sine and Cosine Transforms of Derivatives

Engineering Mathematics, Dr. A. Selk Ghafari 40

11.9 Complex Fourier Transform

Engineering Mathematics, Dr. A. Selk Ghafari

41

11.9 Complex Fourier Transform

Engineering Mathematics, Dr. A. Selk Ghafari 42

11.9.1 Linearity of Complex Fourier Transform

Note: See examples 3 in section 11.9 of your text book (p. 522)

Engineering Mathematics, Dr. A. Selk Ghafari

43

11.9.3 Convolution

Engineering Mathematics, Dr. A. Selk Ghafari