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: [email protected]

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


5

11.1 Fourier Series


11.1 Fourier Series


7

11.1 Fourier Series


11.1 Fourier Series


9

11.1 Fourier Series


11.1 Fourier Series


11

11.2 Fourier Series for Functions of Period 2L


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




15


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




17



11.3.1 Half Range Expansion


19





21



11.4 Complex Fourier Series


23

11.5 Application: Forced Oscillation



(**)

(*)


25



11.6 Approximation by Trigonometric Polynomials


27





29

11.7 Fourier Integral



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


31





33

11.7.1 FourierCosine & Sine Integral


11.8 Fourier Transform


35

11.8.1 Fourier Cosine & Sine Transform


11.8.1 Fourier Sine & Cosine Transform



37

11.8.4 Fourier Sine and Cosine Transform Linear Operation


11.8.5 Transforms of Derivatives


39

11.8.5 Sine and Cosine Transforms of Derivatives


11.9 Complex Fourier Transform


41

11.9 Complex Fourier Transform


11.9.1 Linearity of Complex Fourier Transform



43

11.9.3 Convolution
