This document outlines the lecture topics for Engineering Mathematics covering Fourier series, integrals, and transforms taught by Dr. A. Selk Ghafari. The lecture covers Fourier series, Fourier series for periodic functions, even and odd functions, half range expansions, Fourier integrals, Fourier transforms, Fourier sine and cosine transforms, transforms of derivatives, and complex Fourier transforms. Examples from the textbook are noted for several topics.

1. 1
Lecture One:
Fourier Series, Integrals, and
Transforms (Ch. 11)
School of Science and Engineering
Sharif University of Technology International Campus
Dr. A. Selk Ghafari
Email: 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 33
11.7.1FourierCosine&SineIntegral
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

10. 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

11. 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