Department of Mathematical Sciences, KFUPM Math 301 Syllabus (061) Dr. Faisal A. Fairag Course Title: Methods of Applied Mathematics Textbook: Advanced Engineering Mathematics by Zill and Cullen (2nd Edition, 1999) Course Description: Special functions. Bessel’s functions and Legendre polynomials. Vector analysis including vector fields, divergence, curl, line and surface integrals, Green’s, Gauss’ and Stokes’ theorems. Systems of differential equations. Sturm-Liouville theory. Fourier series and transforms. Introduction to partial differential equations and boundary value problems.

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Date

Sec.

Section Title

Homework

1

Sep. 9-14*

9.1

9.5

9.7

Vector Functions

The Directional Derivative

Divergence and Curl

3,11,20,25,28,41

3,6,9,13,21,30

8,14,23,30

2

Sep. 16-20

9.8

9.9

Line Integrals

Line Integrals Independent of the Path

5,10,16,22,30

7,15,18,23,28

3

Sep. 25**-27

9.12

9.13

Green’s Theorem

Surface Integrals

2,6,17,25

3,11,26,33

3b

Contd

9.14

9.16

Stokes’ Theorem

Divergence Theorem

3,6,14,17

2,4,11

4

Sep. 30-Oct .4

4.1

4.2

Definition of the Laplace transform

Inverse Transform, Transforms of Derivatives

3,5,17, 29,38,40(c)

5,13,15,19,35,36

First Major Exam: Monday, Oct. 9, 2006

5

Oct .7-11

4.3

4.4

4.5

Translation Theorems

Dirac Delta Function

8,13,20,24, 47,60,66

5,16,19(b),23,34, 45

4,8,12

Eid al-Fitre Vacation: October 12, 2006 – October 27, 2006

6

Oct. 28-Nov.1

12.1

12.2

Orthogonal Functions

Fourier Series

6,12,16,18

4,6,16,20

7

Nov.4-8

12.3

12.4

Fourier Cosine and Sine Series

Complex Fourier Series

4,6,14,16,26,38

2,4,6,11

8

Nov.11-15

12.5

Sturm-Liouville Theorem

2,4,6,8,14

9

Nov.18-22

12.6

# Bessel and Legendre Series

2,4,6,8,10,20

10

Nov.25-29

13.1

13.3

Separable Partial Differential Equation

Heat Equation

2,10,14,18,20,24,28

2,4,6,8,10

11

Dec. 2-6

13.4

13.5

Wave Equation

Laplace’s Equation

2,4,6,8,10,11

2,4,8,10,14

Second Major Exam: Monday,Dec. 11, 2006

12

Dec. 9-13

14.2

14.3

Problems in Polar and Cylindrical Coordinates

Problems in Spherical Coordinates

2,4,8,10

4,6,12

13

Dec.16-20

15.2

# Applications of the Laplace Transform

6,8,10,14,28

Id al-Adha Vacation: December 21, 2006-January 5, 2007

14

Jan. 6-10

15.3

Fourier Integral Theorem,

4,8,12,18

15

Jan.13-17

15.4

Fourier Transforms

6,10,12,18

*Thursday 14 September is a normal Saturday class

**Saturday 23 September is a national holiday.

#### KFUPM attendance policy will be enforced. DN grade for 9 or more unexcused absences.

Final examination shall be comprehensive.