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.

Wk

Date

Sec

Material

Homework

1

Feb 12 – 15, Th 16

9.1

Vector Functions

6,10,17,26,38,41,45

9.5

The Directional Derivative

1,6,10,17,22,30

9.7

Divergence and Curl

2,6,14,22,28

2

Feb 18-22

9.8

Line Integrals

2,8,12,16,34

9.9

Line Integrals Independent of the Path

1,4,15,21,24,26

3

Feb 25- March 1

9.12

Green’s Theorem

1,4,6,18,24

9.13

Surface Integrals

3,5,10,28,34

4

March 4-8

9.14

Stokes’ Theorem

2,3,6,8,16

9.16

Divergence Theorem

1,4,8,11

5

March 11-15

4.1

Definition of the Laplace transform

2,5,14,26,30,38,40(b)

4.2

Inverse Transform, Transforms of Derivatives

1,10,18,19,32,36

6

March 18-22

4.3

Translation Theorems

6,13,20,24,37,48,63

4.4

Additional Properties

2,10,16,22,38,46

4.5

Dirac Delta Function

1,4,8,12

7

March 25-29

12.1

Orthogonal Functions

3,6,11,14,21

12.2

Fourier Series

2,6,11,20

April 1-2 Midterm Break

8

April 3-5

12.3

Fourier Cosine and Sine Series

1,8,12,16,25,36

12.4

Complex Fourier Series

3,6,11

9

April 8-12

12.5

Sturm-Liouville Theorem

2,4,6,12

10

April 15-19

12.6

Bessel and Legendre Series

2,4,6,8,15,20

11

April 22-26

13.1

Separable Partial Differential Equation

1,8,13,16,20,26,28

13.3

Heat Equation

2,3,6,8,9

12

April 29-May 3

13.4

Wave Equation

2,4,8,10,16

13.5

Laplace’s Equation

1,4,7,10,14

13

May 6-10

14.2

Problems in Polar and Cylindrical Coordinates

3,4,9,10

14.3

Problems in Spherical Coordinates

1,5,11,12

14

May 13-17

15.2

Applications of the Laplace Transform

2,4,8,10,14,28

15

May 20-24

15.3

Fourier Integral Theorem

1,5,10,18

15.4

Fourier Transforms

2,6,10,12,16

16

May 27-28

Revision