Department of Mathematical Sciences, KFUPM |
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Math 301 Syllabus (061) |
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Dr. Faisal A. Fairag |
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Course Title: |
Methods of Applied Mathematics |
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Textbook: |
Advanced Engineering Mathematics by Zill and Cullen (2nd Edition, 1999) |
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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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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 |
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9.7 |
Divergence and Curl |
2,6,14,22,28 |
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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 |
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3 |
Feb 25- March 1 |
9.12 |
Green’s Theorem |
1,4,6,18,24 |
9.13 |
Surface Integrals |
3,5,10,28,34 |
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4 |
March 4-8 |
9.14 |
Stokes’ Theorem |
2,3,6,8,16 |
9.16 |
Divergence Theorem |
1,4,8,11 |
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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 |
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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 |
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4.5 |
Dirac Delta Function |
1,4,8,12 |
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7 |
March 25-29 |
12.1 |
Orthogonal Functions |
3,6,11,14,21 |
12.2 |
Fourier Series |
2,6,11,20 |
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April 1-2 Midterm Break |
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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 |
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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 |
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12 |
April 29-May 3 |
13.4 |
Wave Equation |
2,4,8,10,16 |
13.5 |
Laplace’s Equation |
1,4,7,10,14 |
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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 |
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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 |
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16 |
May 27-28 |
Revision |