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