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 Campus PNEC Programs PG Session Fall Semester 2016 Course Title Advanced Engineering Mathematics Course Code MATH-812 Credit Hours 3-0 Pre-Requisutes Course Objectives The main objective of the course is to acquaint students with the advanced analytical techniques that will be foundation for their research areas. Application of these techniques in engineering program and enable students to obtain closed form solution of engineering problem. Detail Content Series solution methods; Legendre equation and its solution, Generating function of Legendre function, Orthogonality of Legendre function. Bessel equation and its solution, Generating and orthogonality of Bessel function, Fourier Bessel series and its applications. Method of Separation of Variables; The principle of superposition, Orthogonality of function, Application to one, two and three dimensional Laplace & heat conduction boundary value problem in Cartesian, cylindrical and spherical coordinates. Method of Fourier Transform; Dirichlet’s conditions, Fourier integral formula, The complex Fourier transform, Fourier sine & cosine transform, Convolution or falting theorem for Fourier transform, Multiple Fourier transform and application of Fourier transform to boundary value problem Strum-Liouville Eigen value problem; Heat flow in non-uniform material with and without source, Self adjoint operator and Strum-Liouville problems, Rayleigh Quotient and asymptotic behavior. Methods of Eigen function expansion with homogeneous boundary condition Methods of Eigen function expansion using Green’s Formula with or without homogeneous boundary conditions. Method of characteristics for linear and quasi linear heat transfer equations. Text/Ref Books Applied Partial differential equation by Richard Haberman. Partial Differential Equations and Boundary-Value Problems with Applications by Mark A. Pinsky Boundary Value Problems of Heat Conduction By M. NecatiÖzişik Partial Differential equation and Fourier Analysis by Ka Kit Tung. Time Schedule Fall Semester 2014 Faculty/Resource Person DrAsifMansoor PhD (University of Karachi) PK Discipline: Applied Mathematic Specialization: Computational Fluid dynamic