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 Campus SCME Programs PG Session Fall Semester 2016 Course Title Advanced Engineering Mathematics Course Code CHE-901 Credit Hours 3.0 Pre-Requisutes Course Objectives This course covers the mathematical techniques necessary for understanding chemical engineering topics such as energetic materials, structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. Detail Content Mathematical and numerical investigation of direct, iterative & semi-terative methods of solution of linear systems. Singular algebraic systems and least squares computations. Methods for calculation of eigenvalues and eigenvectors. Differential Equations: Ordinary Differential Equations: Ordinary differential equations including existence and uniqueness theorems and the theory of linear systems. Topics may also include stability theory, the study of singularities, and boundary value problems. Applied Differential Equations: Wave, heat and Laplace equations. Solutions by separation of variables and expansion in Fourier Series or other appropriate orthogonal sets. Use of power series as a tool in solving ordinary differential equations. Solutions in series of eigenfunctions, maximum principles, the method of characteristics, Green's functions, and discussion of well-posedness problems. Perturbation theory and asymptotic approximations: Perturbation theory for algebraic equations; Regular perturbation theory (power series) and its shortcomings; Asymptotics and uniformity; stretched time; Boundary-layer problems. Text/Ref Books Advanced Engineering Mathematics, Kreyszig, E. 7th. edn., Wiley 1993. Perturbation Methods, E. J. Hinch. Perturbation Methods in Applied Mathematics, J. D. Cole. Computational and Applied Mathematics for Engineering Analysis, A. S. Cakmak. Fourier Series, G. P. Tolstov. Basic Partial Differential Equations, D. Bleecker and G. Csordas. An online textbook from Georgia Tech: Linear Methods of Applied Mathematics, Evans Harrell and James Herod (http://www.mathphysics.com/pde/). Applied Mathematics: A Contemporary Approach, J. D. Logan. Time Schedule Fall Semester, 2011 Faculty/Resource Person Dr Iftikhar Gul