National University of Sciences and Technology
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CSE-881 Applied Mathematics for Computational Science & Engineering
Campus RCMS
Programs PG
Session Spring Semester 2017
Course Title Applied Mathematics for Computational Science & Engineering
Course Code CSE-881
Credit Hours 3-0
Course Objectives This course is intended to prepare the student with the mathematical tools and techniques those are essential for the solutions of advanced problems encountered in the fields of applied physics and engineering. It covers the foundations of mathematical modeling and solutions of ordinary and partial differential equations.
Detail Content
  • Iterative Methods: Mathematical and numerical investigation of direct, iterative & semi-iterative methods of solution of linear system. Singular algebraic systems and least squares computations. Methods for calculation of eigenvalues and eigenvectors.
  • Differential Equations: Basic theory and introduction of Differential Equations (DE): First and second order Ordinary Differential Equations (ODEs) including existence and uniqueness theorems and the theory of linear systems. Use of power series as a tool in solving Ordinary Differential Equations; 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. Solutions by Laplace and Fourier transform techniques. Solutions in series of eigen functions, maximum principles, the method of characteristics, Green’s functions, and discussion of well-posedness of problems.
  • Numerical Solutions of ordinary and Partial Differential Equations: Finite difference method for general one dimensional elliptic boundary value problems with different boundary conditions; Finite difference methods for two dimensional elliptic PDEs (may include multi-grid and fast Poisson solvers); Finite difference methods for one and two dimensional parabolic PDEs, e.g. the heat equation; Von Neumann stability analysis; Finite difference methods for one and two dimensional hyperbolic PDEs, e.g. the wave equation, numerical methods for conservation laws.
Text/Ref Books
  • Advanced Engineering Mathematics, Kreyszig, E. 7th ed., Wiley 1993.
  • Computational and Applied Mathematics for Engineering Analysis, A. S. Cakmak.
  • Fourier Seires, G. P. Tolstov.
  • Basic ParitalDifferntail Equations, D. Bleecher and G. Csordas.
  • An online textbook from Georgia Tech: Linear Methods of Applied Mathematics, Evans Harrell and James Herod (
  • Applied Mathematics: A Contemporary Approach, J. D. Logan
  • Numerical Solution of Partial Differential Equations, K. W. Morton and D. F. Mayers, Cambridge press, 1995.
Time Schedule Spring Semester 2017
Faculty/Resource Person Dr Ammar Mushtaq
PhD (National University of Science and Technology (NUST)
Discipline: Computational Science & Engineering
Specialization: Computational Fluid Dynamics (CFD)