AMAT 22572: Numerical Methods II

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Course Code    : AMAT 22572

Title                 : Numerical Methods II

Pre-requisites   : AMAT 12543

 

Learning Outcomes:

At the end of the course, the student should be able;

  • to find numerical solutions to system of equations using indirect methods,
  • to develop and use algorithms and theorems to find numerical solutions of ordinary differential equations, numerical differentiation and numerical integration

 Course Contents:

Numerical Linear Algebra: Vector Norms, Matrix norms, General properties of vector and matrix norms.   

 Numerical Differentiation and Integration: Numerical Differentiation, Open and closed Newton-Cotes formulae, Trapezoidal, Simpson’s 1/3 and 3/8 rules, Simpson quadratic formulae, Romberg integration method, Gaussian quadrature.

 Modern Methods for Solving Linear Systems of Equations: Relative error bound, Condition number, Iterative and Relaxation Methods: Jacobi, Gauss-Siedel methods and their convergence, Richardson, SOR Iterative, Gradient Methods: Conjugate Gradient Method

 Numerical Solutions of Ordinary Differential Equations: Explicit and Implicit numerical schemes, Taylor-Series Method, Picard’s Method of Successive Approximations, Euler’s method, Heun’s method, , Midpoint method ,Runge-Kutta Methods, Computation of error bound, Stability of methods, Predictor-Corrector methods.

 Method of Teaching and Learning: A combination of lectures and tutorial discussions.

 Assessment: Based on tutorials, tests, presentations and end of course examination.

 Recommended Reading      : 

  1. Burden, R.L., Faires, J.D, Burden, M.L. Numerical Analysis (10e), Cengage Learning. (2015).
  2. Trefethen L.N. & Bau D., Numerical Linear Algebra, Philadelphia, USA. (1997).
  3. Golub H., Vanloan C.F., Matrix computations, JHU Press, 2013
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