Courses Catalogue

Numerical Analysis Ii

COURSE CODE: MAT 3202
COURSE CREDIT UNIT: 3
ACADEMIC PROGRAMME: Education (Mathematics) - B.Ed
COLLEGE/SCHOOL/FACULTY: College of Education, Open and Distance Learning
STATUS: Elective
PROGRAMME TYPE: Undergraduate

Course Content and Outline

COURSE CONTENT

·      Approximation theory. Basic definition of approximation, the Weierstrass theorem, the Korovkin Theorem, best approximations, Chebyshev polynomials, trigonometric approximations, splines and dual functional.

·      Numerical Solution of ODEs. Ordinary differential equations: Euler's method and beyond. Multistep methods. Runge–Kutta methods. Stiff equations. Geometric numerical integration. Error control.

·      Nonlinear algebraic systems. The Poisson equation. Finite difference schemes. The finite element method. Spectral methods. Gaussian elimination for sparse linear equations.

·      Classical iterative methods for sparse linear equations. Multigrid techniques. Conjugate gradients. Fast Poisson solvers. Boundary-Value Problems. The Shooting Method. Finite Differences. Boundary Derivative Conditions. Characteristic-Value Problems. Introduction to numerical methods for partial differential equations.

·      The diffusion equation. Hyperbolic equations. Application with MATLAB.

MODE OF DELIVERY

·         Lecture and discussion

·         Group discussion

  • Reading and problem assignments

INSTRUCTIONAL MATERIALS/EQUIPMENT

  • Whiteboard and Markers
  • Flip Charts
  • LCD Projectors
  • CDs, DVDs and Tapes