Courses Catalogue

Numerical Analysis I

COURSE CODE: MAT2102
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

·         Numerical Computing and Computers. What is Numerical Analysis.

·         Bisection Method; Errors. Floating-Point Arithmetic. Floating-Point Arithmetic (continued); Measuring Efficiency.

·         MATLAB programming: data types and structures, arithmetic operations, functions, input and output, interface programming, graphics;

·         Solving Nonlinear Equations. The secant method. Newton's method and Fixed-Point Iterations. Errors and Convergence. Roots of Polynomials. Multiple Roots; Golden Section Search. Solving Sets of Equations.

·         Review of Linear Algebra. Elimination Methods. The LU decomposition. The cost of elimination. Improve the stability by pivoting. Norms and Condition Numbers. Iterative methods for linear systems.

·         Estimation of eigenvalues and eigenvectors (power method, Rayleigh quotient and Gerschgorin's circles).

·         Interpolation and Curve Fitting. Lagrange and Neville Interpolation. Divided Differences. Least Squares Approximation. Errors and Complexity. Approximation of Functions. Chebyshev polynomials. Padé approximations.

·         Numerical Differentiation and Numerical Integration. Interpolation for Derivatives and Integrals. Extrapolation and Newton-Cotes integration formulas. Composite Rules and Romberg Integration. Gaussian Quadrature.

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