MTH 2203: Numerical Analysis I, 3CU
Pre-requisites: MTH1102, MTH1201
Course Description:
Numerical Analysis plays an indispensable role in solving real life mathematical, physical and
engineering problems. Numerical computations have been in use for centuries even before digital
computers appeared on the scene. Great Mathematicians like Gauss, Newton, Lagrange, Fourier
and many others developed numerical techniques. Numerical analysis is an approach to solving
complex mathematical problems using simple approximating operations and carrying out an
analysis on the resulting errors. In this course, the following areas of Numerical analysis will be
covered: finite differences, interpolation, differentiation, integration, solution of non-linear
equations and solution of a system of linear equations.
Course Objectives
By the end of this course, the student should be able to:
Interpolate data
Carry out numerical integration and differentiation
Solve non-linear equations and systems of linear equations using numerical techniques.
Write codes for simple numerical analysis algorithms.
Detailed Course Outline
Introduction to one of the high level languages e.g. Matlab, Maple, Fortran (9hrs)
Finite Differences
Forward finite difference operator, backward finite difference operator, central finite difference
operator, averaging operator, shift operator. (5hrs)
Interpolation
Definition of interpolation, finite difference Interpolation, finite difference tables, Newton’s
forward difference interpolating polynomial, Newton’s backward difference interpolating
polynomial.
Lagrange interpolation, linear, quadratic and higher degree Lagrange interpolating polynomials,
error analysis in Lagrange interpolating polynomial.
Divided difference interpolation, definition of a divided difference, Newton’s divided difference
interpolation, codes for interpolation. (10hrs)
Numerical Differentiation
Why numerical differentiation, numerical differentiation using finite differences, derivatives using
Newton’s forward formula, derivatives using Newton’s backward difference formula. Error
Analysis in numerical differentiation. (8hrs)
Numerical integration
Trapezoidal rule, Simpson’s rule, analysis of errors in Trapezoidal and Simpson’s rule, computer
codes for the algorithms learnt. (3hrs)
Numerical solution of non-linear equations
Bisection method, secant method, fixed point/Iteration/successive substitutions, Regular false,
Newton Raphson’s method, computer codes for the algorithms learnt. (4hrs)
Numerical solution of a system of linear equations
Direct methods, Gaussian Elimination, Triangular decomposition, Cholesky’s decomposition,
Iterative techniques, Jacob and Gauss Seidel, convergence analysis of iterative methods. (6hrs)
Reading list
The reading list will include but is not limited to the following texts.
Froberg C.E (1994); Introduction to Numerical Analysis. Addison-Wesley.
Richard L. Burden et al (1989): Numerical Analysis (second edition) prindle, Weber and
Schmidt. Boston, Massachusetts.
Oates. P.J. et al (1981); Numerical Analysis, Edward Arnold (Publishing) Ltd.
J. Mango: Introduction to Numerical Analysis, IACE, Makerere University.
E.M.Kizza: Lecture notes in Numerical Analysis. Mathematics Department, Makerere
University.
Learning Outcome
o Interpolate data
o Carry out numerical integration and differentiation
o Solve non-linear equations and systems of linear equations using numerical techniques.
o Write codes for simple numerical analysis algorithms
