Mathematics

Numerical Analysis 1

Module code: G5084
Level 4
15 credits in spring teaching
Teaching method: Lecture, Practical, Workshop
Assessment modes: Unseen examination, Coursework

In this module, you will cover topics such as:

Part I: Introduction to Computing with MATLAB 

  • basic arithmetic and vectors
  • m-file functions
  • for-loops
  • if and else
  • while statements.

Part II: Introduction to Numerical Analysis

  • operating with floating point numbers, round-off error, cancellation error
  • polynomial interpolation, basic idea of interpolation, order of approximation, Lagrangian interpolation, Runge's example, piecewise linear interpolation
  • numerical differentiation, finite difference quotients, order of approximation
  • numerical integration, derive standard numerical integration scheme's and analyse, using polynomial interpolation (midpoint formula, trapezoidal rule, Simpson's formula)
  • nonlinear equations, bisection method, fixed point iteration method, Newton's method/secant method.

Module learning outcomes

  • Write and compile simple MATLAB programs。
  • Carry out numerical differentiation using finite difference quotients and determine order of convergence.
  • Derive numerical integration schemes
  • Solve nonlinear equations using the bisection method, fixed point iteration and the Newton's method.