# Mathematics

## Numerical Analysis 1

Module code: G5084
Level 4
15 credits in spring semester
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 programsã€‚
• 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.