# 2024/25 Undergraduate Module Catalogue

## MATH2600 Numerical Analysis

### 10 creditsClass Size: 140

Module manager: Srikanth Toppaladoddi

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2024/25

### Pre-requisite qualifications

MATH1005 or MATH1010 or (MATH1050 and MATH1060) or (MATH1050 and MATH1331), or equivalent.

### This module is mutually exclusive with

 MATH2601 Numerical Analysis with Computation

This module is not approved as a discovery module

### Module summary

Most of the problems that students meet when they are introduced to, for example, integration or differential equations, will have nice analytic solutions. In real life though this is typically not the case and so solutions have to be evaluated numerically (ie with the aid of a computer). This module explains how to express mathematical operations in terms of operations that can be performed on a computer. It is a good preparation for modules in Numerical Methods.

### Objectives

On completion of this module, students should be able to:
- describe how errors arise in computations
- solve simple non-linear equations by root-finding techniques
- calculate the interpolating polynomial through discrete data points
- derive and use quadrature formulae based on integration of polynomial interpolates
- write down suitable numerical schemes for solving first order ordinary differential equations
- solve linear systems of algebraic equations using Gaussian elimination and LU factorisation.

### Syllabus

1. Introduction. Computer arithmetic. Errors; round-off error, truncation error.
2. Solution of nonlinear equations in one variable. Bisection method; fixed point iteration; Newton-Raphson iteration; secant method. Order of convergence.
3. Interpolation. Lagrange interpolation; error term. cubic splines.
4. Numerical integration. Trapezoidal rule. Method of undetermined coefficients. Simpson's rule. Newton-Cotes formulae. Composite integration methods. Richardson extrapolation; Romberg integration.
5. Ordinary differential equations (initial value problems). Euler's method; errors. Runge-Kutta methods. Multi-step methods. Stability.
6. Linear systems of algebraic equations. Gaussian elimination. Pivoting. LU factorisation.

### Teaching methods

 Delivery type Number Length hours Student hours Workshop 10 1.00 10.00 Lecture 22 1.00 22.00 Private study hours 68.00 Total Contact hours 32.00 Total hours (100hr per 10 credits) 100.00

### Private study

Studying and revising of course material.
Completing of assignments and assessments.

### Opportunities for Formative Feedback

Regular problem solving assignments

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 15.00 Total percentage (Assessment Coursework) 15.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 85.00 Total percentage (Assessment Exams) 85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated