2022/23 Undergraduate Module Catalogue
MATH2600 Numerical Analysis
10 creditsClass Size: 120
Module manager: Srikanth Toppaladoddi
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2022/23
Pre-requisite qualificationsMATH1005 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 approved as a discovery module
Module summaryMost 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.
ObjectivesOn 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.
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.
|Delivery type||Number||Length hours||Student hours|
|Private study hours||68.00|
|Total Contact hours||32.00|
|Total hours (100hr per 10 credits)||100.00|
Private studyStudying and revising of course material.
Completing of assignments and assessments.
Opportunities for Formative FeedbackRegular problem solving assignments
Methods of assessment
|Assessment type||Notes||% of formal assessment|
|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.
|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
Reading listThe reading list is available from the Library website
Last updated: 13/09/2022
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