2020/21 Undergraduate Module Catalogue

MATH2601 Numerical Analysis with Computation

15 creditsClass Size: 80

Module manager: Dr Evy Kersale
Email: E.Kersale@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2020/21

Pre-requisite qualifications

(MATH1920 or MATH2920) and {MATH1010 or MATH1005 or [MATH1050 and (MATH1060 or MATH1331)]}, or equivalent.

This module is mutually exclusive with

MATH2600

Numerical Analysis

This module is not approved as a discovery module

Objectives

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 the Level 3 module in Numerical Methods (MATH 3474). This module also involves a practical implementation of the algorithmic ideas. Students should improve their programming skills begun in MATH1920, and gain confidence and facility with computational mathematics.

In order to pass the module, students must pass the MATH2600 component (which is at least 40% on exam and in-course assessment combined) and score at least 40% on the Computer Exercises.

Learning outcomes
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;
- implement numerical algorithms computationally and interpret the results of programs;
- understand some of the practical issues associated with mathematical programming.

Syllabus

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

Teaching methods

Delivery type	Number	Length hours	Student hours
Workshop	10	1.00	10.00
Lecture	11	1.00	11.00
Practical	5	2.00	10.00
Tutorial	5	1.00	5.00
Private study hours			114.00
Total Contact hours			36.00
Total hours (100hr per 10 credits)			150.00

Private study

Students should spend 68 hours in the same way as for MATH2600. The remaing 35 hours are spent writing computer code, analysing results, and writing up work.

Opportunities for Formative Feedback

Five fortnightly pieces of coursework are marked and feedback given. Of these, 2 are assessed towards the final module grade.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
Computer Exercise	In order to pass the module, students must pass the MATH2600 component (which is at least 40% on exam and in-course assessment combined) and score at least 40% on the Computer Exercises.	30.00
In-course Assessment	*	10.00
Total percentage (Assessment Coursework)		40.00

Students who have failed the MATH2600 component will need to resit the exam; students who have failed the computer exercises will need to resubmit these. There is no resit available for the 10% in-course assessment component of this module. If the module is failed, the mark for this component will be carried forward and added to the resit exam and/or computer exercises mark with the same weighting as listed above.

Exams

Exam type	Exam duration	% of formal assessment
Open Book exam	2 hr 00 mins	60.00
Total percentage (Assessment Exams)		60.00

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

Reading list

The reading list is available from the Library website

Last updated: 10/08/2020 08:42:06

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