## CAPE2000 Mathematical Techniques 2

### 20 creditsClass Size: 255

Module manager: Dr JEJ Staggs
Email: j.e.j.staggs@leeds.ac.uk

Taught: Semesters 1 & 2 View Timetable

Year running 2019/20

### Pre-requisite qualifications

A-level mathematics or attendance at CAPE1050 Foundation Mathematics

### Pre-requisites

 CAPE1040 Mathematical Techniques 1

This module is not approved as a discovery module

### Objectives

The aim of the module is to provide sufficient mathematical background knowledge to support the understanding of the various Engineering disciplines taught across SCAPE.

Learning outcomes
At the end of the module students should:
- Have a knowledge of advanced mathematical techniques to enable study in numerate engineering subjects such as heat transfer, fluid dynamics and thermodynamics.
- Have basic skills in statistics and numerical methods.
- Further develop problem solving skills.

### Syllabus

Vectors - Scalar/vector definitions, vector types, vector addition, unit vector, magnitude. Direction cosine, scalar product, vector product, angle between two vectors. Vector calculus: grad, div, curl & Laplacian; directional derivative, line, surface and volume integration.
Series - Series/sequences definition, arithmetic progressions, arithmetic mean, geometric progression, geometric mean, sum of 'n' numbers in series. Series - Infinite series, limiting values approaching infinity, convergence, divergence. Power series, Maclaurin series, limiting values approaching 0, L'Hopital's rule, Taylor series. Fourier series and their applications. Introduction to Fourier integrals and Fourier transforms.
Laplace Transforms - Definition, Theorem 1, 2, 3. Inverse Transforms, solution of differential equations. Solution of second order differential equations, simultaneous equations.
Statistics - Revision of basic concepts; Discrete distributions: the binomial distribution and Poisson distribution. Continuous distributions: the normal distribution (and the relationship with the binomial distribution); Sampling: properties of the estimated values; sampling distribution of mean and variance; confidence intervals. Significance tests. Goodness of fit.
Numerical Methods - Numerical integration and Error Estimates; Introduction to solution of first order ODES; Numerical solution of initial value problems; Approximate solution of algebraic equations.

### Teaching methods

 Delivery type Number Length hours Student hours Example Class 25 1.00 25.00 Lecture 48 1.00 48.00 Independent online learning hours 7.00 Private study hours 120.00 Total Contact hours 73.00 Total hours (100hr per 10 credits) 200.00

### Private study

Review of lectures (48 hours)
Problems/example sheets (56 hours)
Revision for open book exams (6 hours)
Preparation of coursework (10 hours)
Using web resources to practice techniques and solve problems (20 hours).

### Opportunities for Formative Feedback

There are four formative assessments throughout the year that will provide feedback on progress in preparation for the exams.

### Methods of assessment

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 50.00 Standard exam (closed essays, MCQs etc) 2 hr 50.00 Total percentage (Assessment Exams) 100.00

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