# 2022/23 Undergraduate Module Catalogue

## 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 (Sep to Jun) View Timetable

Year running 2022/23

### 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 Chemical and Process Engineering.

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

- Power series and applications
- Fourier series
- Review of vectors, matrices and determinates
- Concepts of vector calculus
- Applications of vector calculus to fluid dynamics and heat transfer

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 20 1.00 20.00 Lecture 40 1.00 40.00 Private study hours 140.00 Total Contact hours 60.00 Total hours (100hr per 10 credits) 200.00

### Private study

Working through weekly problem sheets
Reviewing lectures

### Opportunities for Formative Feedback

One formative assessment and weekly problem classes that will provide feedback on progress in preparation for the exams.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Assignment Assignment 25.00 Total percentage (Assessment Coursework) 25.00

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

Exams
 Exam type Exam duration % of formal assessment Unseen exam 2 hr 50.00 Unseen exam 1 hr 25.00 Total percentage (Assessment Exams) 75.00

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