# Detailed module information

Module information on this degree can be found below, separated by year of study.

The module information below applies for the current academic year. The academic year runs from August to July; the 'current year' switches over at the end of July.

Students select optional courses subject to rules specified in the Mechanical Engineering Student Handbook,  for example at most three Design and Business courses. Please note that numbers are limited on some optional courses and selection criteria will apply.

## Mathematics and Computing 1

### Module aims

This module develops key mathematical and computational skills relevant to the wider mechanical engineering programme.

Topics include vector algebra, real analysis, limits, curve sketching, series, applications of integration, complex analysis, functions of more than one variable, matrix algebra, second order ordinary differential equations, and vector calculus . Practical implementation through programming is studied to solve problems selected from the topic areas. These skills are in support of ME1, ME2, ME3 and ME4 modules.

ECTS: 15

### Learning outcomes

On completion of this module, students will be able to:
1. Use vector algebra and calculus to solve simple geometric and engineering problems.
2. Express and manipulate functions of one real variable, two real variables and one complex variable.
3. Determine the limiting behaviour of functions of one variable, and apply the concept of the limit to differentiation, integration and series expansions.
4. Sketch functions of one and two variables, including all characteristic features.
5. Determine Taylor and Fourier series expansions for functions of one variable, by applying the concepts of convergence and orthogonality.
6. Apply the concept of integration to solve fundamental problems in engineering analysis.
7. Apply matrix algebra to the solution of systems of linear algebraic equations and eigenvalue problems.
8. Classify and solve second order ordinary differential equations.
9. Create python code to implement numerical methods and solve problems selected from the topic areas.

### Module syllabus

Vector algebra

Real analysis

Limits

Curve sketching

Series

Applications of integration

Complex analysis

Functions of more than one variable

Matrix algebra

Second order ordinary differential equations

Fourier series

Programming in python

Vector calculus

Numerical methods

### Teaching methods

 Allocation of study hours Hours Lectures 80 Group teaching 57 Lab/ practical 16 Other scheduled Independent study 222 Placement Total hours 375 ECTS ratio 25

### Assessments

 Assessment type Assessment description Weighting Grading method Pass mark Must pass? Examination 3 Hour exam 80% Numeric 40% Y Examination Progress test 4% 40% N Coursework Programming coursework 1 8% 40% N Coursework Programming coursework 2 8% 40% N

### Great maths books for finding more explanations and exercises on topics you are learning...

• #### Mathematics for engineers and scientists

Jeffrey, Alan.

6th ed., Chapman & Hall/CRC

• #### Mathematical methods for physics and engineering [electronic resource] / K.F. Riley, M.P. Hobson and S.J. Bence

Riley, K. F. (Kenneth Franklin), 1936

Cambridge University Press

Kreyszig, Erwin, author.

10th edition / Erwin Kreyszig in collaboration with Herbert Kreyszig, Edward J. Norminton.; International student version., Hoboken, New Jersey : John Wiley & Sons, Inc.

• #### Mathematical methods in the physical sciences

Boas, Mary L.

Third edition., John Wiley & Sons

• #### Advanced Mathematical Methods for Engineering and Science Students

Stephenson, G ; Radmore, P. M

Cambridge University Press

• #### Engineering mathematics

Stroud, K. A., author.

7th edition., South Norwalk, CT : Industrial Press, Inc.