# 2022/23 Undergraduate Module Catalogue

## ELEC1704 Further Engineering Mathematics

### 10 creditsClass Size: 160

**Module manager:** Professor Christoph Walti**Email:** c.walti@leeds.ac.uk

**Taught:** Semester 2 (Jan to Jun) View Timetable

**Year running** 2022/23

**This module is not approved as a discovery module**

### Objectives

Building on the Semester 1 mathematics topics, this module provides students with a knowledge and understanding of the key mathematical principles necessary to underpin their education in engineering. On completion of this module students should be able to apply mathematical methods, tools and notations to the analysis and solution of engineering problems, especially within the field of electronics.**Learning outcomes**

On completion of this module students should be able to:

1. Add, subtract and multiply simple matrices and perform spatial transformations using matrices.

2. Express and solve simultaneous linear algebraic equations in matrix form.

3. Calculate the inverse of a square matrix, and use the inverse to solve simultaneous linear equations.

4. Calculate the determinant of a square matrix, and find the eigenvalues and eigenvectors of a square matrix.

5. Diagonalise a square matrix.

6. Formulate differential equations corresponding to 2nd order linear systems and solve 2nd order differential equations with constant coefficients.

7. Solve coupled 1st order differential equations.

8. Derive and use Laplace Transforms of piecewise continuous and periodic functions.

9. Derive the Laplace Transforms of basic mathematical functions.

10. Use Laplace transformation to derive the s-domain equivalents of circuits containing L, C and R, and predict system response based on the location of the system poles.

### Syllabus

Topics may include, but are not limited to:

Matrices: Basic matrix algebra and properties, Matrix solution of simultaneous linear equations

Row reduction methods, Gaussian & Gauss Jordan elimination, Consistency of simultaneous linear equations, Transpose and inverse of a matrix

Use of inverse to solve simultaneous linear equations, Determinants

Properties, Eigenvalues and Eigenvectors

Diagonalisation

Differential Equations: 1st and 2nd order linear differential equations with constant coefficients, solution via the auxiliary equation, nonhomogenous equations, application to electrical systems

Coupled 1st order linear differential equations

Transformation of higher order linear differential equations on to coupled differential equations

Laplace Transforms: Introduction to transforms and operators, Laplace transforms of basic functions

Unit step function, Transforms of 1st and 2nd derivatives, Application to electric circuits

Transfer functions, Inverse Laplace transforms, derivation using partial fractions

Direct (s-domain) analysis of electrical circuits, Interpretation of s-domain functions

System poles and their effect on system response

Initial & final value theorems, Transforms of piecewise continuous functions

### Teaching methods

Delivery type | Number | Length hours | Student hours |

Office Hour Discussions | 10 | 1.00 | 10.00 |

Individual Support | 10 | 1.00 | 10.00 |

Seminar | 10 | 1.00 | 10.00 |

Tutorial | 10 | 1.00 | 10.00 |

Independent online learning hours | 20.00 | ||

Private study hours | 40.00 | ||

Total Contact hours | 40.00 | ||

Total hours (100hr per 10 credits) | 100.00 |

### Private study

Students are expected to use private study time to consolidate their understanding of course materials, to undertake preparatory work for seminars, workshops, tutorials, examples classes and practical classes, and also to prepare for in-course and summative assessments.### Opportunities for Formative Feedback

Students studying ELEC modules will receive formative feedback in a variety of ways, including the use of self-test quizzes on Minerva, practice questions/worked examples and (where appropriate) through verbal interaction with teaching staff and/or post-graduate demonstrators.### Methods of assessment

**Coursework**

Assessment type | Notes | % of formal assessment |

Assignment | MATLAB coursework | 25.00 |

Total percentage (Assessment Coursework) | 25.00 |

Resits for ELEC and XJEL modules are subject to the School's Resit Policy and the Code of Practice on Assessment (CoPA), which are available on Minerva. Students should be aware that, for some modules, a resit may only be conducted on an internal basis (with tuition) in the next academic session.

**Exams**

Exam type | Exam duration | % of formal assessment |

Online MCQ | 1 hr 00 mins | 25.00 |

Online MCQ | 1 hr 00 mins | 25.00 |

Online MCQ | 1 hr 00 mins | 25.00 |

Total percentage (Assessment Exams) | 75.00 |

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

### Reading list

There is no reading list for this moduleLast updated: 03/05/2022 14:36:20

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

Errors, omissions, failed links etc should be notified to the Catalogue Team.PROD