## 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