## ELEC1701 Introduction to Engineering Mathematics

### 20 creditsClass Size: 180

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

Taught: Semesters 1 & 2 (Sep to Jun) View Timetable

Year running 2024/25

### Pre-requisite qualifications

Acceptance onto the BEng/MEng Electronic and Electrical Engineering, BEng/MEng Electronics and Computer Engineering, or BEng/MEng Mechatronics and Robotics Engineering programme

This module is not approved as a discovery module

### Module summary

This module provides students with a knowledge and understanding of the key mathematical principles necessary to underpin their education in engineering.

### Objectives

This module has the following objectives:
- To provide students with the foundational principles of engineering mathematics.
- To offer students extensive opportunities for practising mathematical skills.
- To learn how to apply mathematical methods, tools and notations to the analysis and solution of engineering problems.

Learning outcomes
On successful completion of the module students will have demonstrated the following learning outcomes:
1. Apply basic knowledge of mathematics to the solution of well-defined problems.

Skills learning outcomes

On successful completion of the module students will have demonstrated the following skills:
a) Application of science, mathematics and/or engineering principles

### Syllabus

Topics may include, but are not limited to:
* Exponential functions
* Logarithms and natural logarithms
* Logarithmic scales
* Application to calculate decibel quantities and decibel changes
* Hyperbolic functions
* Principle of differentiation
* Differentiation of standard functions
* Differentiation of a product and a quotient
* Chain rule
* Differentiation from first principles
* Practical application of differentiation
* Determination of maxima and minima
* Taylor and Maclaurin series
* Series expansion of exponential, logarithmic and trigonometric functions
* Principle of integration
* Integrals of standard functions
* Methods of integration: substitutions, integration by parts and via partial fractions
* The trapezium rule
* Vectors: Practical examples of vector quantities
* Vector notations
* Addition and subtraction of vectors in 2 and 3 dimensions
* Scalar product, Vector product and Scalar triple product
* Complex numbers: Cartesian and polar forms
* Argand diagrams and vector representation
* Arithmetic of complex numbers
* De Moivre's theorem
* Complex roots of equations: complex solutions of the quadratic formula
* Complex roots of polynomials
* Graphical interpretation
* Complex representation of sine & cosine & analogy with hyperbolic functions
* 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, non-homogenous 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

Methods of Assessment

We are currently refreshing our modules to make sure students have the best possible experience. Full assessment details for this module are not available before the start of the academic year, at which time details of the assessment(s) will be provided.

Assessment for this module will consist of:

1 x Coursework
2 x Exam

### Teaching methods

 Delivery type Number Length hours Student hours Practicals 6 2.00 12.00 Examples Class 22 1.00 22.00 Seminar 44 1.00 44.00 Independent online learning hours 44.00 Private study hours 78.00 Total Contact hours 78.00 Total hours (100hr per 10 credits) 200.00

### Opportunities for Formative Feedback

Students studying ELEC modules will receive formative feedback in a variety of ways, which may include 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 In-course Assessment Coursework 30.00 Total percentage (Assessment Coursework) 30.00

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

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 3 hr 00 mins 30.00 Standard exam (closed essays, MCQs etc) 3 hr 00 mins 40.00 Total percentage (Assessment Exams) 70.00

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