## ELEC1702 Engineering Mathematics

### 10 creditsClass Size: 160

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

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2022/23

### This module is mutually exclusive with

 ELEC1701 Introduction to Engineering Mathematics

This module is not approved as a discovery module

### Objectives

This module provides an opportunity to revise essential engineering mathematics concepts and to develop understanding in new areas of mathematics applicable to engineering.

Learning outcomes
On completion of this module students should be able to:

1. Manipulate basic algebraic expressions.
2. Use trigonometric functions and perform calculations involving triangle and circle geometry.
3. Sketch trigonometric, exponential, natural log and polynominal functions.
4. Explain the connection between derivative and slope and quote the derivatives of basic functions.
5. Identify stationary points and classify the stationary points of simple functions.
6. Quote the general form of the Maclaurin and Taylor series, and determine the series of basic functions.
7. Quote the indefinite integrals of basic functions, integrate by parts, and use substitutions to evaluate integrals.
8. Perform a simple partial fraction expansion of a function and use it to integrate.
9. Add, subtract, multiply and divide complex numbers and apply De Moivre's theorem.
10. Add and subtract two-dimensional and three-dimensional vectors and calculate scalar and vector products.

### 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 substraction 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

### Teaching methods

 Delivery type Number Length hours Student hours Laboratory 3 2.00 6.00 Office Hour Discussions 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 44.00 Total Contact hours 36.00 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