## ELEC1701 Introduction to Engineering Mathematics

### 20 creditsClass Size: 30

Module manager: Dr. Joshua Freeman
Email: j.r.freeman@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2022/23

### This module is mutually exclusive with

 ELEC1702 Engineering Mathematics ELEC1703 Algorithms and Numerical Mathematics

This module is not approved as a discovery module

### Objectives

This module provides a thorough treatment of the foundational principles of engineering mathematics, and offers students extensive opporunities for practising mathematical skills.

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:

Algebra: manipulation of algebraic expressions and equations. Factorisation of quadratic equations. Quadratic formula. Concept of a function. Graph sketching. Polynomial functions and their roots. Co-ordinate geometry
Properties of right angled triangles: sine, cosine, tangent and their graphs. CAST. Area of triangles. Sine and cosine rules
Properties of trigonometric functions. Trigonometric identities and their applications. Cotangent, secant and cosecant. Inverse trigonometric functions. Circle geometry, equation of a circle, circular motion & relation to trigonometric functions
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 from first principles. Practical application of differentiation. Determination of maxima and minima
Binomial series. 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 trapezoidal rule: Interpretation as a discrete system
Vectors: Concept of a vector. 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 20 2.00 40.00 Independent online learning hours 40.00 Private study hours 104.00 Total Contact hours 56.00 Total hours (100hr per 10 credits) 200.00

### 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 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