## 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 2020/21

### This module is mutually exclusive with

 ELEC1702 Engineering Mathematics ELEC1703 Algorithms and Numerical Mathematics

This module is not approved as a discovery module

### Module summary

The teaching and assessment methods shown below will be kept under review during 2020-21. In particular, if conditions allow for alternative formats of delivery, we may amend the timetable and schedule appropriate classes in addition to (or in place of) the Online Learning Workshops. For Semester 2 (from January 2021), we anticipate that this will be most likely, in which case online teaching will be substituted for traditional face-to-face teaching methods, including lectures and practical classes. â€˜Independent online learningâ€™ will involve watching pre-recorded lecture material or screen-casts, engaging in learning activities such as online worked examples or remote/virtual laboratory work, etc. Students will be expected to fully engage with all of these activities. The time commitment for independent online learning, and also the frequency and duration of Online Learning Workshops, are approximate and intended as a guide only. Further details will be confirmed when the module commences.

### Objectives

This module provides a careful, 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 algebraic expressions with confidence.
2. Use trigonometric functions with confidence and perform calculations involving triangle and circle geometry.
3. Sketch trigonometric, exponential, natural log and polynominal functions.
4. Understand the connection between derivative and slope and quote the derivatives of basic functions.
5. Know what is meant by a stationary point and be able to classify the stationary points of simple functions.
6. Quote the general form of the Maclaurin and Taylor series, and determine the series of simple functions.
7. Be able to quote the indefinite integrals of basic functions, integrate by parts, and use substitutions to evaluate integrals.
8. Carry out 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 2 dimensional and 3 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 On-line Learning 18 2.00 36.00 Independent online learning hours 64.00 Private study hours 100.00 Total Contact hours 36.00 Total hours (100hr per 10 credits) 200.00

### Private study

Students are expected to use private study time to consolidate the material covered in lectures, to undertake preparatory work for examples classes and to prepare for summative assessments.

### Opportunities for Formative Feedback

Feedback will be mainly provided through the weekly examples classes.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Online Assessment Online Assessment/Test 1 10.00 Online Assessment Online Assessment/Test 2 30.00 Online Assessment Online Assessment/Test 3 30.00 Online Assessment Online Assessment/Test 4 30.00 Total percentage (Assessment Coursework) 100.00

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.