2017/18 Undergraduate Module Catalogue
ELEC1701 Introduction to Engineering Mathematics
20 creditsClass Size: 30
Module manager: Dr. Marco Califano
Email: m.califano@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2017/18
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 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:
- manipulate algebraic expressions with confidence
- use trigonometric functions with confidence
- perform calculations involving triangle and circle geometry
- sketch trigonometric, exponential, natural log and polynominal functions;
- understand the connection between derivative and slope and quote the derivatives of basic functions;
- know what is meant by a stationary point and be able to classify the stationary points of simple functions;
- quote the general form of the Maclaurin and Taylor series, and determine the series of simple functions;
- be able to quote the indefinite integrals of basic functions;
- integrate by parts, and use substitutions to evaluate integrals;
- carry out a simple partial fraction expansion of a function and use it to integrate;
-- add, subtract, multiply and divide complex numbers;
- apply De Moivre's theorem;
- add and subtract 2-dimensional and 3-dimensional vectors;
- calculate scalar and vector products;
Syllabus
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 |
| Example Class | 30 | 2.00 | 60.00 |
| Laboratory | 3 | 2.00 | 6.00 |
| Private study hours | 134.00 | ||
| Total Contact hours | 66.00 | ||
| Total hours (100hr per 10 credits) | 200.00 | ||
Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| In-course Assessment | Matlab Test | 10.00 |
| In-course Assessment | 3 x Written Tests | 40.00 |
| Total percentage (Assessment Coursework) | 50.00 | |
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Exams
| Exam type | Exam duration | % of formal assessment |
| Standard exam (closed essays, MCQs etc) | 2 hr 00 mins | 50.00 |
| Total percentage (Assessment Exams) | 50.00 | |
Re-sits for ELEC modules are subject to the rules in the School’s Code of Practice on Assessment. Students should be aware that, for some modules, a re-sit may only be conducted on an internal basis (with tuition) in the next academic session.
Reading list
There is no reading list for this moduleLast updated: 08/05/2017
Browse Other Catalogues
- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue
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