MATHEMATICS 1 - 2017/8

Module code: ENG1084

Module provider

Civil and Environmental Engineering

Module Leader


Number of Credits


ECT Credits



FHEQ Level 4

JACs code


Module cap (Maximum number of students)


Module Availability

Semester 1

Overall student workload

Lecture Hours: 44

Tutorial Hours: 11

Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION 70%
School-timetabled exam/test IN SEMESTER TEST 20%
Coursework COURSEWORK 10%

Alternative Assessment


Prerequisites / Co-requisites

Normal entry requirements for the degree programmes in Civil Engineering or Chemical and Process Engineering.

Module overview

A first level engineering mathematics module designed to briefly revise and then extend A-Level maths material and introduce more mathematical techniques to support engineering science modules.

Module aims

Consolidate and extend students' knowledge of basic mathematical concepts and techniques relevant to the solution of engineering problems

Make students aware of possible pitfalls

Enable students to select appropriate methods of solution

Enable students to apply their mathematical knowledge and skills to engineering problems

Learning outcomes

Attributes Developed
Use of vector algebra and applications of this to mechanics
Manipulation of standard functions
Use of complex numbers
Use of the techniques of differential and integral calculus for functions of one variable
Application of differentiation and  integration to determine physical engineering properties e.g. in mechanics
Manipulation of simple series and their use in e.g. approximations

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Module content

Indicative content includes:

Vectors:  Vectors as quantities with magnitude and direction, graphical representation, addition and subtraction. Unit vectors; algebraic representation of vectors; addition subtraction, multiplication by constant; scalar (dot) product, projection, resolution into components; cross (vector) product. Vectors in plane polar coordinates.

Functions:  Concept of a function; domain, range. Odd, even and periodic functions. Inverse functions. Exponential and logarithmic functions and their properties, inverse trigonometric functions, hyperbolic functions and their inverses, solution of trigonometric and hyperbolic equations.

Complex numbers: Real and imaginary parts, polar form, Argand diagram, exp(jx), De Moivre’s theorem and applications.

Differentiation: Concept of derivative and rules of differentiation for a function of one variable. Applications to gradients, tangents and normals, extreme points and curve sketching.

Series and Limits: Arithmetic and geometric progressions, Maclaurin and Taylor series, use of series in approximations, Newton Raphson method, various techniques for the evaluation of limits.

Integration: Concept of indefinite integration as the inverse of differentiation and standard methods for integration such as substitution, integration by parts and integration of rational functions. Definite integration, area under curves, use of recurrence relationships. Applications of integration to curve lengths, surfaces and volumes of revolution, first moments and centroids, second moments and radii of gyration.

Methods of Teaching / Learning

The learning and teaching strategy is designed to familiarise students with mathematical concepts and techniques, supported by extensive use of examples and applications; students themselves are engaged in the solution of problems and application of techniques in tutorials/problems classes.

The learning and teaching methods include:

Lectures (4 hrs/wk, for 11 weeks) to revise underpinning prior learning and bring students from varying background to a common level of knowledge, and to introduce new concepts and techniques and provide illustrative examples and applications.
Recommended wider reading of matching sections of relevant recommended texts.
Problem sheets of examples for technique selection and skill development.
Tutorials/problems classes (1 hr/wk for 11 weeks) with staff and PG assistance for the development of skills in technique application and also in selection of appropriate techniques, using the above problems sheets; assistance is given both at individual level, and for the group on common areas of difficulty
Coursework (summative but also formative) to assess technique selection and skill development


Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate their knowledge of mathematical concepts and rules, and to show their skills in solving mathematical and engineering problems using appropriately selected techniques. The coursework will have two elements. One of these will be a timed class test, covering simpler material and with shorter questions where the final answer is the critical factor; this test may be computer based. The other element will be a coursework assignment with longer, more complex questions where the method as well as a final answer is important.

 Thus, the summative assessment for this module consists of:

Examination  [Learning outcomes 1-6]  2 hrs  70%

In semester test [Learning outcomes 1,2,3,4] 20%

Coursework assignment [Learning outcomes 4,5,6] 10%  

Formative assessment and feedback

Formative ‘assessment’ is a regular ongoing process all semester through work on the tutorial questions. Formative feedback is provided orally on a one-to-one basis and to the whole group in tutorial/problems classes, and through the issue using the VLE of fully worked solutions to tutorial problems some time after the class.

The summative assessment is also formative, with individual comments on performance being returned along with scripts and also with overview comments posted on the VLE.



Reading list

Reading list for MATHEMATICS 1 :

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.