MATHEMATICS 2 - 2017/8

Module code: ENG1085

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 2

Overall student workload

Independent Study Hours: 95

Lecture Hours: 44

Tutorial Hours: 11

Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION (2 HOURS) 60
School-timetabled exam/test MID-TERM TEST (1 HOUR) 20
Coursework COURSEWORK 20

Alternative Assessment


Prerequisites / Co-requisites

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

Module overview

Engineers frequently use mathematical models, and in particular differential equations in one or more variables and matrices are common in this context. This is a further first level engineering mathematics module designed to support teaching in other engineering science modules by introducing students to concepts and solution methods in these areas. Statistics and probability also play a significant role in the assessment of real-life engineering problems, and an introduction to key concepts in this area is also included.

Module aims

Further understanding and knowledge of mathematical and statistical concepts and techniques

Skills in the selection and implementation of mathematical techniques to engineering problems

An appreciation of the importance of mathematical modelling of physical problems and the interpretation of mathematical results

Learning outcomes

Attributes Developed
Select and apply appropriate techniques of differential and integral calculus to engineering problems KC
Solve straightforward ordinary differential equations as encountered in engineering problems KCP
Discuss the role of mathematical modelling and be able to produce and explain simple mathematical models of physical problems. CPT
Solve typical engineering-related second order partial differential equations KC
Manipulate matrices in appropriate contexts and use matrix methods to solve sets of linear algebraic equations KC
Determine matrix eigenvalues and eigenvectors, use to solve engineering systems modelled by differential equations and relate the results to characteristics of the physical system KCP
Present and summarise simple statistical data graphically and numerically KCPT
Recognise appropriate probability distributions and use them to calculate probabilities and apply to e.g. simple ideas of quality control KCP

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Module content

Indicative content includes:

Functions of several variables: Partial derivatives for functions of several variables, total derivative, application to small changes in a function and errors. Extrema of functions of two variables. Simple double integrals.
Ordinary differential equations: First order, first degree ODE's of separable type and the integrating factor method. Second order ODE's with constant coefficients (complementary solution and particular integrals). Initial and boundary value problems.
Matrices, determinants, eigenvalues: Matrix addition, multiplication, etc., determinants, Cramer's rule. Matrix operations involving transpose, inverse, rank of matrix. Solving systems of equations using matrices, esp. Gaussian elimination. Eigenvalues and eigenvectors; applications to systems of linear differential equations and normal modes.
Partial differential equations  Introduction to PDE's, separation of variables method using trial solution; outline of full method
Probability and Statistics: Descriptive statistics: numerical (mean, mode, median, variance  etc) and graphical summaries.  Basic Probability: elementary laws, random variables, mean and variance. Probability distributions: Discrete probability distributions (binomial, Poisson); continuous probability distributions (normal). Application to e.g. quality control.

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, in which students themselves are engaged in both lectures and, more  extensively, in tutorials/problems classes.

The learning and teaching methods include:

Lectures (4 hrs/wk, for 11 weeks) to introduce new concepts and techniques and provide illustrative examples and applications; students are engaged with performance of examples, questioning on concept and observations.
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 and also elements of modelling and interpretation of physical problems

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate their ability to recognise problem types, select appropriate solution methods and carry out various solution techniques.

Thus, the summative assessment for this module consists of:

Pieces coursework covering the full breadth of topics and techniques taught , with examples, to not only cover ‘standard’ problems but also some modelling.

Learning outcomes 1-6           20%

Mid-term test covering the topics and techniques taught in the first half of the semester.

Learning outcomes 1,5,6         20%

One two-hour examination with problems on topics from across the whole syllabus but inevitably in the time not covering every technique/concept and with some weighting on those areas from later in the module

Learning outcomes 1,2 ,4-8       60%       

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, via uploaded feedback videos and through the issue using the VLE of selected samples of fully worked solutions to tutorial problems.

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 2 :

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Liberal Arts and Sciences BA (Hons)/BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Civil Engineering MEng 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Chemical and Petroleum Engineering BEng (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Chemical and Petroleum Engineering MEng 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Chemical Engineering BEng (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Chemical Engineering MEng 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Civil Engineering BEng (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module

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.