# MATHEMATICS 2 - 2021/2

Module code: ENG1085

## 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.

### Module provider

Sustainability, Civil & Env Engineering

WALKER Martin (Civl Env Eng)

## Overall student workload

Independent Learning Hours: 85

Seminar Hours: 22

Tutorial Hours: 11

Guided Learning: 10

Captured Content: 22

Semester 2

None

## Module content

Indicative content includes:

• 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.

• 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.

• Partial differential equations  Introduction to PDE's, separation of variables method using trial solution; outline of the full method

• Laplace and Fourier Transforms: concepts, properties and definition, identification of signal frequencies using Fourier transform, Laplace transforms of common functions, inverse Laplace transform and application to ODEs. Applications to engineering problems.

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework COURSEWORK 30
Examination Online ONLINE (OPEN BOOK) EXAM WITHIN 24HR WINDOW 70

N/A

## 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:
(1) Two pieces of coursework covering most of the topics and techniques taught. These will not only cover standard problems but also some aspects of
modelling i.e. mathematically modelling engineering problems. This will constitute 30% of the assessment.
(2) 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. This will constitute 70% of the assessment. Learning outcomes 1-7 70%
Formative assessment and feedback
Formative ‘assessment’ is a regular ongoing process in all semester through work on the tutorial questions. Formative feedback is provided during
the tutorial/problems classes. The "ideal" coursework solutions will also provide formative feedback.

## 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

 Ref Attributes Developed 002 Manipulate matrices in appropriate contexts and use matrix methods to solve sets of linear algebraic equations KC SM2B, SM2M 003 Compute invariant properties such as determinant, trace or principal values KC SM2B, SM2M 004 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 SM2B, SM2M, EA2 005 Solve straightforward ordinary differential equations as encountered in engineering problems KCP SM2B, SM2M 006 Solve typical engineering-related second order partial differential equations KC SM2B, SM2M, EA3B 007 Apply Fourier and Laplace Transforms to engineering problems KCP SM2B, SM2M, EA3B 001 Discuss the role of mathematical modelling and be able to produce and explain simple mathematical models of physical problems. CPT SM2B, SM2M, B

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## 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

• Examination

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.