Engineering Mathematics 2

Module summary

Module code: MATH1145
Level: 5
Credits: 15
School: Engineering and Science
Department: Engineering
Module Coordinator(s): Robert Jenner

Specification

Pre and co requisites

None.

Aims

The intention of this module is to build upon the fundamentals of engineering mathematics and equip students with the knowledge and skill to be able to analyse a variety of engineering systems by the use of numerical and computer modelling techniques. Whilst following this module, students will acquire the confidence to be able to select appropriate modelling techniques and apply them to realistic engineering problems selected from a range of engineering disciplines. Students will also acquire experience in the use of mathematical simulators such as MATLAB® to create accurate and reliable computer models of engineering systems for analysis purposes. The module is designed to enhance self-study and team working skills by the use of numerical and computer modelling projects.

Learning outcomes

On successful completion of this module a student will be able to:

1 Demonstrate an understanding of various mathematical modelling techniques and theory and how they relate to the solution of a range of engineering problems.

2 Use knowledge gained to analyse case studies involving the application of systems modelling techniques and implement said systems using leading mathematical software such as MATLAB® .

3 Undertake detailed system analysis and verification by the use of mathematical techniques and computer simulations.


Indicative content

Simultaneous and differential equations, Cramer’s rule, mesh analysis, nodal analysis, modelling of dynamic components, partial differential equations, review of Laplace transforms, analysis of, transfer functions, block diagrams, pole-zeros and the s-plane, stability analysis, computation of frequency and transient response of systems. Fourier transforms, discrete Fourier transforms, fast Fourier transforms, introduction to spectral analysis of deterministic systems, frequency response & Bode plots. Numerical solution of state equations, Eigenvalues and Eigenvectors, stability of systems using state variable concepts, qualitative behaviour of non-linear systems. Numerical solution of ordinary differential equations, finite difference methods of solving differential equations. Difference equations, the Z-Transform, frequency and transient response of sampled systems, polynomial modelling of digital signals. Review of probability, distribution and density functions, Gaussian random variables, reliability of systems, scheduling (First-In First-Out, Last-In Last-Out, processor sharing, Shortest-Job First), queuing networks, heavy traffic/diffusion approximations. Iterative methods for nonlinear equations, discussion of errors (including rounding errors), polynomial interpolation and orthogonal polynomials. Continuous random variables, limit theorems, multivariate normal distribution, transition matrices, one-dimensional random walks and absorption probabilities. Industrial applications of numerical and computer modelling and associated financial and efficiency implications.

Teaching and learning activity

Learning and teaching will be via lectures and tutorials which will be supported by computer laboratories. The module is comprised of two parts. In term 1, the students will typically engage with a weekly common lecture (1hr) followed by a subject specific tutorial (2hr) concerning numerical modelling. In term 2, the students will engage in a subject specific computer modelling challenge which will involve a weekly computer laboratory (2hr) and a challenge instruction session (1hr). The computer modelling challenge will form the coursework element of the module and will require the application of the core knowledge delivered in term 1. Typical computer modelling challenges could include transient and frequency response of dynamic systems, state variable analysis of systems, or 2D & 3D finite element modelling of systems. Both parts of the module will be supported by detailed self-study materials which will be available online.

This course aims to meet the engineering benchmarking standards in the following areas:

Partial CEng:
Underpinning Science and Mathematics, and Associated Disciplines: US1, US2
Engineering Analysis: EA1, EA2, EA3, EA4
Engineering Practice: P1, P2, P3

Greenwich Graduate Attributes
Scholarship & Autonomy
SA1 Have an informed understanding of their discipline or professional practice, and the ability to question its principles, practices and boundaries
SA2 Think independently, analytically and creatively, and engage imaginatively with new areas of investigation
SA3 Appreciate disciplines and forms of professional practice beyond their own and draw connections between them
SA4 Are intellectually curious, responsive to challenges, and demonstrate initiative and resilience
Creativity & Enterprise
CE1 Recognise and create opportunities, and respond effectively to unfamiliar or unprecedented situations or problems
CE2 Generate new ideas and develop creative solutions or syntheses
CE3 Communicate clearly and effectively, in a range of forms, taking account of different audiences
CE4 Make use of familiar and emerging information & communication technologies
CE5 Seize and shape the opportunities open to them on leaving university
Cross‐cultural & International Awareness
CCI1 Engage effectively in groups whose members are from diverse backgrounds
CCI2 Appreciate the importance of behaving sustainably
CCI3 Move fluently between different cultural,social and political contexts
CCI4 Value the ability to communicate in more than one language

Module Activities & Greenwich Graduate Activities
Module Activity Greenwich Graduate Attribute
Numerical modelling SA1-4, CE1-2, CCI1
Computer modelling SA1-4, CE1-2, CCI1
Research & data handling SA1-4, CE1, CE4
Teamwork CE1-3, CCI1, CCI3
Reporting CE3-4, CCI1, CCI3-4
Modelling Project Design SA1-4, CE1-2, CCI1




Assessment

Examination - 60%
LO - 1,3.
Pass mark - 40%
End of year 2hr closed book examination.

Report - 40%
LO - 1,2,3.
Pass mark - 40%
7 pages.
Computer Challenge.
Group report (2pgs).
Individual report (5pgs).

In order to meet professional body requirements, students are expected to pass this course at 40% overall and with a minimum of 30% for each component.

Students are required to pass all components in order to pass the course.

Nature of FORMATIVE assessment supporting student learning:
Online quizzes and examination practice tests held throughout the module, mock exam.