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Unit information: Engineering Mathematics III in 2020/21

Unit name Engineering Mathematics III
Unit code EMAT30012
Credit points 10
Level of study H/6
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Mike Jeffrey
Open unit status Not open
Pre-requisites

EMAT10010 Engineering Mathematics 1, EMAT20200 Engineering Mathematics 2 (or equivalent background for all three units and understanding of the relevant topics).

Co-requisites

None.

School/department Department of Engineering Mathematics
Faculty Faculty of Engineering

Description

Description: This unit focuses on advanced mathematics methods for solving continuum problems in mechanics and other areas of engineering. Students will learn how to derive approximations of continuum physical processes in the form of partial and ordinary differential equations and their solutions. Partial differential equations, complex variables, and asymptotic methods are introduced with application in physical and biological contexts.

Aims: Students will acquire a firm grounding in the mathematical techniques used to analyse models in continuum mechanics, including solution methods for partial differential equations, the geometry and integration of complex functions, and asymptotic and perturbative methods to solve ODEs, PDEs, and integrals. The course aims to give an appreciation of how mathematical analysis provides a solid grounding for physical intuition.

Intended learning outcomes

By the end of this unit, students should have:
1. The ability to derive approximations and solutions of ODEs, PDEs, and integrals, using asymptotics and perturbative methods.
2. The ability to use the properties of functions of a complex variable (such as analyticity, conformality), to perform mappings, to solve contour integrals using residue theorems, with application to real integrals and inversion of Laplace and Fourier transforms.

Teaching details

Teaching will be delivered through a combination of synchronous and asynchronous sessions, including lectures, problem-solving activities supported by weekly workshops and problem sheets.

Assessment Details

1 Summative Assessment, 100% - January Timed Assessment. This will assess all ILOs.

Reading and References

  • Schaum’s Outline of Complex Variables by Spiegel
  • Complex Analysis by Stewart and Tall
  • Complex Variables with Applications by Ponnusamy and Silverman
  • Perturbative Methods by Hinch
  • An Introduction to Phase Integral Methods by Heading
  • Advanced Mathematics Methods for Scientists and Engineergs, Bender & Orszag

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