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Unit information: Engineering Mathematics 3 in 2020/21

Please note: you are viewing unit and programme information for a past academic year. Please see the current academic year for up to date information.

Unit name Engineering Mathematics 3
Unit code EMATM0035
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Mike Jeffrey
Open unit status Not open
Pre-requisites

EMAT10005 Engineering Physics 1, EMAT20010 Engineering Physics 2, 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 topics in Engineering Mechanics, along with the mathematical methods required to solve them. Students will learn how to derive models of continuum physical processes starting from simple constructive assumptions or variational principles. Asymptotics and complex variable methods for solving integrals and trascendental equations are also introduced with application in physical and biological contexts.

Aims: Students will acquire a solid background in continuum mechanics, particularly how mathematical models of continuum physical processes can be derived from first principles. The course provides a firm grounding in the mathematical techniques used to analyse such models, including the geometry and integration of complex functions and asymptotic analysis. 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. An in-depth understanding of mathematics underlying key concepts in physics and mechanics of materials, including analysis and classification of stresses in beams, nonlinear behaviour of loaded materials, vibrations and three-dimensional bodies.

2. An in-depth understanding of basic tensor calculus and its use for representing physics of deformable bodies in three dimensions.

3. An in-depth understanding of the basic properties of functions of a complex variable, the properties of analytic and harmonic functions, and more advanced topics including contour integration and residue theorems, with application to inversion of Laplace transforms, and the basic idea of a conformal mapping.

Teaching details

24 hours of lectures

6 hours of tutorials

70 hours of guided Independent study, including assessment.

Assessment Details

The assessment consists of 2 hour examination worth 90% (all learning outcomes) and a 1 hour in class test worth 10% (reinforcing basic concepts).

Reading and References

Bedford, A., Engineering Mechanics: Statics & Dynamics

Meriam, J. L., Kraige, L. G. Engineering Mechanics Vol 1, Statics, Vol 2, Dynamics

Gere, J. M., Mechanics of Materials

Bourne, D. E. & Kendall, P. C., Vector Analysis & Cartesian Tensors (chs. 8 & 9), Chapman & Hall

Priestley, H. A., Introduction to Complex Analysis, Oxford.

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