| 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 |
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 | School of Engineering Mathematics and Technology |
| Faculty | Faculty of Engineering |
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.
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.
Lectures
The assessment consists of 2 hour examination worth 90% (all learning outcomes) and a 1 hour in class test worth 10% (reinforcing basic concepts).
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.
