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for a past academic year. Please see the current academic year for up to date information.
| Unit name |
Continuum Mathematics |
| Unit code |
EMAT31410 |
| Credit points |
20 |
| Level of study |
H/6
|
| Teaching block(s) |
Teaching Block 4 (weeks 1-24)
|
| 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)
|
| Co-requisites |
None
|
| School/department |
School of Engineering Mathematics and Technology |
| Faculty |
Faculty of Engineering |
Description including Unit Aims
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 in the form of partial and ordinary differential equations, starting from simple constructive assumptions or variational principles. Tensor calculus and complex variable methods are also introduced with application in various physical 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, which prepares them to handle much more challenging engineering problems. The rest of the course provides a firm grounding in the mathematical techniques used to analyse such models, including tensor calculus, solution methods for partial differential equations, and the geometry and integration of complex functions. 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:
- 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.
- Understand basic tensor calculus and its use for representing physics of deformable bodies in three dimensions.
- Understand how to derive common partial differential equations, such as heat, wave and Laplace from first principles based on constitutive laws.
- Understand how to solve partial differential equations using methods such as characteristics and separation of variables.
- Understand 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 Information
Lectures
Assessment Information
3-hour written examination: 100% (all learning outcomes)
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
- Goodbody, A. M. Cartesian Tensors with Applications to Mechanics, Fluid Mechanics and Elasticity (1982) Ellis Horwood
- Ockendon, J., Howison, S., Lacey, A., Movchan, A., Applied partial differential equations, Oxford
- Priestley, H. A., Introduction to Complex Analysis, Oxford.
- Kreyszig, E., Advanced Engineering Mathematics, John Wiley & Son
