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 | Department of Engineering Mathematics |

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 in the form of partial and ordinary differential equations, starting from simple constructive assumptions or variational principles. Partial differential equation and complex variable methods 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, 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 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.’

By the end of this unit, students should have:

• 1) An in-depth understanding of mathematics underlying key concepts in physics and mechanics.

• 2) Understand how to derive physical relationships from first principals using multivariable calculus, in particular how to use perturbative analysis to study physical properties such as deformation.

• 3) Be able to derive common partial differential equations, such as heat, wave and Laplace from first principles based on constitutive laws.

• 4) Be able to solve partial differential equations using methods such as characteristics and separation of variables.

• 5) Demonstrate an understand 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

3 hour examination worth 90% (all learning outcome) and a 40 min 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
- 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