# Unit information: Continuum Mathematics in 2018/19

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Unit name Continuum Mathematics EMAT31410 20 H/6 Teaching Block 4 (weeks 1-24) Dr. Mike Jeffrey Not open EMAT10005 Engineering Physics 1, EMAT20010 Engineering Physics 2, EMAT20200 Engineering Mathematics 2 (or equivalent) None Department of Engineering Mathematics 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 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.’

## 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.
• 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

## Assessment Details

3 hour examination worth 90% (all learning outcome) and a 40 min in class test worth 10% (reinforcing basic concepts).