Unit information: Continuum Mathematics in 2020/21

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	EMAT10010 Engineering Mathematics 1, 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 mathematics methods for solving continuum problems in mechanics and other areas of engineering. Students will learn how to derive approximations of continuum physical processes in the form of partial and ordinary differential equations and their solutions. Partial differential equations, complex variables, and asymptotic methods are introduced with application in physical and biological contexts.

Aims: Students will acquire a firm grounding in the mathematical techniques used to analyse models in continuum mechanics, including solution methods for partial differential equations, the geometry and integration of complex functions, and asymptotic and perturbative methods to solve ODEs, PDEs, and integrals, plus wider methods for solving PDEs. 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. The ability to derive approximations and solutions of ODEs, PDEs, and integrals, using asymptotics and perturbative methods.
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. An 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 Information

Teaching will be delivered through a combination of synchronous and asynchronous sessions, including lectures, problem-solving activities supported by weekly workshops and problem sheets.

Assessment Information

1 Summative Assessment, 100% - Summer Timed Assessment. This will assess all ILOs.

Reading and References

• Schaum’s Outline of Complex Variables by Spiegel
• Complex Analysis by Stewart and Tall
• Complex Variables with Applications by Ponnusamy and Silverman
• Perturbative Methods by Hinch
• An Introduction to Phase Integral Methods by Heading
• Advanced Mathematics Methods for Scientists and Engineers, Bender & Orszag