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Unit information: Continuum Mathematics in 2023/24

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
Units you must take before you take this one (pre-requisite units)

EMAT10010 Engineering Mathematics 1, EMAT20200 Engineering Mathematics 2 (or equivalent)

Units you must take alongside this one (co-requisite units)

None

Units you may not take alongside this one
School/department School of Engineering Mathematics and Technology
Faculty Faculty of Engineering

Unit Information

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.

Your learning on this unit

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.

How you will learn

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

How you will be assessed

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

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. EMAT31410).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the University Workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

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