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MATH4381: Topics in Applied Mathematics IV

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Type	Open
Level	4
Credits	20
Availability	Not available in 2024/2025
Module Cap	None.
Location	Durham
Department	Mathematical Sciences

Prerequisites

Analysis in Many Variables II (MATH2031), Fluid Mechanics III (MATH3101)

Corequisites

None

Excluded Combinations of Modules

None

Aims

To introduce some important ideas in modern applied mathematics.
To develop an understanding of two particular models: MHD and non-linear elasticity.
To prepare students for future research in Applied Mathematics.

Content

Equations of magnetohydrodynamics (MHD), and their ideal and diffusive limits.
MHD equilibria: potential, force-free and magnetohydrostatic solutions.
Alfven waves.
Introduction to dynamo theory.
Stress and strain tensors and the governing equations of non-linear elasticity.
Energy formulations.
Equilibrium solutions such as the expanding balloon.
Bistability explored further through strips.
Collapsing spheres and cavitation.

Learning Outcomes

Subject-specific Knowledge:

By the end of the module students will:
be able to solve novel and/or complex problems in Applied Mathematics.
have a systematic and coherent understanding of the mathematical formulation behind the MHD and nonlinear elasticity models.
have acquired a coherent body of knowledge of MHD and nonlinear elasticity through study of fundamental behaviour of the models as well as specific examples.

Subject-specific Skills:

Students will develop specialised mathematical skills in mathematical modelling which can be used with minimum guidance.
They will be able to formulate applied mathematical models for various situations.

Key Skills:

Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
Formatively assessed assignments provide practice in the application of logic and a high level of rigour as well as feedback for the students and the lecturer on the students progress.
The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total
Lectures	42	2 per week in Michealmas and Epiphany; 2 in Easter	1 Hour	42
Problems Classes	8	Fortnightly in Michaelmas and Epiphany	1 Hour	8
Preparation and Reading				150
Total				200

Summative Assessment

Component: Examination		Component Weighting: 100%
Element	Length / Duration	Element Weighting	Resit Opportunity
End of year written examination	3 hours	100

Formative Assessment

More information

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