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Faculty Handbook Archive

# Archive Module Description

## Department: Mathematical Sciences

### MATH4381: Topics in Applied Mathematics IV

Type Level Credits Availability Module Cap Location Open 4 20 Available in 2021/22 None. Durham

#### Prerequisites

• Analysis in Many Variables II (MATH2031), Fuid Dynamcis III (MATH3101)

• None

• 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 studentsâ€™ 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/Hours 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: 90%
Element Length / duration Element Weighting Resit Opportunity
End of year written examination 3 hours 100% none
Component: Continuous Assessment Component Weighting: 10%
Element Length / duration Element Weighting Resit Opportunity
Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students. 100%

#### Formative Assessment:

â–  Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University