Module Details |
| The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module. |
| Title | LINEAR DIFFERENTIAL OPERATORS IN MATHEMATICAL PHYSICS | ||
| Code | MATH421 | ||
| Coordinator |
Dr I Thompson Mathematical Sciences Ian.Thompson@liverpool.ac.uk |
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| Year | CATS Level | Semester | CATS Value |
| Session 2015-16 | Level 7 FHEQ | First Semester | 15 |
Aims |
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This module provides a comprehensive introduction to the theory of partial differential equations, and it provides illustrative applications and practical examples in the theory of elliptic boundary value problems, wave propagation and diffusion problems. |
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Learning Outcomes |
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This module will enable students to understand and actively use the basic concepts of mathematical physics, such as generalised functions, weak solutions and Green''s functions, and apply powerful mathematical methods to problems of electromagnetism, elasticity, heat conduction and wave propagation. |
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Syllabus |
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| 1 |
1 • Generalised derivatives. Definition and simple properties of generalised derivatives. Limits and generalised derivatives. • Laplace''s equation and harmonic functions. Dirichlet and Neumann boundary value problems. Elements of the potential theory. • Fundamental solutions of differential equations. Singular solutions of Laplace''s equation, the wave equation, the Helmholtz equation and the heat equation. • Green''s functions and Poisson''s formulae. • Spectral analysis for the Dirichlet and Neumann problems for finite domains. • The heat conduction equation. Maximum principle. Uniqueness theorem. • The wave equation. Wave propagation and the characteristic cone. • Cauchy problems for the wave equation and the heat conduction equation. |
Teaching and Learning Strategies |
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Lecture - |
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Teaching Schedule |
| Lectures | Seminars | Tutorials | Lab Practicals | Fieldwork Placement | Other | TOTAL | |
| Study Hours |
36 |
36 | |||||
| Timetable (if known) | |||||||
| Private Study | 114 | ||||||
| TOTAL HOURS | 150 | ||||||
Assessment |
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| EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
| Written Exam | 2.5 hours | First Semester | 90 | Standard University Policy | Assessment 2 Notes (applying to all assessments) Homeworks Full marks will be awarded for complete answers to FIVE questions. Only the best 5 answers will be taken into account. | |
| CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
| Coursework | First | 10 | Standard university policy | Assessment 1 | ||
Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. Explanation of Reading List: |
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