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 | FURTHER METHODS OF APPLIED MATHEMATICS | ||
Code | MATH323 | ||
Coordinator |
Dr GT Piliposyan Mathematical Sciences G.Piliposyan@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2023-24 | Level 6 FHEQ | First Semester | 15 |
Aims |
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•To give an insight into some specific methods for solving important types of ordinary differential equations. •To provide a basic understanding of the Calculus of Variations and to illustrate the techniques using simple examples in a variety of areas in mathematics and physics. •To build on the students'' existing knowledge of partial differential equations of first and second order. |
Learning Outcomes |
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(LO1) After completing the module students should be able to: - solve simple integral extremal problems including cases with constraints; - classify a system of simultaneous 1st-order linear partial differential equations, and to find the Riemann invariants and general or specific solutions in appropriate cases; - classify 2nd-order linear partial differential equations and, in appropriate cases, find general or specific solutions. |
Syllabus |
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Ordinary differential equations; some methods, including the variation of arbitrary constants, for solving certain types of equations. Introduction to the Calculus of Variations for problems without and with constraints. Simultaneous first-order linear partial differential equations; Riemann invariants. Second-order linear partial differential equations; classification, reduction to standard forms, conformal mappings. Fourier transforms. |
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. |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
MATH102 CALCULUS II; MATH101 Calculus I; MATH103 Introduction to Linear Algebra; MATH221 Differential Equations |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Final Assessment on campus | 100 | 70 | ||||
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Class test | 75 | 30 |