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Module MA2327: Ordinary Differential Equations
- Credit weighting (ECTS)
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5 credits
- Semester/term taught
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Hilary term 2016-17
- Contact Hours
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11 weeks, 3 lectures including tutorials per week
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- Lecturer
- Prof Paschalis Karageorgis
- Learning Outcomes
- On successful completion of this module, students will be able to:
- Apply various standard methods (separation of variables, integrating factors, reduction of order, undetermined coefficients) to solve certain types of differential equations (separable, 1st-order linear, linear with constant coefficients;
- Give examples of differential equations for which either existence or uniqueness of solution fails;
- Compute the exponential of a square matrix;
- Apply standard methods (linearization, Lyapunov theorems) to check the stability of critical points for automous systems
- Module Content
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- Terminology (order, scalar vs. system, linear vs. nonlinear, invariant);
- Separable equations, first-order equations, Gronwall inequality;
- Existence and uniqueness of solutions, blow up in finite time;
- First-order linear systems, exponential of a matrix;
- Reduction of order, undetermined coefficients, variation of parameters;
- Autonomous systems, phase portraits, stability, Lyapunov functions.
- Module Prerequisite
- Introduction to Set Theory and General Topology (MA1126)
- Assessment Detail
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This module will be examined in a 2 hour examination in Trinity term. Continuous assessment will contribute 20% to the final grade for the module at the annual
examination session. Supplemental exams if required will consist of 100% exam.