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Module MAU23205: Ordinary Differential Equations
 Credit weighting (ECTS)
 5 credits
 Semester/term taught
 Hilary term 201920
 Contact Hours
 11 weeks, 3 lectures including tutorials per week
 Lecturer
 Dr. Gurpreet Singh
 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, 1storder 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

 Terminology (order, scalar vs. system, linear vs. nonlinear, invariant);
 Separable equations, firstorder equations, Gronwall inequality;
 Existence and uniqueness of solutions, blow up in finite time;
 Firstorder linear systems, exponential of a matrix;
 Reduction of order, undetermined coefficients, variation of parameters;
 Autonomous systems, phase portraits, stability, Lyapunov functions.
 Module Prerequisite
 MAU11100, MAU11204
 Assessment Detail
 This module will be examined in a 2 hour examination in Michaelmas term. Continuous assessment will contribute 20% to the final grade with the exam counting for the remaining 80%. Supplementals if required will consist of 100% exam.