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Ordinary Differential Equations I - MAT4843

Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Purpose: To enable the learner to apply the investigative techniques of the qualitative theory of nonlinear ordinary differential equations. Dynamical systems, modelled in terms of nonlinear differential equations, have many applications in the physical, biological and social sciences. However, it is not in general possible to obtain an analytical solution to an arbitrary differential equation - and even when an analytical solution can be found, it is sometimes very difficult to "see" the main feature of the solution from it. In the qualitative study of differential equations, quite detailed information on the nature of the solution to a differential equation is obtained without constructing an exact solution. Contents: Phase diagrams, periodic solutions, limit cycles, energy balance and harmonic balance, stability, Lyapunov methods.