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Semester 1

Honours Differential Equations (MATH10066)







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Visiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling.

Course Summary

Core course for Honours Degrees involving Mathematics.This is a second course on differential equations discussing higher order linear equations, Laplace transforms, systems of First Order Linear ODEs, non-linear systems of ODEs, Fourier Series, use of separation of variables in standard PDEs and Sturm-Liouville Theory. In the skills section of the course, we will work on symbolic manipulation, computer algebra, graphics and a final project. Platform: Python in computer labs.

Course Description

Syllabus : Systems of First Order Linear ODEs with constant coefficients using linear andmatrix algebra methods.Numerical methods: Euler, Heun, RK Nonlinear systems of ODEs: critical points, linear approximation around a critical point; introduction to nonlinear methods: Lyapunov functions. Fourier seriesPDEs by separation of variablesSturm-Liouville theoryLaplace transformSkills : Python brush up: functions, plotting.Systems of 1st order ODEs: plotting phase portraits, using SciPy ODE solvers.Nonlinear systems: exploring dynamical systems (limit cycles, chaos in the Lorenz model, in the periodically perturbed pendulum...) using SciPy ODEsolvers.Numerical methods for ODEs: implementing Euler, Heun, etc.Fourier: comparison function/truncated series, perhaps computation of Fourier coefficients.PDEs: plots of 2D functions, animations.

Assessment Information

Written Exam 70%, Coursework 30%, Practical Exam 0%

Additional Assessment Information

Coursework 30%, Examination 70%

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