Overview
This topic includes: First and second order differential equations in the phase plane. Linear approximations at equilibrium points. Index of a point; limit cycles; averaging, regular and singular perturbation methods. Stability and Liapunov's method. Bifurcation. Basic ideas of calculus of variations. The Euler-Lagrange equations; eigenvalue problems. Applications to second and … For more content click the Read More button below.
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Tuition pattern
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Aims
This topic aims to provide the ability to formulate, analyse and solve problems from applied mathematics, with a focus on techniques for solving ordinary differential equations. In particular, this will involve evaluating alternative techniques and defending the selection of one for a given problem.
Learning outcomes
On completion of this topic you will be expected to be able to:
1.
Evaluate key techniques for solving or approximating the solution to a given ordinary differential equation
2.
Justify the derivation and use of techniques to solve or approximate solutions to ordinary differential equations
3.
Construct mathematical model of physical phenomena with justification
4.
Draw conclusions about physical phenomena by analysing a mathematical model
Assessments
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Requisites information
Anti-requisites:
Assumed knowledge
Linear algebra, ordinary differential equations and multivariable calculus as introduced in NEW Linear Algebra and Differential Equations GE and NEW Multivariable Calculus GE.