MA30062: Analysis of nonlinear ordinary differential equations
[Page last updated: 15 October 2020]
Academic Year:  2020/1 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Honours (FHEQ level 6) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must take MA20218 AND take MA20220 
Description:  Aims: To provide an accessible but rigorous treatment of initialvalue problems for nonlinear systems of ordinary differential equations, including existence and uniqueness of maximal solutions and Lyapunov stability theory, illustrated by examples. Foundations will be laid for advanced studies in dynamical systems, mechanics and control. The material is also useful in mathematical biology and numerical analysis. Learning Outcomes: After taking this unit, students should be able to: * Demonstrate understanding of and prove basic results in the theory of ordinary differential equations including: existence and uniqueness for the initialvalue problem, basic properties of flows and limit sets, Lyapunov's stability theorem and LaSalle's invariance principle. * Apply the theory to analyse the behaviour of simple examples. Skills: Numeracy T/F, A Problem Solving T/F, A Written Communication F (on problem sheets) Content: General definition of an ODE. Examples from diverse areas. Elementary methods: separation of variables, variation of constant, estimates using Gronwall's lemma. Existence and uniqueness for maximal solutions for ODEs with sufficiently regular coefficients (via contraction mapping theorem), continuous dependence on initial conditions. Autonomous ODEs: introduction to local and global flows, orbits, limit sets, integral invariance principle, stability, Lyapunov functions, Lyapunov stability theorem, LaSalle's invariance principle, application to examples. 
Programme availability: 
MA30062 is Optional on the following programmes:Department of Mathematical Sciences

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