Registry
Module Specifications
Archived Version 2021 - 2022
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Description The purpose of this module is to equip students with the knowledge and skills relevant to elementary ordinary differential equations. This will involve dealing with the theory of such equations, as well as learning methods of solution for the most important classes of these equations. The importance of using rigorous mathematical arguments in this analysis will be emphasised. Students will attend workshop style lectures in which they reconstruct the main results and methods of the topic through guided enquiry. They will also attend review lectures and tutorials that recap on previously encountered material. They will undertake exercises and problems to be presented for assessment. | |||||||||||||||||||||||||||||||||||||
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Learning Outcomes 1. Classify ordinary differential equations; 2. Synthesise different mathematical techniques to determine quantitative and qualitative information about those equations and their solutions; 3. Construct mathematical models using differential equations and study those models and their applications; 4. Apply rigorous mathematical analysis to the study of the theory of ordinary differential equations. | |||||||||||||||||||||||||||||||||||||
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml |
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Indicative Content and
Learning Activities IntroductionDefinitions and classification. Solutions of differential equations. Applications of ordinary differential equations.First Order EquationsInitial value problems. Geometric interpretation and direction fields. The existence and uniqueness theorem. Linear, separable, homogeneous and exact equations.Modelling with First Order EquationsRadioactive decay. Newton s law of cooling. Modelling populations: exponential and logistic growth; logistic growth with harvesting. Mixing problems.Second Order Linear EquationsHomogeneous equations with constant coefficients. Non-homogeneous equations; method of undetermined coefficients, variation of parameters. Fundamental solutions and Wronskians; Abel s theorem.Linear SystemsHomogeneous linear systems solved by finding eigenvalues and eigenvectors (or generalised eigenvectors), simple inhomogeneous systems | |||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||
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