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Differential equations arise as common models in the physical, mathematical, biological and engineering sciences. This subject covers linear differential equations, both ordinary and partial, using concepts from linear algebra to provide the general structure of solutions for ordinary differential equations and linear systems. The differences between initial value problems and boundary value problems are discussed and eigenvalue problems arising from common classes of partial differential equations are introduced. Laplace transform methods are used to solve dynamical models with discontinuous inputs and the separation of variables method is applied to simple second order partial differential equations. Fourier series are derived and used to represent the solutions of the heat and wave equation and Fourier transforms are introduced. The subject balances basic theory with concrete applications.
Intended learning outcomes
At the completion of this subject, students should be able to
- understand the solution structure of linear ordinary differential equations;
- appreciate how partial differential equations arise in physical applications;
- be able to find exact solutions of simple first and second-order partial differential equations in two variables;
- know how eigenfunction and transform methods arise naturally and can be applied in differential equation problems.
In addition to learning specific skills that will assist students in their future careers in science, engineering, commerce, education or elsewhere, they will have the opportunity to develop generic skills that will assist them in any future career path. These include
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis.
Last updated: 5 June 2022