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On successful completion of the module, students should be able to:
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Solve linear inhomogeneous ordinary differential equations, involving elementary and special functions, with initial conditions or boundary conditions
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Recognise and use the basic theory of linear, ordinary differential equations (Sturm-Liouville theory, orthogonal function expansions)
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Solve partial differential equations using separation of variables (with specific applications to the wave equation, the heat equation and Laplace's equation)
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Recognise solutions of the three-dimensional Laplace operator in terms of spherical harmonic functions
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Apply the principles of complex analysis to integrate complex functions using the calculus of residues to compute definite integrals
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Manipulate integral transforms and evaluate Fourier transforms
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