Mathematical Methods and Fluid Mechanics: Block 3: Block 3

Open University Course Team

ISBN 10: 0749223154 / ISBN 13: 9780749223151

Editore: Open University Worldwide 0, 1750

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• Titolo: Mathematical Methods and Fluid Mechanics: Block 3: Block 3
• Editore: Open University Worldwide 0
• Data di pubblicazione: 1750
• Lingua: Inglese
• ISBN 10: 0749223154
• ISBN 13: 9780749223151
• Rilegatura: paperback
• Condizione: Good
• Tipo di libro: book

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Riassunto

Block 3 contains units 9 - 11 which look at a class of differential equations typified by the wave equation, the diffusion equation and Laplace's equation, which arise frequently in fluid mechanics and in other branches of applied mathematics. Unit 9 - Second-order partial differential equations shows how a second-order partial differential equation can be classified as one of three standard types, and how to reduce an equation to its standard form. Some general solutions (including d Alembert's solution to the wave equation) are found. Unit 10 - Fourier series reviews and develops an important method of approximating a function. The early sections refer to trigonometric Fourier series, and it is shown how these series, together with separation of variables, can be used to represent the solutions of initial-boundary value problems involving the diffusion equation and the wave equation. Later sections generalise to the Fourier series that arise from Sturm-Liouville problems (eigenvalue problems with the differential equation put into a certain standard format), including Legendre series. Unit 11 - Laplace's equation is a particular second-order partial differential equation that can be used to model the flow of an irrotational, inviscid fluid past a rigid boundary. Solutions to Laplace s equation are found and interpreted in the context of fluid flow problems, for example, the flow of a fluid past a cylinder and past a sphere.