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Inhaltsangabe
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.
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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.
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Mathematical Methods and Fluid Mechanics - Block 3
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Paperback. Zustand: Used; Good. Dispatched, from the UK, within 48 hours of ordering. This book is in good condition but will show signs of previous ownership. Please expect some creasing to the spine and/or minor damage to the cover. Bestandsnummer des Verkäufers CHL2821560
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Mathematical Methods and Fluid Mechanics - Block 3
Verlag:
Open University Worldwide, United Kingdom, Milton Keynes, 2009
ISBN 10: 0749223154
ISBN 13: 9780749223151
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Mathematical Methods and Fluid Mechanics: Block 3: Block 3
Verlag:
Open University Worldwide 0, 1750
ISBN 10: 0749223154
ISBN 13: 9780749223151
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paperback
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paperback. Zustand: Good. Good. book. Bestandsnummer des Verkäufers ERICA82907492231543
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