Mathematical Methods and Fluid Mechanics - Block 3

Open University Course Team

ISBN 10: 0749223154 / ISBN 13: 9780749223151

Editore: Open University Worldwide, 1750

The book has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged. Codice articolo GOR004133617

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.

Dati bibliografici

Titolo: Mathematical Methods and Fluid Mechanics - ...
Casa editrice: Open University Worldwide
Data di pubblicazione: 1750
Legatura: Paperback
Condizione: Very Good