Analytic Methods for Partial Differential Equations

G. Evans

ISBN 10: 3540761241 / ISBN 13: 9783540761242

Verlag: Springer London, Springer Berlin Heidelberg Nov 1999, 1999

Beschreibung

Neuware -The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. J ames Clerk Maxwell, for example, put electricity and magnetism into a unified theory by estab lishing Maxwell's equations for electromagnetic theory, which gave solutions for problems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechankal processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier-Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forcasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 316 pp. Englisch.

Bestandsnummer des Verkäufers 9783540761242

Bibliografische Details

• Titel: Analytic Methods for Partial Differential Equations
• Verlag: Springer London, Springer Berlin Heidelberg Nov 1999
• Erscheinungsjahr: 1999
• Sprache: Englisch
• ISBN-10: 3540761241
• ISBN-13: 9783540761242
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 178 H x 18 T Millimeter Breite: 235 mm, Höhe: 178 mm, Tiefe: 18 mm
• Gewicht: 553 Gramm

Über diesen Titel

Inhaltsangabe

This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.