Michael E. Taylor

Partial Differential Equations I

Basic Theory

• Broschiertes Buch

Produktbeschreibung

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.

Produktdetails

• Applied Mathematical Sciences 115
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4614-2726-1
• 2. Aufl.
• Seitenzahl: 676
• Erscheinungstermin: 25. Dezember 2012
• Englisch
• Abmessung: 235mm x 155mm x 37mm
• Gewicht: 1010g
• ISBN-13: 9781461427261
• ISBN-10: 1461427266
• Artikelnr.: 36858579

Autorenporträt

Michael E. Taylor is a Professor at North Carolina University in the Department of Mathematics.

Inhaltsangabe

Contents of Volumes II and III.- Preface.- 1 Basic Theory of ODE and Vector Fields.- 2 The Laplace Equation and Wave Equation.- 3 Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE.- 4 Sobolev Spaces.- 5 Linear Elliptic Equation.- 6 Linear Evolution Equations.- A Outline of Functional Analysis.- B Manifolds, Vector Bundles, and Lie Groups.- Index.

Rezensionen

From the reviews:

"These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted." (SIAM Review, June 1998)

From the reviews of the second edition:

"This substantial three-volume work is an upgraded version of the comprehensive qualitative analysis of partial differential equations presented in the earlier edition. ... Graduate students ... will find these three volumes to be not just a fine and rigorous treatment of the subject, but also a source of inspiration to apply their knowledge and ability to the solution of other challenging problems in the field of partial differential equations. ... an excellent text for all devotees of the charming and thought-provoking byways of higher mathematics." (Christian Constanda, The Mathematical Association of America, June, 2011)