An Introduction to Partial Differential Equations (Texts in Applied Mathematics, 13) (Volume 13)

Michael Renardy, Robert C. Rogers

ISBN 10: 0387979522 / ISBN 13: 9780387979526

Editore: Springer, 1993

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Dati bibliografici

• Titolo: An Introduction to Partial Differential Equations (Texts in Applied Mathematics, 13) (Volume 13)
• Editore: Springer
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 0387979522
• ISBN 13: 9780387979526
• Rilegatura: Hardcover
• Condizione: Good
• Condizione della sovraccoperta: No Jacket

Descrizione articolo

Riassunto

Partial differential equations are fundamental to the modeling of natural phenomena; they arise in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. Unfortunately, in the standard graduate curriculum, the subject of partial differential equations is seldom taught with the same thoroughness as algebra or integration theory. The present book is aimed at rectifying this situation. It is based on a four-semester course taught at Virginia Polytechnic Institute and State University. The goal of this course was to provide the background necessary to initiate work on a PhD thesis in partial differential equations. The level of the book is aimed at beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables, but no knowledge is required of Lebesgue integration theory or functional analysis.

Dalla quarta di copertina

 

Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. Like algebra, topology, and rational mechanics, PDEs are a core area of mathematics.

This book aims to provide the background necessary to initiate work on a Ph.D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in chapter 10, and the necessary tools from functional analysis are developed within the coarse. The book can be used to teach a variety of different courses.

This new edition features new problems throughout, and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added. The material on Sobolev spaces has been rearranged and expanded. A new section on nonlinear variational problems with "Young-measure" solutions appears. The reference section has also been expanded.