An introduction to partial differential equations
著者
書誌事項
An introduction to partial differential equations
（Texts in applied mathematics, 13）
Springer-Verlag, c1993
- : us
- : gw
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注記
"May 26, 1992."
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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: us ISBN 9780387979526
内容説明
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.
目次
- Preface
- Introduction
- Characteristics
- Conservation Laws and Shocks
- Maximum Principles
- Distributions
- Function Spaces
- Operator Theory
- Linear Elliptic Equations
- Nonlinear Elliptic Equations
- EnergyMethods for Evolution Problems
- Semigroup Methods
- Index.
- 巻冊次
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: gw ISBN 9783540979524
内容説明
This book is intended for a three or four semester course in "Partial Differential Equations". It is based on a four-semester course taught at Virginia Polytechnic Institute and State University. The goal of this class was to provide the background necessary to initiate work on a PhD thesis in partial differential equations. The book opens with an introduction to the subject matter and its characteristics which contain the Cauchy-Kovalevskaya Theorem and Holmgren's Uniqueness Theorem. Conversation laws and shocks are then covered, followed by maximum principles and function spaces. Linear elliptic equations and nonlinear elliptic equations are also included. The text concludes with energy methods for evolution problems and semigroup methods. In the standard graduate curriculum, the subject of partial differential equations is seldom taught with the same thoroughness as algebra or integration theory. This book is aimed at rectifying the situation, by going further than the competition. There are numerous other textbooks on partial differntial equations, but few are directed at a beginning graduate audience as this one is.
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 Lebesque integration theory or functional analysis. This book should provide a thorough introduction to partial differential equations, bringing the students up to the level at which research can begin.
目次
Preface* Introduction* Characteristics* Conservation Laws and Shocks* Maximum Principles* Distributions* Function Spaces* Operator Theory * Linear Elliptic Equations * Nonlinear Elliptic Equations * Energy Methods for Evolution Problems * Semigroup Methods * Index
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