PDF Ebook Partial Differential Equations: Basic Theory (Texts in Applied Mathematics), by Michael E. Taylor
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Partial Differential Equations: Basic Theory (Texts in Applied Mathematics), by Michael E. Taylor
PDF Ebook Partial Differential Equations: Basic Theory (Texts in Applied Mathematics), by Michael E. Taylor
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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as weIl as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sci� ences (AMS) series, which will focus on advanced textbooks and research level monographs.
- Sales Rank: #2790990 in Books
- Published on: 2008-05-23
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.33" w x 6.10" l, 1.79 pounds
- Binding: Paperback
- 588 pages
Review
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)
From the Back Cover
THIS TEXT PROVIDES AN INTRODUCTION TO THE THEORY OF PARTIAL DIFFERENTIAL EQUATIONS. IT INTRODUCES BASIC EXAMPLES OF PARTIAL DIFFERENTIAL EQUATIONS, ARISING IN CONTINUUM MECHANICS, ELECTROMAGNETISM, COMPLEX ANALYSIS AND OTHER Areas, AND DEVELOPS A NUMBER OF TOOLS FOR THEIR SOLUTION, INCLUDING PARTICULARLY FOURIER ANALYSIS, DISTRIBUTION THEORY, AND Sobolev SPACES.
About the Author
Michael E. Taylor is a Professor at North Carolina University in the Department of Mathematics.
Most helpful customer reviews
31 of 31 people found the following review helpful.
Great PDE book
By Ian Langmore
I like this book. Right from the beginning, Taylor uses concepts from smooth manifold theory to obtain results in a coordinate free fashion (on a Riemannian/Lorenz manifold) when possible. At the same time, he will go to coordinates when necessary, or even revert to R^n when stronger results are possible there. As an added "bonus" the book contains surprisingly few errors, or at least I found less than usual, so maybe I'm getting slow!
I didn't find this to be an introductory (as in first year of grad school) level book. The proofs are often given in less detail than those found in the standard introductory graduate texts. Reading and understanding this text requires knowledge of Real Analysis and smooth manifolds/differential geometry at the introductory graduate level. Fourier transforms and distributions are built up from scratch, but the treatment is quick and probably assumes you have some previous knowledge. Note that my opinion is formed after using this book for self-study, so you can probably relax the prerequisites slightly if this book is used as part of a course.
Another point worth mentioning is that the exercises are often quite easier than verifying the individual proofs in the chapter.
Why not 5 stars? I found the book and chapter introductions to be quite uninspiring and not very useful. He essentially lists off the material that will be covered with no thought to motivation. I like to read something about why one particular approach is necessary or better or just different than another approach. Simply listing off concepts to be covered has little meaning if one has no idea what those concepts mean! The discussion of results is also rather sparse, sort of like Rudin.
16 of 20 people found the following review helpful.
Complete, accurate and well-written.
By Bernardo Vargas
The author accomplished the goal of presenting this broad and many-faceted subject in a thorough and comprehensive manner. Beginning from the fundamentals of ODE theory to the most sophisticated methods for solving important PDE's of mathematical physics, this series of three volumes comprises all what a modern analyst must know about the topic and much more.
The contents of volume 1 are: Basic theory of ODE; Laplace and wave equations; Fourier analysis, distributions, and constant-coefficient linear PDE; Sobolev spaces; linear elliptic equations; linear evolution equations. Appendices: Outline of functional analysis; manifolds, vector bundles, and Lie groups.
Originally intended for graduate students and working mathematicians, most of the material is suitable for advanced undergraduate courses. Includes excercises for each section and extensive references.
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