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Partial Differential Equations II: Qualitative Studies of Linear Equations (Applied Mathematical Sciences), by Michael E. Taylor
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This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.
- Sales Rank: #3112540 in Books
- Published on: 1996-06-25
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.25" w x 6.14" l, 2.01 pounds
- Binding: Hardcover
- 556 pages
Review
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
Taylor, Reader in Government, University of Essex.
Most helpful customer reviews
5 of 6 people found the following review helpful.
Modern approach to important topics of mathematical physics.
By Bernardo Vargas
This second volume focuses on several interesting problems arising from mathematical physiscs, making a perfect connection between the purely theoretical digression and the sources from which it originated.
The contents are: Pseudodifferential operators; spectral theory; scattering by obstacles; Dirac operators and index theory; Brownian motion and potential theory; the "D"-bar Neumann problem. Appendix: Connections and curvature.
Useful for mathematics and physics advanced undergraduates, graduate students, and researchers. Plenty of excercises and references.
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