Partial Differential Equations II: Qualitative Studies of Linear Equations

by Michael E. Taylor

Overview

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.

Product Details

ISBN-13:	9781441970527
Publisher:	Springer-Verlag New York, LLC
Publication date:	11/02/2010
Series:	Applied Mathematical Sciences , #116
Sold by:	Barnes & Noble
Format:	eBook
Pages:	614
File size:	15 MB
Note:	This product may take a few minutes to download.

About the Author

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

Table of Contents

Preface.- 7 Pseudodifferential Operators.- 8 Spectral Theory.- 9 Scattering by Obstacles.- 10 Dirac Operators and Index Theory.- 11 Brownian Motion and Potential Theory.- 12 The ∂-Neumann Problem.- C Connections and Curvature.- Index.

Editorial Reviews

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 Publisher