00000cmm a22000004a 4500 UP-99796217611212477 Buklod 20230215085534.0 m go j cr |n |||auu|a 101109s2011 xxu u eng d 1441970525 (eBook) 9781441970527 (eBook) (iLib)UPD-00215704250 DML eng DMLUC QA 377 T39 2011 pt.IIeb Taylor, Michael Eugene 1946- Partial differential equations II qualitative studies of linear equations [electronic resource] Michael E. Taylor. New York Springer c2011 1 online resource (xxii, 614 p.) Applied mathematical sciences 116 IP-based subscription, access limited to within on campus computer network. Access via Electronic Resources of the UPD University Library Website. 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, centered 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. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. In this second edition, there are seven new sections including Sobolev spaces on rough domains, boundary layer phenomena for the heat equation, the space of pseudodifferential operators of harmonic oscillator type, and an index formula for elliptic systems of such operators. In addition, several other sections have been substantially rewritten, and numerous others polished to reflect insights obtained through the use of these books over time. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: 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) Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Differential equations, Partial. Electronic books. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://link.springer.com/book/10.1007/978-1-4419-7052-7 FO Monograph UPD DMLR Electronic Resource