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Partial Differential Equations II - Qualitative Studies of Linear Equations (3rd ed. 2023)
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Partial Differential Equations II - Qualitative Studies of Linear Equations (3rd ed. 2023)
Series: Applied Mathematical Sciences, 116
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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, 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. The third edition further expands the material by
incorporating new theorems and applications throughout the book,
and by deepening connections and relating concepts across
chapters. It includes new sections on rigid body motion, on
probabilistic results related to random walks, on aspects of
operator theory related to quantum mechanics, on overdetermined
systems, and on the Euler equation for incompressible
fluids. The appendices have also been updated with
additional results, ranging from weak convergence of measures to
the curvature of Kahler manifolds. 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.” (Peter Lax, SIAM
review, June 1998)
General
Imprint: |
Springer International Publishing AG
|
Country of origin: |
Switzerland |
Series: |
Applied Mathematical Sciences, 116 |
Release date: |
September 2023 |
Firstpublished: |
2023 |
Authors: |
Michael E Taylor
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Dimensions: |
235 x 155mm (L x W) |
Pages: |
691 |
Edition: |
3rd ed. 2023 |
ISBN-13: |
978-3-03-133699-7 |
Categories: |
Books
|
LSN: |
3-03-133699-2 |
Barcode: |
9783031336997 |
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