Lectures on linear partial differential equations

By:

Eskin, G

Publication details: American Mathematical Society, 2011 Providence:Description: xvii, 410p. ; hb 26 cmISBN:

9780821852842

Subject(s):

DDC classification:

515.3533 ESK

Summary: This book is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces with many examples and applications to equations with constant coefficients. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory. The book also covers microlocal analysis, including the theory of pseudo-differential and Fourier integral operators, and the propagation of singularities for operators of the real principal type. Among the more advanced topics are the global theory of Fourier integral operators and the geometric optics construction in the large, the Atiyah-Singer index theorem in Rn, and the oblique derivative problem.

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	515.3533 ESK (Browse shelf(Opens below))	1	Available		030979

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Previous	515.353 VAS Partial differential equations: an accessible route through theory and applications	515.353 WLO Partial differential equations	515.3533 CAO Singularly perturbed methods for nonlinear elliptic problems	515.3533 ESK Lectures on linear partial differential equations	515.3534 FRI Partial differential equations of parabolic type	515.3535 DES Numerical methods for Eulerian and Lagrangian conservation laws	515.355 HAL Oscillations in nonlinear systems	Next

Includes bibliography

This book is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form.
The first three chapters are on elementary distribution theory and Sobolev spaces with many examples and applications to equations with constant coefficients. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory. The book also covers microlocal analysis, including the theory of pseudo-differential and Fourier integral operators, and the propagation of singularities for operators of the real principal type. Among the more advanced topics are the global theory of Fourier integral operators and the geometric optics construction in the large, the Atiyah-Singer index theorem in Rn, and the oblique derivative problem.

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