Vladimir E. Nazaikinskii - Böcker

The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories. While there has recently been much progress in the field, many of these results have remained scattered in journals and preprints.Starting from an elementary level and finishing with the most recent results, this book gives a systematic exposition of both analytical and topological aspects of elliptic theory on manifolds with singularities. The presentation includes a review of the main techniques of the theory of elliptic equations, offers a comparative analysis of various approaches to differential equations on manifolds with singularities, and devotes considerable attention to applications of the theory. These include Sobolev problems, theorems of Atiyah-Bott-Lefschetz type, and proofs of index formulas for elliptic operators and problems on manifolds with singularities, including the authors' new solution to the index problem for manifolds with nonisolated singularities.A glossary, numerous illustrations, and many examples help readers master the subject. Clear exposition, up-to-date coverage, and accessibility-even at the advanced undergraduate level-lay the groundwork for continuing studies and further advances in the field.

This volume presents a systematic and mathematically rigorous exposition of methods for studying linear partial differential equations. It focuses on quantization of the corresponding objects (states, observables and canonical transformations) in the phase space. The quantization of all three types of classical objects is carried out in a unified way with the use of a special integral transform. This book covers recent as well as established results, treated within the framework of a universal approach. It also includes applications and provides a useful reference text for graduate and research-level readers.

Characteristic Features• Includes nearly 4,000 linear partial differential equations (PDEs) with solutions• Presents solutions to numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences, electrical engineering, and other fields• Outlines basic analytical methods for solving various problems in science and engineering• Contains many more linear PDEs, problems, solutions, and transformations than any other book currently available• Provides a database of test problems for numerical and approximate analytical methods for solving linear PDEs and systems of coupled PDEs.New to the Third Edition• Chapter on linear ODEs and PDEs with delays• Chapter on linear ODEs and PDEs with fractional derivatives• Some individual PDEs, solutions, transformations, formulas, and problems• Two sections on special functions used to solve linear ODEs and PDEs with delay or fractional derivatives.To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, and they outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity.

Includes nearly 4,000 linear partial differential equations (PDEs) with solutionsPresents solutions of numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences, electrical engineering, and other fieldsOutlines basic methods for solving various problems in science and engineeringContains much more linear equations, problems, and solutions than any other book currently availableProvides a database of test problems for numerical and approximate analytical methods for solving linear PDEs and systems of coupled PDEsNew to the Second Edition More than 700 pages with 1,500+ new first-, second-, third-, fourth-, and higher-order linear equations with solutionsSystems of coupled PDEs with solutionsSome analytical methods, including decomposition methods and their applicationsSymbolic and numerical methods for solving linear PDEs with Maple, Mathematica, and MATLAB® Many new problems, illustrative examples, tables, and figuresTo accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity.

The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories. While there has recently been much progress in the field, many of these results have remained scattered in journals and preprints.Starting from an elementary level and finishing with the most recent results, this book gives a systematic exposition of both analytical and topological aspects of elliptic theory on manifolds with singularities. The presentation includes a review of the main techniques of the theory of elliptic equations, offers a comparative analysis of various approaches to differential equations on manifolds with singularities, and devotes considerable attention to applications of the theory. These include Sobolev problems, theorems of Atiyah-Bott-Lefschetz type, and proofs of index formulas for elliptic operators and problems on manifolds with singularities, including the authors' new solution to the index problem for manifolds with nonisolated singularities.A glossary, numerous illustrations, and many examples help readers master the subject. Clear exposition, up-to-date coverage, and accessibility-even at the advanced undergraduate level-lay the groundwork for continuing studies and further advances in the field.

This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries.

This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries.

No detailed description available for "Contact Geometry and Linear Differential Equations".