Cohomological Analysis of Partial Differential Equations and Secondary Calculus

Cohomological Analysis of Partial Differential Equations and Secondary Calculus
Author :
Publisher : American Mathematical Soc.
Total Pages : 268
Release :
ISBN-10 : 0821897993
ISBN-13 : 9780821897997
Rating : 4/5 (93 Downloads)

Book Synopsis Cohomological Analysis of Partial Differential Equations and Secondary Calculus by : A. M. Vinogradov

Download or read book Cohomological Analysis of Partial Differential Equations and Secondary Calculus written by A. M. Vinogradov and published by American Mathematical Soc.. This book was released on 2001-10-16 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations. This theory grew up from the classical geometry of PDE's originated by S. Lie and his followers by incorporating some nonclassical ideas from the theory of integrable systems, the formal theory of PDE's in its modern cohomological form given by D. Spencer and H. Goldschmidt and differential calculus over commutative algebras (Primary Calculus). The main result of this synthesis is Secondary Calculus on diffieties, new geometrical objects which are analogs of algebraic varieties in the context of (nonlinear) PDE's. Secondary Calculus surprisingly reveals a deep cohomological nature of the general theory of PDE's and indicates new directions of its further progress. Recent developments in quantum field theory showed Secondary Calculus to be its natural language, promising a nonperturbative formulation of the theory. In addition to PDE's themselves, the author describes existing and potential applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants, theory of geometric structures, variational calculus, control theory, etc. This book, focused mainly on theoretical aspects, forms a natural dipole with Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, Volume 182 in this same series, Translations of Mathematical Monographs, and shows the theory "in action".


Cohomological Analysis of Partial Differential Equations and Secondary Calculus Related Books

Cohomological Analysis of Partial Differential Equations and Secondary Calculus
Language: en
Pages: 268
Authors: A. M. Vinogradov
Categories: Mathematics
Type: BOOK - Published: 2001-10-16 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations. This the
Translations of Mathematical Monographs
Language: en
Pages: 247
Authors:
Categories: Differential equations, Nonlinear
Type: BOOK - Published: 1962 - Publisher:

DOWNLOAD EBOOK

Kikagakuteki Henbun Mondai
Language: en
Pages: 236
Authors: Seiki Nishikawa
Categories: Mathematics
Type: BOOK - Published: 2002 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

A minimal length curve joining two points in a surface is called a geodesic. One may trace the origin of the problem of finding geodesics back to the birth of c
An Introduction to Morse Theory
Language: en
Pages: 244
Authors: Yukio Matsumoto
Categories: Mathematics
Type: BOOK - Published: 2002 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

Finite-dimensional Morse theory is easier to present fundamental ideas than in infinite-dimensional Morse theory, which is theoretically more involved. However,
Advances in Moduli Theory
Language: en
Pages: 328
Authors: Kenji Ueno
Categories: Mathematics
Type: BOOK - Published: 2002 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

The word ``moduli'' in the sense of this book first appeared in the epoch-making paper of B. Riemann, Theorie der Abel'schen Funktionen, published in 1857. Riem