Geometry in Partial Differential Equations
Title | Geometry in Partial Differential Equations PDF eBook |
Author | Agostino Prastaro |
Publisher | World Scientific |
Pages | 482 |
Release | 1994 |
Genre | Mathematics |
ISBN | 9789810214074 |
This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.
Partial Differential Equations arising from Physics and Geometry
Title | Partial Differential Equations arising from Physics and Geometry PDF eBook |
Author | Mohamed Ben Ayed |
Publisher | Cambridge University Press |
Pages | 471 |
Release | 2019-05-02 |
Genre | Mathematics |
ISBN | 1108431631 |
Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.
Geometry In Partial Differential Equations
Title | Geometry In Partial Differential Equations PDF eBook |
Author | Themistocles M Rassias |
Publisher | World Scientific |
Pages | 480 |
Release | 1994-01-17 |
Genre | Mathematics |
ISBN | 9814504130 |
This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.
Differential Geometry: Partial Differential Equations on Manifolds
Title | Differential Geometry: Partial Differential Equations on Manifolds PDF eBook |
Author | Robert Everist Greene |
Publisher | American Mathematical Soc. |
Pages | 585 |
Release | 1993 |
Genre | Mathematics |
ISBN | 082181494X |
The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem
Geometric Analysis and Nonlinear Partial Differential Equations
Title | Geometric Analysis and Nonlinear Partial Differential Equations PDF eBook |
Author | Stefan Hildebrandt |
Publisher | Springer Science & Business Media |
Pages | 663 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642556272 |
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.
Nonlinear partial differential equations in differential geometry
Title | Nonlinear partial differential equations in differential geometry PDF eBook |
Author | Robert Hardt |
Publisher | American Mathematical Soc. |
Pages | 356 |
Release | 1996 |
Genre | Mathematics |
ISBN | 9780821804315 |
This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.
Geometry of PDEs and Mechanics
Title | Geometry of PDEs and Mechanics PDF eBook |
Author | Agostino Prastaro |
Publisher | World Scientific |
Pages | 764 |
Release | 1996 |
Genre | Science |
ISBN | 9789810225209 |
This volume presents the theory of partial differential equations (PDEs) from a modern geometric point of view so that PDEs can be characterized by using either technique of differential geometry or algebraic geometry. This allows us to recognize the richness of the structure of PDEs. It presents, for the first time, a geometric theory of non-commutative (quantum) PDEs and gives a general application of this theory to quantum field theory and quantum supergravity.