Arithmetic Differential Equations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Arithmetic Differential Equations PDF full book. Access full book title Arithmetic Differential Equations by Alexandru Buium. Download full books in PDF and EPUB format.
Author: Alexandru Buium
Publisher: American Mathematical Soc.
ISBN: 0821838628
Category : Mathematics
Languages : en
Pages : 346
Get Book Here
Book Description
For most of the book the only prerequisites are the basic facts of algebraic geometry and number theory."--BOOK JACKET.
Author: Alexandru Buium
Publisher: American Mathematical Soc.
ISBN: 0821838628
Category : Mathematics
Languages : en
Pages : 346
Get Book Here
Book Description
For most of the book the only prerequisites are the basic facts of algebraic geometry and number theory."--BOOK JACKET.
Author: R.-P. Holzapfel
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 192
Get Book Here
Book Description
Author: Alexandru Buium
Publisher: American Mathematical Society
ISBN: 1470475774
Category : Mathematics
Languages : en
Pages : 357
Get Book Here
Book Description
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Author: Dana Schlomiuk
Publisher: American Mathematical Soc.
ISBN: 0821828053
Category : Mathematics
Languages : en
Pages : 194
Get Book Here
Book Description
This book focuses on finiteness conjectures and results in ordinary differential equations (ODEs) and Diophantine geometry. During the past twenty-five years, much progress has been achieved on finiteness conjectures, which are the offspring of the second part of Hilbert's 16th problem. Even in its simplest case, this is one of the very few problems on Hilbert's list which remains unsolved. These results are about existence and estimation of finite bounds for the number of limit cycles occurring in certain families of ODEs. The book describes this progress, the methods used (bifurcation theory, asymptotic expansions, methods of differential algebra, or geometry) and the specific results obtained. The finiteness conjectures on limit cycles are part of a larger picture that also includes finiteness problems in other areas of mathematics, in particular those in Diophantine geometry where remarkable results were proved during the same period of time. There is a chapter devoted to finiteness results in D The volume can be used as an independent study text for advanced undergraduates and graduate students studying ODEs or applications of differential algebra to differential equations and Diophantine geometry. It is also is a good entry point for researchers interested these areas, in particular, in limit cycles of ODEs, and in finiteness problems. Contributors to the volume include Andrey Bolibrukh and Alexandru Buium. Available from the AMS by A. Buium is Arithmetic Differential Equations, as Volume 118 in the Mathematical Surveys and Monographs series.
Author: Rolf-Peter Holzapfel
Publisher:
ISBN: 9783817112814
Category : Differential equations, Partial
Languages : en
Pages : 184
Get Book Here
Book Description
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
ISBN: 1461208513
Category : Mathematics
Languages : en
Pages : 482
Get Book Here
Book Description
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
Author: B L J Braaksma
Publisher: World Scientific
ISBN: 9814487430
Category : Mathematics
Languages : en
Pages : 343
Get Book Here
Book Description
This volume is the record of a workshop on differential equations and the Stokes phenomenon, held in May 2001 at the University of Groningen. It contains expanded versions of most of the lectures given at the workshop. To a large extent, both the workshop and the book may be regarded as a sequel to a conference held in Groningen in 1995 which resulted in the book The Stokes Phenomenon and Hilbert's 16th Problem (B L J Braaksma, G K Immink and M van der Put, editors), also published by World Scientific (1996).Both books offer a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations. Apart from the asymptotics of solutions, Painlevé properties and the algebraic theory, new topics addressed in the second book include arithmetic theory of linear equations, and Galois theory and Lie symmetries of nonlinear differential equations.
Author: Steven G. Krantz
Publisher: CRC Press
ISBN: 1498735029
Category : Mathematics
Languages : en
Pages : 481
Get Book Here
Book Description
Differential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge techniques for a contemporary, undergraduate-level, one- or two-semester course on ordinary differential equations. Authored by a widely respected researcher and teacher, the text covers standard topics such as partial diff
Author: James M. Hill
Publisher: CRC Press
ISBN: 9780849344428
Category : Mathematics
Languages : en
Pages : 232
Get Book Here
Book Description
Differential Equations and Group Methods for Scientists and Engineers presents a basic introduction to the technically complex area of invariant one-parameter Lie group methods and their use in solving differential equations. The book features discussions on ordinary differential equations (first, second, and higher order) in addition to partial differential equations (linear and nonlinear). Each chapter contains worked examples with several problems at the end; answers to these problems and hints on how to solve them are found at the back of the book. Students and professionals in mathematics, science, and engineering will find this book indispensable for developing a fundamental understanding of how to use invariant one-parameter group methods to solve differential equations.
Author: Michio Kuga
Publisher: Springer Science & Business Media
ISBN: 1461203295
Category : Mathematics
Languages : en
Pages : 147
Get Book Here
Book Description
First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience---an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world. English reading students now have the opportunity to enjoy this lively presentation, from elementary ideas to cartoons to funny examples, and to follow the mind of an imaginative and creative mathematician into a world of enduring mathematical creations.
