Arithmetic Differential Equations

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Arithmetic Differential Equations

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Author : Alexandru Buium
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Arithmetic Differential Equations written by Alexandru Buium and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

For most of the book the only prerequisites are the basic facts of algebraic geometry and number theory."--BOOK JACKET.

Introduction To Numerical Methods In Differential Equations

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Author : Mark H. Holmes
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-05

Introduction To Numerical Methods In Differential Equations written by Mark H. Holmes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-05 with Mathematics categories.

The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, let’s start with the expression “di?erential equations.” These are essential in science and engineering, because the laws of nature t- ically result in equations relating spatial and temporal changes in one or more variables.Todevelopanunderstandingofwhatisinvolvedin?ndingsolutions, the book begins with problems involving derivatives for only one independent variable, and these give rise to ordinary di?erential equations. Speci?cally, the ?rst chapter considers initial value problems (time derivatives), and the second concentrates on boundary value problems (space derivatives). In the succeeding four chapters problems involving both time and space derivatives, partial di?erential equations, are investigated. This brings us to the next expression in the title: “numerical methods.” This is a book about how to transform differential equations into problems that can be solved using a computer.The fact is that computers are only able to solve discrete problems and generally do this using ?nite-precision arithmetic. What this means is that in deriving and then using a numerical algorithmthecorrectnessofthediscreteapproximationmustbeconsidered,as must the consequences of round-o? error in using ?oating-point arithmetic to calculatetheanswer.Oneoftheinterestingaspectsofthesubjectisthatwhat appears to be an obviously correct numerical method can result in complete failure. Consequently, although the book concentrates on the derivation and use of numerical methods, the theoretical underpinnings are also presented andusedinthedevelopment.

Differential Equations

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Author : Steven G. Krantz
language : en
Publisher:
Release Date : 2024-10-14

Differential Equations written by Steven G. Krantz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-14 with Mathematics categories.

This book delivers a stimulating exposition of modeling and computing, preparing students for higher-level mathematical and analytical thinking. Designed for an undergraduate-level course on ordinary differential equations, the text presents classical ideas and cutting-edge techniques in dynamical systems and other areas, highlighting applicatio

Foundations Of Arithmetic Differential Geometry

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Author : Alexandru Buium
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-20

Foundations Of Arithmetic Differential Geometry written by Alexandru Buium and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-20 with Mathematics categories.

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.

Galois Theory Of Linear Differential Equations

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Author : Marius van der Put
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Galois Theory Of Linear Differential Equations written by Marius van der Put and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Linear differential equations form the central topic of this volume, Galois theory being the unifying theme. A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used. This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students.

Ordinary And Partial Differential Equations

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Author : Victor Henner
language : en
Publisher: CRC Press
Release Date : 2013-01-29

Ordinary And Partial Differential Equations written by Victor Henner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-29 with Mathematics categories.

Covers ODEs and PDEs—in One Textbook Until now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn’t exist. Fulfilling this need, Ordinary and Partial Differential Equations provides a complete and accessible course on ODEs and PDEs using many examples and exercises as well as intuitive, easy-to-use software. Teaches the Key Topics in Differential Equations The text includes all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations. It also discusses other optional but important topics such as integral equations, Fourier series, and special functions. Numerous carefully chosen examples offer practical guidance on the concepts and techniques. Guides Students through the Problem-Solving Process Requiring no user programming, the accompanying computer software allows students to fully investigate problems, thus enabling a deeper study into the role of boundary and initial conditions, the dependence of the solution on the parameters, the accuracy of the solution, the speed of a series convergence, and related questions. The ODE module compares students’ analytical solutions to the results of computations while the PDE module demonstrates the sequence of all necessary analytical solution steps.

Handbook Of Ordinary Differential Equations

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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2017-11-15

Handbook Of Ordinary Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-15 with Mathematics categories.

The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.

Green S Functions And Linear Differential Equations

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Author : Prem K. Kythe
language : en
Publisher: CRC Press
Release Date : 2011-01-21

Green S Functions And Linear Differential Equations written by Prem K. Kythe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-21 with Mathematics categories.

Green's Functions and Linear Differential Equations: Theory, Applications, and Computation presents a variety of methods to solve linear ordinary differential equations (ODEs) and partial differential equations (PDEs). The text provides a sufficient theoretical basis to understand Green's function method, which is used to solve initial and boundary

Geometry And Arithmetic Around Euler Partial Differential Equations

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Author : R.-P. Holzapfel
language : en
Publisher: Springer
Release Date : 1986-08-31

Geometry And Arithmetic Around Euler Partial Differential Equations written by R.-P. Holzapfel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-08-31 with Mathematics categories.

Numerical Methods For Elliptic And Parabolic Partial Differential Equations

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Author : Peter Knabner
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-26

Numerical Methods For Elliptic And Parabolic Partial Differential Equations written by Peter Knabner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with Mathematics categories.

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.