Analytic Theory Of Differential Equations

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Lectures On Analytic Differential Equations

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Author : I︠U︡. S. Ilʹi︠a︡shenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Lectures On Analytic Differential Equations written by I︠U︡. S. Ilʹi︠a︡shenko 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 2008 with Mathematics categories.

The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the mor The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. on several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.

Analytic Theory Of Differential Equations

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Author : P. F. Hsieh
language : en
Publisher:
Release Date : 2014-01-15

Analytic Theory Of Differential Equations written by P. F. Hsieh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Analytic Theory Of Differential Equations

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Author : P. F. Hsieh
language : en
Publisher: Springer
Release Date : 2006-11-15

Analytic Theory Of Differential Equations written by P. F. Hsieh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Theory Of Stochastic Differential Equations With Jumps And Applications

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Author : Rong SITU
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-06

Theory Of Stochastic Differential Equations With Jumps And Applications written by Rong SITU 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 2006-05-06 with Technology & Engineering categories.

Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.

Analysis And Differential Equations

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Author : Odile Pons
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-01-19

Analysis And Differential Equations written by Odile Pons and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-19 with Mathematics categories.

This book presents advanced methods of integral calculus and the classical theory of the ordinary and partial differential equations. It provides explicit solutions of linear and nonlinear differential equations and implicit solutions with discrete approximations. Differential equations that could not be explicitly solved are discussed with special functions such as Bessel functions. New functions are defined from differential equations. Laguerre, Hermite and Legendre orthonormal polynomials as well as several extensions are also considered.It is illustrated by examples and graphs of functions, with each chapter containing exercises solved in the last chapter.

Ordinary Differential Equations

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Author : Hartmut Logemann
language : en
Publisher: Springer
Release Date : 2014-07-08

Ordinary Differential Equations written by Hartmut Logemann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Mathematics categories.

The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature. The following topics are particularly emphasised: • existence, uniqueness and continuation of solutions, • continuous dependence on initial data, • flows, • qualitative behaviour of solutions, • limit sets, • stability theory, • invariance principles, • introductory control theory, • feedback and stabilization. The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability. Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.

Methods For Constructing Exact Solutions Of Partial Differential Equations

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Author : Sergey V. Meleshko
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-18

Methods For Constructing Exact Solutions Of Partial Differential Equations written by Sergey V. Meleshko 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 2006-06-18 with Technology & Engineering categories.

Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

Galois Theory Of Linear Differential Equations

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Author : Marius van der Put
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-21

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 2003-01-21 with Mathematics categories.

From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews

Analytic Methods For Partial Differential Equations

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Author : G. Evans
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Analytic Methods For Partial Differential Equations written by G. Evans 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.

The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. J ames Clerk Maxwell, for example, put electricity and magnetism into a unified theory by estab lishing Maxwell's equations for electromagnetic theory, which gave solutions for problems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechankal processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier-Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forcasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.

Special Functions And Analysis Of Differential Equations

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Author : Praveen Agarwal
language : en
Publisher: CRC Press
Release Date : 2020-09-08

Special Functions And Analysis Of Differential Equations written by Praveen Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-08 with Mathematics categories.

Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.