Download or read book Power Geometry in Algebraic and Differential Equations written by A.D. Bruno and published by Elsevier. This book was released on 2000-08-03 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed. The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems. The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.
Download or read book Analytic Algebraic and Geometric Aspects of Differential Equations written by Galina Filipuk and published by Birkhäuser. This book was released on 2017-06-23 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.
Download or read book Introduction to Linear Algebra and Differential Equations written by John W. Dettman and published by Courier Corporation. This book was released on 2012-10-05 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.
Download or read book Linear Differential Equations and Group Theory from Riemann to Poincare written by Jeremy Gray and published by Springer Science & Business Media. This book was released on 2010-01-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
Download or read book Formal and Analytic Solutions of Diff Equations written by Galina Filipuk and published by Springer. This book was released on 2018-09-24 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff. (differential, partial differential, difference, q-difference, q-difference-differential.... ) Equations. They consist of selected contributions from the conference "Formal and Analytic Solutions of Diff. Equations", held at Alcalá de Henares, Spain during September 4-8, 2017. Their topics include summability and asymptotic study of both ordinary and partial differential equations. The volume is divided into four parts. The first paper is a survey of the elements of nonlinear analysis. It describes the algorithms to obtain asymptotic expansion of solutions of nonlinear algebraic, ordinary differential, partial differential equations, and of systems of such equations. Five works on formal and analytic solutions of PDEs are followed by five papers on the study of solutions of ODEs. The proceedings conclude with five works on related topics, generalizations and applications. All contributions have been peer reviewed by anonymous referees chosen among the experts on the subject. The volume will be of interest to graduate students and researchers in theoretical and applied mathematics, physics and engineering seeking an overview of the recent trends in the theory of formal and analytic solutions of functional (differential, partial differential, difference, q-difference, q-difference-differential) equations in the complex domain.
Download or read book Analysis and Applications ISAAC 2001 written by Heinrich G.W. Begehr and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of survey articles gives and idea of new methods and results in real and complex analysis and its applications. Besides several chapters on hyperbolic equations and systems and complex analysis, potential theory, dynamical systems and harmonic analysis are also included. Newly developed subjects from power geometry, homogenization, partial differential equations in graph structures are presented and a decomposition of the Hilbert space and Hamiltonian are given. Audience: Advanced students and scientists interested in new methods and results in analysis and applications.
Download or read book Linear Algebra and Differential Equations written by Alexander Givental and published by American Mathematical Soc.. This book was released on 2001 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material presented in this book corresponds to a semester-long course, ``Linear Algebra and Differential Equations'', taught to sophomore students at UC Berkeley. In contrast with typical undergraduate texts, the book offers a unifying point of view on the subject, namely that linear algebra solves several clearly-posed classification problems about such geometric objects as quadratic forms and linear transformations. This attractive viewpoint on the classical theory agrees well with modern tendencies in advanced mathematics and is shared by many research mathematicians. However, the idea of classification seldom finds its way to basic programs in mathematics, and is usually unfamiliar to undergraduates. To meet the challenge, the book first guides the reader through the entire agenda of linear algebra in the elementary environment of two-dimensional geometry, and prior to spelling out the general idea and employing it in higher dimensions, shows how it works in applications such as linear ODE systems or stability of equilibria. Appropriate as a text for regular junior and honors sophomore level college classes, the book is accessible to high school students familiar with basic calculus, and can also be useful to engineering graduate students.
Download or read book Geometric Numerical Integration written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.
Download or read book Transseries and Real Differential Algebra written by Joris van der Hoeven and published by Springer. This book was released on 2006-10-31 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.
Download or read book Ordinary Differential Equations written by Wolfgang Walter and published by Springer Science & Business Media. This book was released on 2013-03-11 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.
Download or read book Partial Differential Equations and Geometry written by Christopher I. Byrnes and published by Marcel Dekker. This book was released on 1979 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lecture Notes on O Minimal Structures and Real Analytic Geometry written by Chris Miller and published by Springer Science & Business Media. This book was released on 2012-09-14 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations.
Download or read book The Geometric Theory of Ordinary Differential Equations and Algebraic Functions written by Georges Valiron and published by Math Science Press. This book was released on 1984 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Geometry and Its Applications written by John Oprea and published by MAA. This book was released on 2007-09-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.
Download or read book Applying Power Series to Differential Equations written by James Sochacki and published by Springer. This book was released on 2024-03-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed to undergraduate STEM majors and to researchers using ordinary differential equations. It covers a wide range of STEM-oriented differential equation problems that can be solved using computational power series methods. Many examples are illustrated with figures and each chapter ends with discovery/research questions most of which are accessible to undergraduate students, and almost all of which may be extended to graduate level research. Methodologies implemented may also be useful for researchers to solve their differential equations analytically or numerically. The textbook can be used as supplementary for undergraduate coursework, graduate research, and for independent study.
Download or read book Basic Methods Of Soliton Theory written by Ivan V Cherednik and published by World Scientific. This book was released on 1996-08-22 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 25 years of its existence Soliton Theory has drastically expanded our understanding of “integrability” and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local conservation laws, Bäcklund-Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann-Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin-Gordon, and Nonlinear Schrödinger equation.
Download or read book Complex Differential and Difference Equations written by Galina Filipuk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-11-18 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a balanced combination of longer survey articles and shorter, peer-reviewed research-level presentations on the topic of differential and difference equations on the complex domain, this edited volume presents an up-to-date overview of areas such as WKB analysis, summability, resurgence, formal solutions, integrability, and several algebraic aspects of differential and difference equations.
