Download Full eBooks in PDF
Interdisciplinary Mathematics Lie Theoretic Ode Numerical Analysis Mechanics And Differential Systems Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Interdisciplinary Mathematics Lie Theoretic Ode Numerical Analysis Mechanics And Differential Systems book. This book definitely worth reading, it is an incredibly well-written.
Author : Robert Hermann
Publisher : Math-Sci Press
Page : 286 pages
File Size : 55,6 Mb
Release : 1994
Category : Mathematics
ISBN : 0915692457
Author : Robert Hermann
Publisher : Unknown
Page : 312 pages
File Size : 50,8 Mb
Release : 1973
Category : Mathematical physics
ISBN : UOM:39015026883879
Author : Fritz Schwarz
Publisher : CRC Press
Page : 448 pages
File Size : 49,7 Mb
Release : 2007-10-02
Category : Mathematics
ISBN : 1584888903
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble
Author : Robert Mattheij,Jaap Molenaar
Publisher : SIAM
Page : 423 pages
File Size : 49,9 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 0898719178
In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained. Audience: the book is intended for use as a textbook for both undergraduate and graduate courses, and it can also serve as a reference for students and researchers alike.
Author : Victor G. Kac,Peter J. Olver,Pavel Winternitz,Teoman Özer
Publisher : Springer
Page : 199 pages
File Size : 40,7 Mb
Release : 2018-11-04
Category : Mathematics
ISBN : 9783030013769
Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods. The SDEA III, held in honour of the Centenary of Noether’s Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups. This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.
Author : Ernst Hairer,Christian Lubich,Gerhard Wanner
Publisher : Springer Science & Business Media
Page : 660 pages
File Size : 47,7 Mb
Release : 2006-05-18
Category : Mathematics
ISBN : 9783540306665
This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents a theory of symplectic and symmetric methods, which include various specially designed integrators, as well as discusses their construction and practical merits. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.
Author : John Loustau
Publisher : World Scientific Publishing Company
Page : 361 pages
File Size : 49,6 Mb
Release : 2016
Category : Differential equations
ISBN : 9814719498
This text presents numerical differential equations to graduate (doctoral) students. It includes the three standard approaches to numerical PDE, FDM, FEM and CM, and the two most common time stepping techniques, FDM and Runge-Kutta. We present both the numerical technique and the supporting theory. The applied techniques include those that arise in the present literature. The supporting mathematical theory includes the general convergence theory. This material should be readily accessible to students with basic knowledge of mathematical analysis, Lebesgue measure and the basics of Hilbert spaces and Banach spaces. Nevertheless, we have made the book free standing in most respects. Most importantly, the terminology is introduced, explained and developed as needed. The examples presented are taken from multiple vital application areas including finance, aerospace, mathematical biology and fluid mechanics. The text may be used as the basis for several distinct lecture courses or as a reference. For instance, this text will support a general applications course or an FEM course with theory and applications. The presentation of material is empirically-based as more and more is demanded of the reader as we progress through the material. By the end of the text, the level of detail is reminiscent of journal articles. Indeed, it is our intention that this material be used to launch a research career in numerical PDE.
Author : W. Hackbusch
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 43,9 Mb
Release : 1992
Category : Language Arts & Disciplines
ISBN : 354054822X
Derived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR
Author : P. Schiavone,C. Constanda,Andrew Mioduchowski
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201113
This book will appeal to applied mathematicians, mechanical engineers, theoretical physicists, and graduate students researching in the areas of ordinary and partial differential equations, integral equations, numerical analysis, mechanics of solids, fluid mechanics and mathematical physics.
Author : Raffaele D'Ambrosio
Publisher : Springer Nature
Page : 391 pages
File Size : 41,7 Mb
Release : 2023-09-26
Category : Mathematics
ISBN : 9783031313431
This book is focused on the numerical discretization of ordinary differential equations (ODEs), under several perspectives. The attention is first conveyed to providing accurate numerical solutions of deterministic problems. Then, the presentation moves to a more modern vision of numerical approximation, oriented to reproducing qualitative properties of the continuous problem along the discretized dynamics over long times. The book finally performs some steps in the direction of stochastic differential equations (SDEs), with the intention of offering useful tools to generalize the techniques introduced for the numerical approximation of ODEs to the stochastic case, as well as of presenting numerical issues natively introduced for SDEs. The book is the result of an intense teaching experience as well as of the research carried out in the last decade by the author. It is both intended for students and instructors: for the students, this book is comprehensive and rather self-contained; for the instructors, there is material for one or more monographic courses on ODEs and related topics. In this respect, the book can be followed in its designed path and includes motivational aspects, historical background, examples and a software programs, implemented in Matlab, that can be useful for the laboratory part of a course on numerical ODEs/SDEs. The book also contains the portraits of several pioneers in the numerical discretization of differential problems, useful to provide a framework to understand their contributes in the presented fields. Last, but not least, rigor joins readability in the book.
Author : Anonim
Publisher : Unknown
Page : 1320 pages
File Size : 47,6 Mb
Release : 1995
Category : Mathematics
ISBN : UVA:X002518821
Author : Jan Bouwe van den Berg,Jean-Philippe Lessard
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 44,9 Mb
Release : 2018-07-12
Category : Nonlinear mechanics
ISBN : 9781470428143
This volume is based on lectures delivered at the 2016 AMS Short Course “Rigorous Numerics in Dynamics”, held January 4–5, 2016, in Seattle, Washington. Nonlinear dynamics shapes the world around us, from the harmonious movements of celestial bodies, via the swirling motions in fluid flows, to the complicated biochemistry in the living cell. Mathematically these phenomena are modeled by nonlinear dynamical systems, in the form of ODEs, PDEs and delay equations. The presence of nonlinearities complicates the analysis, and the difficulties are even greater for PDEs and delay equations, which are naturally defined on infinite dimensional function spaces. With the availability of powerful computers and sophisticated software, numerical simulations have quickly become the primary tool to study the models. However, while the pace of progress increases, one may ask: just how reliable are our computations? Even for finite dimensional ODEs, this question naturally arises if the system under study is chaotic, as small differences in initial conditions (such as those due to rounding errors in numerical computations) yield wildly diverging outcomes. These issues have motivated the development of the field of rigorous numerics in dynamics, which draws inspiration from ideas in scientific computing, numerical analysis and approximation theory. The articles included in this volume present novel techniques for the rigorous study of the dynamics of maps via the Conley-index theory; periodic orbits of delay differential equations via continuation methods; invariant manifolds and connecting orbits; the dynamics of models with unknown nonlinearities; and bifurcations diagrams.
Author : M. Ainsworth
Publisher : Unknown
Page : 360 pages
File Size : 47,7 Mb
Release : 1995
Category : Mathematics
ISBN : UOM:39015041019475
This book draws together information previously available only in hard-to-find journals to introduce the most recent research in six key areas of numerical analysis: guaranteed error bounds for ordinary differential equations; computational methods for differential equations; numerical solution of differential-algebraic equations; boundary element methods; perturbation theory for infinite dimensional dynamical systems; and delay differential equations. Excellent up-to-date bibliographies are included, but the essential material is expertly presented to avoid lengthy searches. The research assumes a relatively low level of prerequisite knowledge, making it an important tool for graduate students and researchers in computational mathematics and in applications areas in physics and engineering.
Author : D.M. Klimov
Publisher : CRC Press
Page : 240 pages
File Size : 53,7 Mb
Release : 2014-04-21
Category : Mathematics
ISBN : 9781482265224
Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. For the first time, this book gives the systematic group analysis of main postulates of classical and relativistic mechanics. The consistent presentation of Lie group theory is illustrated by plentiful examples. Symmetries and conservat
Author : Eduard Feireisl,Trygve G. Karper,Milan Pokorný
Publisher : Birkhäuser
Page : 186 pages
File Size : 54,6 Mb
Release : 2016-11-25
Category : Mathematics
ISBN : 9783319448350
This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematics. It will help graduate students and researchers to not only better understand problems in mathematical compressible fluid mechanics but also to learn something from the field of mathematical and numerical analysis and to see the connections between the two worlds. Potential readers should possess a good command of the basic tools of functional analysis and partial differential equations including the function spaces of Sobolev type.