[PDF] Ordinary Differential Equations And Their Solutions eBook

Author : George Moseley Murphy
Publisher : Courier Corporation
Page : 466 pages
File Size : 32,5 MB
Release : 2011-01-01
Category : Mathematics
ISBN : 0486485919

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This treatment presents most of the methods for solving ordinary differential equations and systematic arrangements of more than 2,000 equations and their solutions. The material is organized so that standard equations can be easily found. Plus, the substantial number and variety of equations promises an exact equation or a sufficiently similar one. 1960 edition.

Author : Andrei D. Polyanin
Publisher : CRC Press
Page : 1584 pages
File Size : 14,69 MB
Release : 2017-11-15
Category : Mathematics
ISBN : 1351643916

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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.

Author : CK-12 Foundation
Publisher : CK-12 Foundation
Page : 603 pages
File Size : 39,88 MB
Release : 2010-08-15
Category : Mathematics
ISBN : 1935983016

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CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.

Author : L.F. Shampine
Publisher : Routledge
Page : 632 pages
File Size : 15,38 MB
Release : 2018-10-24
Category : Mathematics
ISBN : 1351427555

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This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.

Author : Morris Tenenbaum
Publisher : Courier Corporation
Page : 852 pages
File Size : 49,3 MB
Release : 1985-10-01
Category : Mathematics
ISBN : 0486649407

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Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

Author : Andrei D. Polyanin
Publisher : CRC Press
Page : 728 pages
File Size : 15,83 MB
Release : 1995-05-09
Category : Mathematics
ISBN :

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The Handbook of Exact Solutions for Ordinary Differential Equations contains a collection of more than 5,000 ordinary differential equations and their solutions. Coverage in this volume includes equations that are of interest to researchers but difficult to integrate (Abel equations, Emden-Fowler equations, Painleve equations, etc.), and equations relevant to applications in heat and mass transfer, nonlinear mechanics, hydrodynamics, nonlinear oscillations, combustion, chemical engineering, and other related fields.

Author : Xiaoying Han
Publisher : Springer
Page : 252 pages
File Size : 27,99 MB
Release : 2017-10-25
Category : Mathematics
ISBN : 981106265X

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This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and represent the starting point for the systematic derivation of consistent higher order numerical schemes for RODEs. The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology. A basic knowledge of ordinary differential equations and numerical analysis is required.

Author : Valentin F. Zaitsev
Publisher : CRC Press
Page : 815 pages
File Size : 26,10 MB
Release : 2002-10-28
Category : Mathematics
ISBN : 1420035339

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Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo

Author : James C. Robinson
Publisher : Cambridge University Press
Page : 416 pages
File Size : 48,27 MB
Release : 2004-01-08
Category : Mathematics
ISBN : 1139450026

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This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.