Handbook Of Exact Solutions To Mathematical Equations PDF Download
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Author | : Valentin F. Zaitsev |
Publisher | : CRC Press |
Total Pages | : 815 |
Release | : 2002-10-28 |
Genre | : Mathematics |
ISBN | : 1420035339 |
Download Handbook of Exact Solutions for Ordinary Differential Equations Book in PDF, ePub and Kindle
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 | : A. D. Polianin |
Publisher | : |
Total Pages | : 0 |
Release | : 2024-07 |
Genre | : Mathematics |
ISBN | : 9781032807232 |
Download Handbook of Exact Solutions to Mathematical Equations Book in PDF, ePub and Kindle
Author | : Andrei D. Polyanin |
Publisher | : CRC Press |
Total Pages | : 660 |
Release | : 2024-08-26 |
Genre | : Mathematics |
ISBN | : 1040092934 |
Download Handbook of Exact Solutions to Mathematical Equations Book in PDF, ePub and Kindle
This reference book describes the exact solutions of the following types of mathematical equations: ● Algebraic and Transcendental Equations ● Ordinary Differential Equations ● Systems of Ordinary Differential Equations ● First-Order Partial Differential Equations ● Linear Equations and Problems of Mathematical Physics ● Nonlinear Equations of Mathematical Physics ● Systems of Partial Differential Equations ● Integral Equations ● Difference and Functional Equations ● Ordinary Functional Differential Equations ● Partial Functional Differential Equations The book delves into equations that find practical applications in a wide array of natural and engineering sciences, including the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical engineering sciences, ecology, and more. Most of these equations are of a reasonably general form and dependent on free parameters or arbitrary functions. The Handbook of Exact Solutions to Mathematical Equations generally has no analogs in world literature and contains a vast amount of new material. The exact solutions given in the book, being rigorous mathematical standards, can be used as test problems to assess the accuracy and verify the adequacy of various numerical and approximate analytical methods for solving mathematical equations, as well as to check and compare the effectiveness of exact analytical methods.
Author | : Andrei D. Polyanin |
Publisher | : CRC Press |
Total Pages | : 1584 |
Release | : 2017-11-15 |
Genre | : Mathematics |
ISBN | : 1351643916 |
Download Handbook of Ordinary Differential Equations Book in PDF, ePub and Kindle
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 | : Hans Stephani |
Publisher | : Cambridge University Press |
Total Pages | : 94 |
Release | : 2009-09-24 |
Genre | : Science |
ISBN | : 9781139435024 |
Download Exact Solutions of Einstein's Field Equations Book in PDF, ePub and Kindle
A paperback edition of a classic text, this book contains six new chapters, covering generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics.
Author | : Andrei D. Polyanin |
Publisher | : CRC Press |
Total Pages | : 1496 |
Release | : 2017-11-15 |
Genre | : Mathematics |
ISBN | : 1466569409 |
Download Handbook of Ordinary Differential Equations Book in PDF, ePub and Kindle
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 | : Sergey V. Meleshko |
Publisher | : Springer Science & Business Media |
Total Pages | : 367 |
Release | : 2006-06-18 |
Genre | : Technology & Engineering |
ISBN | : 0387252657 |
Download Methods for Constructing Exact Solutions of Partial Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Andrei D. Polyanin |
Publisher | : CRC Press |
Total Pages | : 349 |
Release | : 2021-09-20 |
Genre | : Mathematics |
ISBN | : 1000463664 |
Download Separation of Variables and Exact Solutions to Nonlinear PDEs Book in PDF, ePub and Kindle
Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general version. In addition, the authors describe the differential constraint method, which generalizes many other exact methods. The presentation involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, and other disciplines are studied. Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest, as they are suitable to assess the accuracy of various approximate analytical and numerical methods. The book contains new material previously unpublished in monographs. It is intended for a broad audience of scientists, engineers, instructors, and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory, chemical engineering science, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering special courses and for practical training.
Author | : W.I. Fushchich |
Publisher | : Springer Science & Business Media |
Total Pages | : 456 |
Release | : 2013-03-14 |
Genre | : Science |
ISBN | : 9401731985 |
Download Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics Book in PDF, ePub and Kindle
by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors' works [55-109, 176-189, 13-16, 7*-14*,23*, 24*] carried out in the Institute of Mathematics, Academy of Sciences of the Ukraine. References to other sources is not intended to imply completeness. As a rule, only those works used directly are cited. The authors wish to express their gratitude to Academician Yu.A. Mitropoi sky, and to Academician of Academy of Sciences of the Ukraine O.S. Parasyuk, for basic support and stimulation over the course of many years; to our cowork ers in the Department of Applied Studies, LA. Egorchenko, R.Z. Zhdanov, A.G. Nikitin, LV. Revenko, V.L Lagno, and I.M. Tsifra for assistance with the manuscript.
Author | : Usama Al Khawaja |
Publisher | : Institute of Physics Publishing |
Total Pages | : 396 |
Release | : 2019-11-15 |
Genre | : Science |
ISBN | : 9780750324298 |
Download Handbook of Exact Solutions to the Nonlinear Schrödinger Equations Book in PDF, ePub and Kindle
This book collects all known solutions to the nonlinear Schrödinger equation (NLSE) in one resource. In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes. For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica Notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics.