Uniqueness And Nonuniqueness Criteria For Ordinary Differential Equations
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Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations
Author | : Ratan Prakash Agarwal,Ravi P. Agarwal,V. Lakshmikantham |
Publsiher | : World Scientific |
Total Pages | : 328 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : 9810213573 |
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This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.
Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations
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Author | : Ravi P. Agarwal |
Publsiher | : Unknown |
Total Pages | : 312 |
Release | : 1993 |
Genre | : MATHEMATICS |
ISBN | : 9814354481 |
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Ordinary and Partial Differential Equations
Author | : Ravi P. Agarwal,Donal O'Regan |
Publsiher | : Springer Science & Business Media |
Total Pages | : 422 |
Release | : 2008-11-13 |
Genre | : Mathematics |
ISBN | : 9780387791463 |
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In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.
Using the Mathematics Literature
Author | : Kristine K. Fowler |
Publsiher | : CRC Press |
Total Pages | : 412 |
Release | : 2004-05-25 |
Genre | : Language Arts & Disciplines |
ISBN | : 0824750357 |
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This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
Fundamentals of Partial Differential Equations
Author | : Atul Kumar Razdan,V. Ravichandran |
Publsiher | : Springer Nature |
Total Pages | : 558 |
Release | : 2022-04-02 |
Genre | : Mathematics |
ISBN | : 9789811698651 |
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The book serves as a primary textbook of partial differential equations (PDEs), with due attention to their importance to various physical and engineering phenomena. The book focuses on maintaining a balance between the mathematical expressions used and the significance they hold in the context of some physical problem. The book has wider outreach as it covers topics relevant to many different applications of ordinary differential equations (ODEs), PDEs, Fourier series, integral transforms, and applications. It also discusses applications of analytical and geometric methods to solve some fundamental PDE models of physical phenomena such as transport of mass, momentum, and energy. As far as possible, historical notes are added for most important developments in science and engineering. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.
Exploring ODEs
Author | : Lloyd N. Trefethen,Asgeir Birkisson,Tobin A. Driscoll |
Publsiher | : SIAM |
Total Pages | : 342 |
Release | : 2017-12-21 |
Genre | : Mathematics |
ISBN | : 9781611975161 |
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Exploring ODEs is a textbook of ordinary differential equations for advanced undergraduates, graduate students, scientists, and engineers. It is unlike other books in this field in that each concept is illustrated numerically via a few lines of Chebfun code. There are about 400 computer-generated figures in all, and Appendix B presents 100 more examples as templates for further exploration.?
Generalized Ordinary Differential Equations
Author | : Jaroslav Kurzweil |
Publsiher | : World Scientific |
Total Pages | : 208 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 9789814324021 |
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Explores the basics of social policy and program analysis, such as designing new programs or evaluating and improving existing ones. Social Policy and Social Programs is distinctive in providing specific criteria for judging the effectiveness of social policies and programs. These criteria can be applied to the analysis of widely different social services such as counseling and therapeutic services, supportive assistance, and "hard" benefits like food stamps, cash, and housing vouchers. By focusing especially on social problems, policies, and programs in major practice areas like child welfare, health, poverty, and mental illness, the author provides students with the tools they need to understand and evaluate the programs in which they are doing their field placements. Upon completing this book readers will be able to: Analyze the effectiveness of current social programs Create new programs based on the criteria provided Apply what they have learned to evaluate their field placement programs Note: MySearchLab does not come automatically packaged with this text. To purchase MySearchLab, please visit: www.mysearchlab.com or you can purchase a ValuePack of the text + MySearchLab (at no additional cost): ValuePack ISBN-10: 0205222943 / ValuePack ISBN-13: 9780205222940.
A Basic Guide to Uniqueness Problems for Evolutionary Differential Equations
Author | : Mi-Ho Giga,Yoshikazu Giga |
Publsiher | : Springer Nature |
Total Pages | : 163 |
Release | : 2023-10-16 |
Genre | : Mathematics |
ISBN | : 9783031347962 |
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This book addresses the issue of uniqueness of a solution to a problem – a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon. This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as well as what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader’s convenience, a list of basic terminology is given at the end of this book.