Generalized Ordinary Differential Equations PDF Download
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Author | : ?tefan Schwabik |
Publisher | : World Scientific |
Total Pages | : 400 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 9789810212254 |
Download Generalized Ordinary Differential Equations Book in PDF, ePub and Kindle
The contemporary approach of J Kurzweil and R Henstock to the Perron integral is applied to the theory of ordinary differential equations in this book. It focuses mainly on the problems of continuous dependence on parameters for ordinary differential equations. For this purpose, a generalized form of the integral based on integral sums is defined. The theory of generalized differential equations based on this integral is then used, for example, to cover differential equations with impulses or measure differential equations. Solutions of generalized differential equations are found to be functions of bounded variations.The book may be used for a special undergraduate course in mathematics or as a postgraduate text. As there are currently no other special research monographs or textbooks on this topic in English, this book is an invaluable reference text for those interested in this field.
Author | : Everaldo M. Bonotto |
Publisher | : John Wiley & Sons |
Total Pages | : 514 |
Release | : 2021-09-15 |
Genre | : Mathematics |
ISBN | : 1119654939 |
Download Generalized Ordinary Differential Equations in Abstract Spaces and Applications Book in PDF, ePub and Kindle
GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. Throughout the book, the focus is on qualitative theory and on corresponding results for other types of differential equations, as well as the connection between Generalized Ordinary Differential Equations and impulsive differential equations, functional differential equations, measure differential equations and dynamic equations on time scales. The book’s descriptions will be of use in many mathematical contexts, as well as in the social and natural sciences. Readers will also benefit from the inclusion of: A thorough introduction to regulated functions, including their basic properties, equiregulated sets, uniform convergence, and relatively compact sets An exploration of the Kurzweil integral, including its definitions and basic properties A discussion of measure functional differential equations, including impulsive measure FDEs The interrelationship between generalized ODEs and measure FDEs A treatment of the basic properties of generalized ODEs, including the existence and uniqueness of solutions, and prolongation and maximal solutions Perfect for researchers and graduate students in Differential Equations and Dynamical Systems, Generalized Ordinary Differential Equations in Abstract Spaces and Applications will also earn a place in the libraries of advanced undergraduate students taking courses in the subject and hoping to move onto graduate studies.
Author | : Jaroslav Kurzweil |
Publisher | : World Scientific |
Total Pages | : 208 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 9814324027 |
Download Generalized Ordinary Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Avner Friedman |
Publisher | : Courier Corporation |
Total Pages | : 352 |
Release | : 2011-11-30 |
Genre | : Mathematics |
ISBN | : 9780486152912 |
Download Generalized Functions and Partial Differential Equations Book in PDF, ePub and Kindle
This self-contained text details developments in the theory of generalized functions and the theory of distributions, and it systematically applies them to a variety of problems in partial differential equations. 1963 edition.
Author | : Ondrej Dosly |
Publisher | : Elsevier |
Total Pages | : 533 |
Release | : 2005-07-06 |
Genre | : Mathematics |
ISBN | : 0080461239 |
Download Half-Linear Differential Equations Book in PDF, ePub and Kindle
The book presents a systematic and compact treatment of the qualitative theory of half-linear differential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE’s with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations. - The first complete treatment of the qualitative theory of half-linear differential equations. - Comparison of linear and half-linear theory. - Systematic approach to half-linear oscillation and asymptotic theory. - Comprehensive bibliography and index. - Useful as a reference book in the topic.
Author | : A.B. Mingarelli |
Publisher | : Springer |
Total Pages | : 333 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540398651 |
Download Volterra-Stieltjes Integral Equations and Generalized Ordinary Differential Expressions Book in PDF, ePub and Kindle
Author | : Joseph Wiener |
Publisher | : World Scientific |
Total Pages | : 428 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : 9789810212070 |
Download Generalized Solutions of Functional Differential Equations Book in PDF, ePub and Kindle
The need to investigate functional differential equations with discontinuous delays is addressed in this book. Recording the work and findings of several scientists on differential equations with piecewise continuous arguments over the last few years, this book serves as a useful source of reference. Great interest is placed on discussing the stability, oscillation and periodic properties of the solutions. Considerable attention is also given to the study of initial and boundary-value problems for partial differential equations of mathematical physics with discontinuous time delays. In fact, a large part of the book is devoted to the exploration of differential and functional differential equations in spaces of generalized functions (distributions) and contains a wealth of new information in this area. Each topic discussed appears to provide ample opportunity for extending the known results. A list of new research topics and open problems is also included as an update.
Author | : Gerald Teschl |
Publisher | : American Mathematical Soc. |
Total Pages | : 356 |
Release | : 2012-08-30 |
Genre | : Mathematics |
ISBN | : 0821883283 |
Download Ordinary Differential Equations and Dynamical Systems Book in PDF, ePub and Kindle
This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Author | : Thomas J. Coakley |
Publisher | : |
Total Pages | : 28 |
Release | : 1969 |
Genre | : Averaging method (Differential equations) |
ISBN | : |
Download A Generalized Averaging Method for Linear Differential Equations with Almost Periodic Coefficients Book in PDF, ePub and Kindle
Author | : Ram P. Kanwal |
Publisher | : Springer Science & Business Media |
Total Pages | : 474 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468400355 |
Download Generalized Functions Theory and Technique Book in PDF, ePub and Kindle
This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.