Download or read book Generalized Ordinary Differential Equations written by Stefan Schwabik and published by World Scientific. This book was released on 1992-10-28 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Generalized Ordinary Differential Equations in Abstract Spaces and Applications written by Everaldo M. Bonotto and published by John Wiley & Sons. This book was released on 2021-09-15 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Generalized Ordinary Differential Equations written by ?tefan Schwabik and published by World Scientific. This book was released on 1992 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book General Linear Methods for Ordinary Differential Equations written by Zdzislaw Jackiewicz and published by John Wiley & Sons. This book was released on 2009-08-14 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn to develop numerical methods for ordinary differential equations General Linear Methods for Ordinary Differential Equations fills a gap in the existing literature by presenting a comprehensive and up-to-date collection of recent advances and developments in the field. This book provides modern coverage of the theory, construction, and implementation of both classical and modern general linear methods for solving ordinary differential equations as they apply to a variety of related areas, including mathematics, applied science, and engineering. The author provides the theoretical foundation for understanding basic concepts and presents a short introduction to ordinary differential equations that encompasses the related concepts of existence and uniqueness theory, stability theory, and stiff differential equations and systems. In addition, a thorough presentation of general linear methods explores relevant subtopics such as pre-consistency, consistency, stage-consistency, zero stability, convergence, order- and stage-order conditions, local discretization error, and linear stability theory. Subsequent chapters feature coverage of: Differential equations and systems Introduction to general linear methods (GLMs) Diagonally implicit multistage integration methods (DIMSIMs) Implementation of DIMSIMs Two-step Runge-Kutta (TSRK) methods Implementation of TSRK methods GLMs with inherent Runge-Kutta stability (IRKS) Implementation of GLMs with IRKS General Linear Methods for Ordinary Differential Equations is an excellent book for courses on numerical ordinary differential equations at the upper-undergraduate and graduate levels. It is also a useful reference for academic and research professionals in the fields of computational and applied mathematics, computational physics, civil and chemical engineering, chemistry, and the life sciences.
Download or read book Generalized Ordinary Differential Equations written by Jaroslav Kurzweil and published by World Scientific. This book was released on 2012 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Volterra Stieltjes Integral Equations and Generalized Ordinary Differential Expressions written by A.B. Mingarelli and published by Springer. This book was released on 2006-11-15 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Half Linear Differential Equations written by Ondrej Dosly and published by Elsevier. This book was released on 2005-07-06 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential 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.
Download or read book Generalized Solutions of Functional Differential Equations written by Joseph Wiener and published by World Scientific. This book was released on 1993 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2012-08-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Thinking about Ordinary Differential Equations written by Robert E. O'Malley and published by Cambridge University Press. This book was released on 1997-01-13 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations - the building blocks of mathematical modelling - are also key elements of disciplines as diverse as engineering and economics. While mastery of these equations is essential, adhering to any one method of solving them is not: this book stresses alternative examples and analyses by means of which the student can build an understanding of a number of approaches to finding solutions and understanding their behaviour. This book offers not only an applied perspective for the student learning to solve differential equations, but also the challenge to apply these analytical tools in the context of singular perturbations, which arises in many areas of application. An important resource for the advanced undergradute, this book would be equally useful for the beginning graduate student investigating further approaches to these essential equations.
Download or read book Differential and Integral Equations Boundary Value Problems and Adjoints written by S. Schwabik and published by Springer. This book was released on 1979-05-31 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Generalized Averaging Method for Linear Differential Equations with Almost Periodic Coefficients written by Thomas J. Coakley and published by . This book was released on 1969 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Functions Theory and Technique written by Ram P. Kanwal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems written by John R Graef and published by World Scientific. This book was released on 2018-09-18 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Download or read book Ordinary Differential Equations written by Morris Tenenbaum and published by Courier Corporation. This book was released on 1985-10-01 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Generalized Functions of Green for Systems of Ordinary Differential Equations written by Oswald Wyler and published by . This book was released on 1959 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
