Excellent introductory material on the calculus of time scales and dynamic equations.; Numerous examples and exercises illustrate the diverse application of dynamic equations on time scales.; Unified and systematic exposition of the topics allows good transitions from chapter to chapter.; Contributors include Anderson, M. Bohner, Davis, Dosly, Eloe, Erbe, Guseinov, Henderson, Hilger, Hilscher, Kaymakcalan, Lakshmikantham, Mathsen, and A. Peterson, founders and leaders of this field of study.; Useful as a comprehensive resource of time scales and dynamic equations for pure and applied mathematicians.; Comprehensive bibliography and index complete this text.
Advances in Dynamic Equations on Time Scales
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Book Description
Editorial Reviews
Review
From the reviews: "The book can be used as a textbook for a second course in dynamic equations...and is an indispensable mongraph for every researcher in the field of dynamic equations on time scale and related topics." ---Mathmatica Bohemica “The monograph under review comes at an excellent time in the rapid development of dynamic equations on time scales. Both authors are authorities in this field of study and they have produced an excellent introduction to it. Much of the material is accessible to upper-level undergraduate mathematics majors, and yet, the results and the techniques are pertinent to active researchers in the area.”(MATHEMATICAL REVIEWS)
From the Back Cover
The subject of dynamic equations on time scales continues to be a rapidly growing area of research. Behind the main motivation for the subject lies the key concept that dynamic equations on time scales is a way of unifying and extending continuous and discrete analysis. This work goes beyond an earlier introductory text Dynamic Equations on Time Scales: An Introduction with Applications (ISBN 0-8176-4225-0) and is designed for a second course in dynamic equations at the graduate level. Key features of the book: excellent introductory material on the calculus of time scales and dynamic equations * numerous examples and exercises * covers the following topics: the exponential function on time scales, boundary value problems, positive solutions, upper and lower solutions of dynamic equations, integration theory on time scales, disconjugacy and higher order dynamic equations, delta, nabla, and alpha dynamic equations on time scales * unified and systematic exposition of the above topics with good transitions from chapter to chapter * useful for a second course in dynamic equations at the graduate level, with directions suggested for future research * comprehensive bibliography and index * useful as a comprehensive resource for pure and applied mathematicians Contributors: R. Agarwal, E. Akin-Bohner, D. Anderson, F. Merdivenci Atici, R. Avery, M. Bohner, J. Bullock, J. Davis, O. Dosly, P. Eloe, L. Erbe, G. Guseinov, J. Henderson, S. Hilger, R. Hilscher, B. Kaymakalan, K. Messer, D. O'Regan, A. Peterson, H. Tran, W. Yin
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Inside This Book
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First Sentence:
In this chapter we introduce some basic concepts concerning the calculus on time scales that one needs to know to read this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nabla differentiable, symplectic dynamic systems, order linear dynamic equations, conjoined basis, normalized conjoined bases, alpha differentiable, nabla integrals, nabla derivative, separated boundary value problems, order dynamic equations, strong normality, conjugate boundary conditions, quasilinearization method, symplectic systems, recessive solution, generalized zeros, interpolating families, upper solutions, delta derivative, monotone methods, nonlinear dynamic equations, measure chains, separated boundary conditions, smallest positive eigenvalues, lower solution Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Theorem, Prove Lemma, Allan Peterson, Picone's Identity, Darboux A-integral, Define the Banach, Therefore Theorem, Use Definition, Using Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter we introduce some basic concepts concerning the calculus on time scales that one needs to know to read this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nabla differentiable, symplectic dynamic systems, order linear dynamic equations, conjoined basis, normalized conjoined bases, alpha differentiable, nabla integrals, nabla derivative, separated boundary value problems, order dynamic equations, strong normality, conjugate boundary conditions, quasilinearization method, symplectic systems, recessive solution, generalized zeros, interpolating families, upper solutions, delta derivative, monotone methods, nonlinear dynamic equations, measure chains, separated boundary conditions, smallest positive eigenvalues, lower solution Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Theorem, Prove Lemma, Allan Peterson, Picone's Identity, Darboux A-integral, Define the Banach, Therefore Theorem, Use Definition, Using Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 23
books:
See all 23 books this book cites
4
books
cite this book:
- New York (Land of Liberty) by Ellen Sturm in Back Matter (1), Back Matter (2), and Back Matter (3)
- Proceedings of Dynamic Systems and Applications by G. S. Ladde in Back Matter (1), and Back Matter (2)
- Quadratic Functionals in Variational Analysis and Control Theory (Mathematical Topics) by Werner Kratz in Back Matter
- Differential Equations, 3rd Edition by Shepley L. Ross in Back Matter
- San Diego by Lee Peterson in Back Matter
See all 23 books this book cites
- Nonoscillation and Oscillation Theory for Functional Differential Equations (Pure and Applied Mathematics) by Ravi P. Agarwal in Back Matter (1), and Back Matter (2)
- Proceedings of the Eighth International Conference on Difference Equations and Applications by Saber N. Elaydi on page 6, and page 170
- Discrete Oscillation Theory (Contemporary Mathematics and Its Applications Book Series) by Ravi P. Agarwal in Back Matter
- Proceedings of the Sixth International Conference on Difference Equations Augsburg, Germany 2001: New Progress in Difference Equations by Bernd Aulbach on page 252
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