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This book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales, taking readers beyond the traditional calculus texts. Covering topics from parameter-dependent integrals to partial differentiation on time scales, the book's nine pedagogically oriented chapters provide a pathway to this active area of research that will appeal to students and researchers in mathematics and the physical sciences. The authors present a clear and well-organized treatment of the concept behind the mathematics and solution techniques, including many practical examples and exercises.
List of contents
1. Time Scales.- 2. Differential Calculus of Functions of One Variable.- 3. Integral Calculus of Functions of One Variable.- 4. Partial Differentiation on Time Scales.- 5. Multiple Integration on Time Scales.- 6. Sequences and Series of Functions.- 7. Parameter-Dependent Integrals.- 8. Line Integrals.- 9. Surface Integrals.- Index.
About the author
Martin Bohner - University of Missouri-Rolla, Department of Mathematics and Statistics, Rolla, Missouri.
Svetlin G. Georgiev - Sofia University, Faculty of Mathematics and Informatics, Department of Differential Equations, Bulgaria.
Summary
This book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales, taking readers beyond the traditional calculus texts. Covering topics from parameter-dependent integrals to partial differentiation on time scales, the book’s nine pedagogically oriented chapters provide a pathway to this active area of research that will appeal to students and researchers in mathematics and the physical sciences. The authors present a clear and well-organized treatment of the concept behind the mathematics and solution techniques, including many practical examples and exercises.
Additional text
“The present book provides a comprehensive treatise on the multivariable calculus on time scales. It is a very natural and nice sequel of the pair of monographs concerning the fundamental theory of the time scale calculus and dynamic equations. … I recommend this book to everybody who is interested in time scale calculus. … the book also very suitable for beginners such as, e.g., undergraduate students.” (Petr Zemánek, zbMATH 1475.26001, 2022)
“This book is a nice addition to an already nice group of books … concerning dynamics equations on time scales. Anyone with an interest in dynamics equations on time scales would be greatly interested in this well-written book. The 275 examples and 239 exercises should be very helpful to the reader in understanding the material.” (Allan C. Peterson, Mathematical Reviews, August, 2017)
Report
"The present book provides a comprehensive treatise on the multivariable calculus on time scales. It is a very natural and nice sequel of the pair of monographs concerning the fundamental theory of the time scale calculus and dynamic equations. ... I recommend this book to everybody who is interested in time scale calculus. ... the book also very suitable for beginners such as, e.g., undergraduate students." (Petr Zemánek, zbMATH 1475.26001, 2022)
"This book is a nice addition to an already nice group of books ... concerning dynamics equations on time scales. Anyone with an interest in dynamics equations on time scales would be greatly interested in this well-written book. The 275 examples and 239 exercises should be very helpful to the reader in understanding the material." (Allan C. Peterson, Mathematical Reviews, August, 2017)
