# Introduction to the Time Scales Calculus

## Editor(s)

Bohner, Martin, 1966- and Peterson, Allan

## Abstract

In this chapter we introduce some basic concepts concerning the calculus on time scales that one needs to know to read this book. Most of these results will be stated without proof. Proofs can be found in the book by Bohner and Peterson [86]. A time scale is an arbitrary nonempty closed subset of the real numbers. Thus R,Z,N,N0, i.e., the real numbers, the integers, the natural numbers, and the nonnegative integers are examples of time scales, as are [0,1]∪[2,3],[0,1]∪N , and the Cantor set, while Q,R∖Q,C(0,1), i.e., the rational numbers, the irrational numbers, the complex numbers, and the open interval between 0 and 1, are not time scales. Throughout this book we will denote a time scale by the symbol T . We assume throughout that a time scale T has the topology that it inherits from the real numbers with the standard topology.

## Recommended Citation

M.
Bohner
et al.,
"Introduction to the Time Scales Calculus," *Advances in Dynamic Equations on Time Scales*, Springer Verlag, Jan 2003.

The definitive version is available at https://doi.org/10.1007/978-0-8176-8230-9_1

## Department(s)

Mathematics and Statistics

## Document Type

Book - Chapter

## Document Version

Citation

## File Type

text

## Language(s)

English

## Rights

© 2003 Springer Verlag, All rights reserved.

## Publication Date

01 Jan 2003