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## Über dieses Buch

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.

## Inhaltsverzeichnis

### Chapter 1. Time Scales

Abstract
A time scale is an arbitrary nonempty closed subset of the real numbers.
Martin Bohner, Svetlin G. Georgiev

### Chapter 2. Differential Calculus of Functions of One Variable

Abstract
Assume that $$f:{\mathbb {T}}\rightarrow {\mathbb {R}}$$ is a function and let $$t\in {\mathbb {T}}^{\kappa }$$.
Martin Bohner, Svetlin G. Georgiev

### Chapter 3. Integral Calculus of Functions of One Variable

Abstract
A function $$f:{\mathbb {T}}\rightarrow {\mathbb {R}}$$ is called regulated provided its right-sided limits exist (finite) at all right-dense points in $${\mathbb {T}}$$ and its left-sided limits exist (finite) at all left-dense points in $${\mathbb {T}}$$.
Martin Bohner, Svetlin G. Georgiev

### Chapter 4. Sequences and Series of Functions

Abstract
Suppose that $$f_n:{\mathbb {T}}\rightarrow {\mathbb {R}}$$, $$n\in {\mathbb {N}}$$, $$S\subset {\mathbb {T}}$$.
Martin Bohner, Svetlin G. Georgiev

### Chapter 5. Parameter-Dependent Integrals

Abstract
Let $${\mathbb {T}}_1$$ and $${\mathbb {T}}_2$$ be time scales.
Martin Bohner, Svetlin G. Georgiev

### Chapter 6. Partial Differentiation on Time Scales

Abstract
Let $$n\in {\mathbb {N}}$$ be fixed. For each $$i\in \{1,2,\ldots ,n\}$$, we denote by $${\mathbb {T}}_i$$ a time scale.
Martin Bohner, Svetlin G. Georgiev

### Chapter 7. Multiple Integration on Time Scales

Abstract
Let $${\mathbb {T}}_i$$, $$i\in \{1,2,\ldots ,n\}$$, be time scales. For $$i\in \{1,2,\ldots ,n\}$$, let $$\sigma _i$$, $$\rho _i$$, and $$\varDelta _i$$ denote the forward jump operator, the backward jump operator, and the delta differentiation, respectively, on $${\mathbb {T}}_i$$.
Martin Bohner, Svetlin G. Georgiev

### Chapter 8. Line Integrals

Abstract
Let $${\mathbb {T}}$$ be a time scale with the forward jump operator $$\sigma$$ and the delta operator $$\varDelta$$. Let $$a,b\in {\mathbb {T}}$$ with $$a<b$$. Assume that $$\phi _i:[a,b]\rightarrow {\mathbb {R}}$$ is continuous, $$i\in \{1,\ldots ,m\}$$.
Martin Bohner, Svetlin G. Georgiev

### Chapter 9. Surface Integrals

Abstract
Let $${\mathbb {T}}_i$$, $$i\in \{1,\ldots , n\}$$, be time scales. Suppose $$\varOmega \subset {\mathbb {T}}_1\times \ldots \times {\mathbb {T}}_n$$. Let $$\phi _i:\varOmega \rightarrow {\mathbb {R}}$$ be continuous functions on $$\varOmega$$.
Martin Bohner, Svetlin G. Georgiev

### Backmatter

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