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## Über dieses Buch

This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background.

## Inhaltsverzeichnis

### Chapter 1. Elements of the Time Scale Calculus

This chapter is devoted to a brief exposition of the time scale calculus that provide the framework for the study of integral equations on time scales.
Svetlin G. Georgiev

### Chapter 2. Introductory Concepts of Integral Equations on Time Scales

A delta integral equation (or in short integral equation) is the equation in which the unknown function $$\displaystyle {\phi (x)}$$ appears inside a delta integral sign.
Svetlin G. Georgiev

### Chapter 3. Generalized Volterra Integral Equations

In this chapter we investigate generalized Volterra integral equations. They are described different methods for finding a solution as an infinite series such as: the Adomian decomposition method, the modified decomposition method, the noise terms phenomenon, the differential equations method and the successive iterations method. It is given a procedure for conversion of generalized Volterra integral equations of the first kind to generalized Volterra integral equations of the second kind. They are provided existence and uniqueness of the solution.
Svetlin G. Georgiev

### Chapter 4. Generalized Volterra Integro-Differential Equations

In this chapter we describe the Adomian decomposition method for generalized Volterra integro-differential equations of the second kind.
Svetlin G. Georgiev

### Chapter 5. Generalized Fredholm Integral Equations

In this chapter we adapt the Adomian decomposition method, the modified decomposition method, the noise term phenomenon, the direct computation method and the successive approximation method for generalized Fredholm integral equations.
Svetlin G. Georgiev

### Chapter 6. Hilbert-Schmidt Theory of Generalized Integral Equations with Symmetric Kernels

Assume that K(xy) is continuous and Hermitian symmetric on $$[a, b]\times [a, b].$$
Svetlin G. Georgiev

### Chapter 7. The Laplace Transform Method

This chapter is devoted on applications of the Laplace transform on time scales to dynamic equations, generalized Volterra integral equations and generalized Volterra integro-differential equations.
Svetlin G. Georgiev

### Chapter 8. The Series Solution Method

In this chapter we describe the series solution method for generalized Volterra integral equations and generalized Volterra integro-differential equations.
Svetlin G. Georgiev

### Chapter 9. Non-linear Generalized Integral Equations

The generalized Volterra integral equation.
Svetlin G. Georgiev

### Backmatter

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