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Foundations Of Iso Differential Calculus Volume I Second Revised And Updated Edition
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Author : Svetlin Georgiev
language : en
Publisher: Nova Science Publishers
Release Date : 2022
Foundations Of Iso Differential Calculus Volume I Second Revised And Updated Edition written by Svetlin Georgiev and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Mathematics categories.
"This is the second edition of Foundations of Iso-Differential Calculus, volume 1, which gives an overview of the development of iso-differential calculus. The second edition introduces a new class of iso-functions, named iso-functions of the fifth kind. Also, further examples, exercises and problems have been added. Chapter 1 reviews Ruggero Maria Santilli's scientific journey, identifying its most important references. Chapter 2 introduces iso-real numbers, some basic functions and their properties. Chapter 3 defines sequences of iso-real numbers and deduces their properties. Chapter 4 gives definitions for five kinds of iso-functions and outlines their properties. Chapter 5 introduces the limits of iso-functions and continuous iso-functions. Chapter 6 presents the first comprehensive study of iso-differential calculus for the specific intent of showing its non-triviality. Chapter 7 reflects integral calculus in the language of iso-mathematics. Lastly, Chapter 8 outlines the isodual iso-mathematics and presents the first comprehensive study of isodual iso-differential calculus"--
Foundations Of Iso Differential Calculus Volume I Second Revised And Updated Edition
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Author : Svetlin G. Georgiev
language : en
Publisher:
Release Date : 2022-02-28
Foundations Of Iso Differential Calculus Volume I Second Revised And Updated Edition written by Svetlin G. Georgiev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-28 with categories.
This is the second edition of Foundations of Iso-Differential Calculus, Volume 1, which gives an overview of the development of iso-differential calculus. The second edition introduces a new class of iso-functions, named iso-functions of the fifth kind. Also, further examples, exercises and problems have been added. Chapter 1 reviews Ruggero Maria Santilli's scientific journey, identifying its most important references. Chapter 2 introduces iso-real numbers, some basic functions and their properties. Chapter 3 defines sequences of iso-real numbers and deduces their properties. Chapter 4 gives definitions for five kinds of iso-functions and outlines their properties. Chapter 5 introduces the limits of iso-functions and continuous iso-functions. Chapter 6 presents the first comprehensive study of iso-differential calculus for the specific intent of showing its non-triviality. Chapter 7 reflects integral calculus in the language of iso-mathematics. Lastly, Chapter 8 outlines the isodual iso-mathematics and presents the first comprehensive study of isodual iso-differential calculus.
Foundations Of Iso Differential Calculus Volume 1
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Author : Svetlin Georgiev
language : en
Publisher: Nova Science Publishers
Release Date : 2014
Foundations Of Iso Differential Calculus Volume 1 written by Svetlin Georgiev and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Differential calculus categories.
The 'genious idea' is the Santilli's generalisation of the basic unit of quantum mechanics into an integro-differential operator. This depends on local variables, and it is assumed to be the inverse of the isotopic element (the Santilli isounit). It was believed for centuries that the differential calculus is independent of the assumed basic unit, since the latter was traditionally given by the trivial number 1. Santilli has disproved this belief by showing that the differential calculus can be dependent on the assumed unit by formulating the isodifferential calculus with basic isodifferential. In this book, the authors introduce the main definitions and properties of isonumbers, isofunctions and isodifferentials. The book is provided with examples and exercises making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects of isodifferential calculus. Alternatively, it may be used for beginning graduate level course and as a reference work. With exercises at the end of each chapter and its straightforward writing style, the book addresses readers who have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as theory of functions and differential calculus.
Foundations Of Iso Differential Calculus
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Author : Svetlin Georgiev
language : en
Publisher: Nova Science Publishers
Release Date : 2014-01-01
Foundations Of Iso Differential Calculus written by Svetlin Georgiev and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-01 with MATHEMATICS categories.
This book introduces the main ideas and fundamental methods of iso-differential calculus for iso-functions of several variables. Introduced are the iso-functions of the first, second, third, fourth and fifth kind, and iso-partial derivatives of the first, second, third, fourth, fifth, sixth and seventh kind. In this book, the main conceptions for multiple, line and surface iso-integrals for iso-functions of several variables are given. The book is provided with examples and exercises making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects of iso-differential calculus. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises at the end of each chapter and its straightforward writing style, the book addresses readers who have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as theory of functions and differential calculus.
Foundations Of Iso Differential Calculus Volume 5
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Author : Svetlin Georgiev
language : en
Publisher: Nova Science Publishers
Release Date : 2015-04-16
Foundations Of Iso Differential Calculus Volume 5 written by Svetlin Georgiev and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-16 with Differential calculus categories.
This book is intended for readers who have had a course in iso-differential calculus and theory of probability. It can be used for a senior undergraduate course.
Foundations Of Iso Differential Calculus
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Author : Svetlin Georgiev
language : en
Publisher:
Release Date : 2015-05
Foundations Of Iso Differential Calculus written by Svetlin Georgiev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05 with Differential calculus categories.
This book is intended for readers who have had or currently have a course in difference equations or iso-differential calculus. It can be used for a senior undergraduate course. Chapter 1 deals with the linear first-order iso-difference equations, equilibrium points, eventually equilibrium points, periodic points and cycles. Chapter 2 are introduces iso-difference calculus and the general theory of the linear homogeneous and nonhomogeneous iso-difference equations. Chapter 3 studies the systems of linear iso-difference equations and the linear periodic systems. Chapter 4 is devoted to the stability theory. They are considered the nonautonomous linear systems, Lyapunov's direct method, and stability by linear approximation. Chapter 5 discusses the oscillation theory. The oscillation theory is defined as the iso-self-adjoint second-order iso-difference equations and they are given some of their properties. They are considered some classes of nonlinear iso-difference equations. Chapter 6 studies the asymptotic behavior of some classes of iso-difference equations. Time scales iso-calculus is introduced in Chapter 7. They are given the main properties of the backward and forward jump iso-operators. They are considered the iso-differentiation and iso-integration. They are introduced as the iso-Hilger's complex plane and the iso-exponential function
Foundations Of Iso Differential Calculus
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READ ONLINE
Author : Svetlin Georgiev
language : en
Publisher: Nova Science Publishers
Release Date : 2014-01-11
Foundations Of Iso Differential Calculus written by Svetlin Georgiev and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-11 with Differential calculus categories.
This book introduces the main ideas and fundamental methods of iso-differential calculus for iso-functions of several variables. Introduced are the iso-functions of the first, second, third, fourth and fifth kind, and iso-partial derivatives of the first, second, third, fourth, fifth, sixth and seventh kind. In this book, the main conceptions for multiple, line and surface iso-integrals for iso-functions of several variables are given. The book is provided with examples and exercises making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects of iso-differential calculus. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises at the end of each chapter and its straightforward writing style, the book addresses readers who have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as theory of functions and differential calculus.
Foundations Of Iso Differential Calculus
DOWNLOAD
READ ONLINE
Author : Svetlin Georgiev
language : en
Publisher: Nova Science Publishers
Release Date : 2015
Foundations Of Iso Differential Calculus written by Svetlin Georgiev and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Differentiable dynamical systems categories.
This book is intended for readers who have had or currently have a course in difference equations or iso-differential calculus. It can be used for a senior undergraduate course. Chapter 1 deals with the linear first-order iso-difference equations, equilibrium points, eventually equilibrium points, periodic points and cycles. Chapter 2 are introduces iso-difference calculus and the general theory of the linear homogeneous and nonhomogeneous iso-difference equations. Chapter 3 studies the systems of linear iso-difference equations and the linear periodic systems. Chapter 4 is devoted to the stability theory. They are considered the non-autonomous linear systems, Lyapunov's direct method, and stability by linear approximation. Chapter 5 discusses the oscillation theory. The oscillation theory is defined as the iso-self-adjoint second-order iso-difference equations and they are given some of their properties. They are considered some classes of nonlinear iso-difference equations. Chapter 6 studies the asymptotic behavior of some classes of iso-difference equations. Time scales iso-calculus is introduced in Chapter 7. They are given the main properties of the backward and forward jump iso-operators. They are considered the iso-differentiation and iso-integration. They are introduced as the iso-Hilger's complex plane and the iso-exponential function.
Foundations Of Iso Differential Calculus
DOWNLOAD
READ ONLINE
Author : Svetlin Georgiev
language : en
Publisher:
Release Date : 2014
Foundations Of Iso Differential Calculus written by Svetlin Georgiev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with MATHEMATICS categories.
Foundations Of Iso Differential Calculus
DOWNLOAD
READ ONLINE
Author : Svetlin Georgiev
language : en
Publisher: Nova Science Publishers
Release Date : 2014-12
Foundations Of Iso Differential Calculus written by Svetlin Georgiev and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12 with Differential calculus categories.
This book is intended for readers who have had a course in iso-differential calculus and it can be used for a senior undergraduate course. Chapter 1 deals with exact iso-differential equations, while first-order iso-differential equations are studied in Chapter 2 and Chapter 3. Chapter 4 discusses iso-integral inequalities. Many iso-differential equations cannot be solved as finite combinations of elementary functions. Therefore, it is important to know whether a given iso-differential equation has a solution and if it is unique. These aspects of the existence and uniqueness of the solutions for first-order initial value problems are considered in Chapter 5. Iso-differential inequalities are discussed in Chapter 6. Continuity and differentiability of solutions with respect to initial conditions are examined in Chapter 7. Chapter 8 extends existence-uniqueness results and continuous dependence on initial data for linear iso-differential systems. Basic properties of solutions of linear iso-differential systems are given in Chapter 9. Chapter 10 deals with the fundamental matrix solutions. In Chapter 11, necessary and sufficient conditions are provided so that a linear iso-differential system has only periodic solutions. The asymptotic behaviour of the solutions of linear systems is investigated in Chapter 12. Chapters 13 and 14 are devoted to some aspects of the stability of solutions of iso-differential systems. The last major topic covered in this book is that of boundary value problems involving second-order iso-differential equations. After linear boundary value problems are introduced in Chapter 15, Green's function and its construction is discussed in Chapter 16.