Foundations of iso-differential calculus
著者
書誌事項
Foundations of iso-differential calculus
（Mathematics research developments series）
Nova Publishers, c2014
- v. 1
- v. 2
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注記
Includes bibliographies and indexes
内容説明・目次
- 巻冊次
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v. 1 ISBN 9781626181601
内容説明
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.
目次
- Foreword
- Physical Origin of the Isodifferential Calculus
- Isoreals
- Sequences of Isoreals
- Isofunctions-Definition & Properties
- Limit of Isofunctions. Continuous Isofunctions
- Isodifferentiable Isofunctions
- Isointegrals
- References
- Index.
- 巻冊次
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v. 2 ISBN 9781633217584
内容説明
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.
目次
- Preface
- Real-Valued Iso-Functions of Several Variables
- Multiple Iso-Integrals
- Line & Surface Iso-Integrals
- Iso-Fourier Iso-Integral
- Elements of the Theory of Iso-Hilbert Spaces
- Elements of Santilli-Lie-Isotopic Time Evolution Theory
- References
- Index.
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