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.
Author(s): Svetlin G. Georgiev
Series: Mathematics Research Developments
Edition: 2
Publisher: Nova Science Publishers
Year: 2022
Language: English
Pages: 382
City: New York
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Mathematics Research Developments
Foundations of Iso-DifferentialCalculus, Volume ISecond Revised and Updated Edition
Contents
Preface to the Second Edition
Preface to the First Edition
Chapter 1Physical Origin of theIso-Differential Calculus
1.1. The Birth of the Differential Calculus
1.2. The Notion of Point-Like Mass
1.3. Interior and Exterior Dynamical Problems
1.4. Santilli’s Lie-Admissible Treatmentof Open Irreversible Systems
1.5. Santilli Lie-Isotopic Treatment of ClosedIrreversible Systems
Chapter 2Iso-Real Numbers
2.1. Algebra of Iso-Real Number Systems
2.2. Sets of Iso-Real Numbers
2.3. Advanced Practical Problems
Chapter 3Sequences of Iso-RealNumbers
3.1. Definition and Properties
3.2. Limit of a Sequence of Iso-Real Numbers
3.3. Infinitely Small and Infinitely Large Sequences
3.4. Increasing and Decreasing Sequencesof Iso-Real Numbers
3.5. Fundamental Sequences of Iso-Real Numbers
3.6. Advanced Practical Problems
Chapter 4Iso-Functions
4.1. Definitions of Iso-Functions of the First,Second, Third, Fourth and Fifth Kind
4.2. Iso-Bijection, Iso-Injection and Iso-Surjection
4.3. Inverse Iso-Image
4.4. Operations with Iso-Functions
4.5. Composition of Iso-Functions
4.6. Bounded and Unbounded Iso-Functions
4.7. Even and Odd Iso-Functions
4.8. Periodic Iso-Functions
4.9. Monotonic Iso-Functions
4.10. Advanced Practical Problems
Chapter 5Limit of Iso-Functions.Continuous Iso-Functions
5.1. Limit of Iso-Functions
5.2. Continuous Iso-Functions
5.3. Advanced Practical Problems
Chapter 6Iso-DifferentiableIso-Functions
6.1. Iso-Differential
6.2. Iso-Derivatives
6.3. Higher Order Iso-Derivatives
6.4. Criteria for Monotonicity of Iso-Functions
6.5. Extreme Values
6.6. Mean Value Theorems
6.7. Convex and Concave Iso-Functions
6.8. Taylor Iso-Series
6.9. Advanced Practical Problems
Chapter 7Iso-Integration
7.1. Definition
7.2. Properties
7.3. Iso-Integration by Parts
7.4. Inequalities for Iso-Integrals
7.5. Improper Iso-Integrals
7.6. Advanced Practical Problems
Chapter 8Elements of IsodualMathematics
8.1. Isodual Reals
8.2. Isodual Sequences
8.3. Isodual Functions
8.4. Limit of Isodual Functions. Continuous IsodualFunctions
8.5. Isodual Differential Calculas
8.6. Isodual Functions of the First Kind
8.7. Isodual Functions of the Second Kind
8.8. Isodual Functions of Third Kind
8.9. Isodual Integrals
8.10. Isodual Functions of the First Kind
8.11. Isodual Functions of the Second Kind
8.12. Isodual Functions of the Third Kkind
References
Additional Resources
About the Author
Index
