FOUNDATIONS OF ISO-DIFFERENTIAL CALCULUS, VOLUME I

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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 Blank Page