Foundations of Iso-Differential Calculus, Volume I, Second Revised and Updated Edition


Series: Mathematics Research Developments
BISAC: MAT005000

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.

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Table of Contents

Foreword to the Second Edition

Foreword to the First Edition

Chapter 1. Physical Origin of the Iso-Differential Calculus

Chapter 2. Iso-Real Numbers

Chapter 3. Sequences of Iso-Real Numbers

Chapter 4. Iso-Functions

Chapter 5. Limit of Iso-Functions. Continuous Iso-Functions

Chapter 6. Iso-Differentiable Iso-Functions

Chapter 7. Iso-Integration

Chapter 8. Elements of Isodual Mathematics



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