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

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  • Formāts: 381 pages
  • Sērija : Mathematics Research Developments
  • Izdošanas datums: 10-Feb-2022
  • Izdevniecība: Nova Science Publishers Inc
  • Valoda: eng
  • ISBN-13: 9781685076870
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Foundations of Iso-Differential Calculus, Volume I, Second Revised and Updated EditionPalielināt
  • Formāts: 381 pages
  • Sērija : Mathematics Research Developments
  • Izdošanas datums: 10-Feb-2022
  • Izdevniecība: Nova Science Publishers Inc
  • Valoda: eng
  • ISBN-13: 9781685076870
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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.
Preface to the Second Edition ix
Preface to the First Edition xi
1 Physical Origin of the Iso-Differential Calculus
1(16)
1.1 The Birth of the Differential Calculus
1(1)
1.2 The Notion of Point-Like Mass
2(1)
1.3 Interior and Exterior Dynamical Problems
3(2)
1.4 Santilli's Lie-Admissible Treatment of Open Irreversible Systems
5(6)
1.5 Santilli Lie-Isotopic Treatment of Closed Irreversible Systems
11(6)
2 Iso-Real Numbers
17(30)
2.1 Algebra of Iso-Real Number Systems
17(22)
2.2 Sets of Iso-Real Numbers
39(7)
2.3 Advanced Practical Problems
46(1)
3 Sequences of Iso-Real Numbers
47(34)
3.1 Definition and Properties
47(5)
3.2 Limit of a Sequence of Iso-Real Numbers
52(9)
3.3 Infinitely Small and Infinitely Large Sequences
61(6)
3.4 Increasing and Decreasing Sequences of Iso-Real Numbers
67(3)
3.5 Fundamental Sequences of Iso-Real Numbers
70(7)
3.6 Advanced Practical Problems
77(4)
4 Iso-Functions
81(68)
4.1 Definitions of Iso-Functions of the First, Second, Third, Fourth and Fifth Kind
81(12)
4.2 Iso-Bijection, Iso-Injection and Iso-Surjection
93(4)
4.3 Inverse Iso-Image
97(2)
4.4 Operations with Iso-Functions
99(15)
4.5 Composition of Iso-Functions
114(4)
4.6 Bounded and Unbounded Iso-Functions
118(10)
4.7 Even and Odd Iso-Functions
128(8)
4.8 Periodic Iso-Functions
136(4)
4.9 Monotonic Iso-Functions
140(4)
4.10 Advanced Practical Problems
144(5)
5 Limit of Iso-Functions. Continuous Iso-Functions
149(18)
5.1 Limit of Iso-Functions
149(13)
5.2 Continuous Iso-Functions
162(2)
5.3 Advanced Practical Problems
164(3)
6 Iso-Differentiable Iso-Functions
167(62)
6.1 Iso-Differential
167(5)
6.2 Iso-Derivatives
172(11)
6.3 Higher Order Iso-Derivatives
183(3)
6.4 Criteria for Monotonicity of Iso-Functions
186(7)
6.5 Extreme Values
193(28)
6.6 Mean Value Theorems
221(4)
6.7 Convex and Concave Iso-Functions
225(1)
6.8 Taylor Iso-Series
226(1)
6.9 Advanced Practical Problems
226(3)
7 Iso-Integration
229(74)
7.1 Definition
229(2)
7.2 Properties
231(8)
7.3 Iso-Integration by Parts
239(4)
7.4 Inequalities for Iso-Integrals
243(26)
7.5 Improper Iso-Integrals
269(33)
7.6 Advanced Practical Problems
302(1)
8 Elements of Isodual Mathematics
303(52)
8.1 Isodual Reals
303(4)
8.2 Isodual Sequences
307(8)
8.3 Isodual Functions
315(5)
8.4 Limit of Isodual Functions. Continuous Isodual Functions
320(1)
8.5 Isodual Differential Calculas
321(2)
8.6 Isodual Functions of the First Kind
323(4)
8.7 Isodual Functions of the Second Kind
327(4)
8.8 Isodual Functions of Third Kind
331(3)
8.9 Isodual Integrals
334(1)
8.10 Isodual Functions of the First Kind
335(3)
8.11 Isodual Functions of the Second Kind
338(3)
8.12 Isodual Functions of the Third Kkind
341(14)
About the Author 355(2)
Index 357
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