Georgiev S.G. Foundations of Iso-Differential Calculus. Volume 1

New York: Nova Science, 2022. — 384 p.Nowadays much attention is being given to the development of cancer tumours’ nanotechnologies, production of novel materials and nano-scale structures. The importance of the simultaneous improvement of corrosion and wear resistance is emphasized by the fact that the cost of damage caused by corrosion is very high. The use of electroless plating promotes overcoming many of the problems in the above-mentioned fields.
The term electroless plating denotes the method of deposition of metals and alloys without using the external electric current source. This method could find wide applications in the above-mentioned tasks and resolution of other problems in various fields of industry, relating to nanoelectronics, microelectronics, fabrication of ICs, printed circuit boards and hard memory discs, catalysis, instrument-making, and machine-building. This book presents new data in this field of study.Preface to the Second Edition
Preface to the First Edition
Physical Origin of theIso-Differential Calculus
The Birth of the Differential Calculus
The Notion of Point-Like Mass
Interior and Exterior Dynamical Problems
Santilli’s Lie-Admissible Treatmentof Open Irreversible Systems
Santilli Lie-Isotopic Treatment of ClosedIrreversible Systems
Iso-Real Numbers
Algebra of Iso-Real Number Systems
Sets of Iso-Real Numbers
Advanced Practical Problems
Sequences of Iso-RealNumbers
Definition and Properties
Limit of a Sequence of Iso-Real Numbers
Infinitely Small and Infinitely Large Sequences
Increasing and Decreasing Sequencesof Iso-Real Numbers
Fundamental Sequences of Iso-Real Numbers
Advanced Practical Problems
Iso-Functions
Definitions of Iso-Functions of the First,Second, Third, Fourth and Fifth Kind
Iso-Bijection, Iso-Injection and Iso-Surjection
Inverse Iso-Image
Operations with Iso-Functions
Composition of Iso-Functions
Bounded and Unbounded Iso-Functions
Even and Odd Iso-Functions
Periodic Iso-Functions
Monotonic Iso-Functions
Advanced Practical Problems
Limit of Iso-FunctionsContinuous Iso-Functions
Limit of Iso-Functions
Continuous Iso-Functions
Advanced Practical Problems
Iso-DifferentiableIso-Functions
Iso-Differential
Iso-Derivatives
Higher Order Iso-Derivatives
Criteria for Monotonicity of Iso-Functions
Extreme Values
Mean Value Theorems
Convex and Concave Iso-Functions
Taylor Iso-Series
Advanced Practical Problems
Iso-Integration
Definition
Properties
Iso-Integration by Parts
Inequalities for Iso-Integrals
Improper Iso-Integrals
Advanced Practical Problems
Elements of IsodualMathematics
Isodual Reals
Isodual Sequences
Isodual Functions
Limit of Isodual Functions Continuous IsodualFunctions
Isodual Differential Calculas
Isodual Functions of the First Kind
Isodual Functions of the Second Kind
Isodual Functions of Third Kind
Isodual Integrals
Isodual Functions of the First Kind
Isodual Functions of the Second Kind
Isodual Functions of the Third KkindAdditional Resources
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