The book contains a detailed account of the first non-Newtonian calculus. In this system, the exponential functions play the role that the linear functions play in the classical calculus of Newton and Leibniz. This nonlinear system provides mathematical tools for use in science, engineering, and mathematics. It appears to have considerable potential for use as an alternative to the classical calculus. It may well be that this non-Newtonian calculus can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.
Author(s): Michael Grossman
Publisher: MATHCO
Year: 1979/ 2006
Language: English
Commentary: Reprinted in 2006
Pages: C+xi, 85, B
Cover
THE FIRST NONLI NEAR SYSTEM OF DIFFERENTIAL AND INTEGRAL CALCULUS
Copyright 1979 by Galilee Institute
P R E F A C E
C 0 N T E N T S
PRELIMINARIES
CHAPTER 1 The Classical Calculus
1.1 INTRODUCTION
1.2 LINEAR FUNCTIONS
1.3 CLASSICAL SLOPE
1.4 THE CLASSICAL GRADIENT
1.5 THE CLASSICAL DERIVATIVE
1.6 THE ARITHMETIC AVERAGE
1.7 THE BASIC THEOREM OF CLASSICAL CALCULUS
1.8 THE BASIC PROBLEM OF CLASSICAL CALCULUS
1.9 THE CLASSICAL INTEGRAL
1.10 THE FUNDAMENTAL THEOREMS OF CLASSICAL CALCULUS
CHAPTER 2 The Exponential Calculus
2.1 INTRODUCTION
2.2 EXPONENTIAL FUNCTIONS
2.3 EXPONENTIAL SLOPE
2.4 THE EXPONENTIAL GRADIENT
2.5 THE EXPONENTIAL DERIVATIVE
2.6 THE GEOMETRIC AVERAGE
2.7 THE BASIC THEOREM OF EXPONENTIAL CALCULUS
2.8 THE BASIC PROBLEM OF EXPONENTIAL CALCULUS
2.9 THE EXPONENTIAL INTEGRAL
2.10 THE FUNDAMENTAL THEOREMS OF EXPONENTIAL CALCULUS
2.11 SUMMARY OF RELATIONSHIPS To THE CLASSICAL CALCULUS
CHAPTER 3 Exponential Arithmetic
3.1 INTRODUCTION
3.2 CLASSICAL ARITHMETIC
3.3 EXPONENTIAL ARITHMETIC
3.4 CoMPARISON OF THE CLASSICAL AND EXPONENTIAL CALCULI
3.5 ARITHMETICS AND CALCULI
CHAPTER 4 Graphical Interpretations
4.1 INTRODUCTION
4.2 EXPONENTIAL GRAPHS
4.3 EXPONENTIAL DISTANCE
4.4 GRAPHICAL INTERPRETATION OF EXPONENTIAL SLOPE
4.5 GRAPHICAL INTERPRETATION OF THE EXPONENTIAL DERIVATIVE
4.6 GRAPHICAL INTERPRETATION OF THE EXPONENTIAL INTEGRAL
4.7 GRAPHICAL INTERPRETATION OF THE GEOMETRIC AVERAGE
CHAPTER 5 Heuristic Principles of Application
5.1 INTRODUCTION
5.2 CLASSICAL AND EXPONENTIAL TRANSLATIONS
5.3 CHOOSING GRADIENTS AND DERIVATIVES
5.4 CHOOSING INTEGRALS
5,5 CHOOSING AVERAGES
5.6 CONSTANTS AND SCIENTIFIC CONCEPTS
CHAPTER 6E xponential Geometry: A Non-Cartesian System
6.1 INTRODUCTION
6.2 CARTESIAN GEOMETRY
6.3 EXPONENTIAL GEOMETRY
CHAPTER 7 Exponential Vectors and Centroids
7.1 EXPONENTIAL VECTORS
7.2 EXPONENTIAL CENTROIDS
CHAPTER 8 The Exponential Method of Least Squares
8.1 INTRODUCTION
8.2 THE CLASSICAL METHOD OF LEAST SQUARES
8.3 THE EXPONENTIAL METHOD OF LEAST SQUARES
8.4 THE RELATIONSHIP BETWEEN THE TWO METHODS
CHAPTER 9 Collateral Issues
9.1 INTRODUCTION
9.2 THE PERCENTAGE DERIVATIVE
9.3 EXPONENTIAL COMPLEX-NUMBERS
9.4 AN INSIGHT BY BOSCOVICH
9.5 CONCLUSION
LIST OF SYMBOLS
I N D E X
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