The non-Newtonian calculi provide a wide variety of mathematical tools for use in science, engineering, and mathematics. They appear to have considerable potential for use as alternatives to the classical calculus of Newton and Leibniz. It may well be that these calculi can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.
Author(s): Michael Grossman, Robert Katz
Publisher: Kepler Press
Year: 1972/2006
Language: English
Commentary: Reprint of 1972
Pages: C+viii, 94, B
Cover
Non-Newtonian Calculus
Copyright
1972 by Michael Grossman and Robert Katz
ISBN 0912938013
F o r e w o r d
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 THE CLASSICAL GRADIENT
1.3 THE CLASSICAL DERIVATIVE
1.4 THE ARITHMETIC AVERAGE
1.5 THE BASIC THEOREM OF CLASSICAL CALCULUS
1.6 THE CLASSICAL INTEGRAL
1. 7 THE FUNDAMENTAL THEOREMS OF CLASSICAL CALCULUS
Chapter 2 THE GEOMETRIC CALCULUS
2.1 INTRODUCTION
2.2 THE GEOMETRIC G~DIENT
2.3 THE GEOMETRIC DERIVATIVE
2.4 THE GEOMETRIC AVERAGE
2.5 THE BASIC THEOREM OF GEOMETRIC CALCULUS
2.6 THE GEOMETRIC INTEGRAL
2.7 THE FUNDAMENTAL THEOREMS OF GEOMETRIC CALCULUS
2.8 RELATIONSHIPS TO THE CLASSICAL CALCULUS
Chapter 3 THE ANAGEOMETRIC CALCULUS
3.1 INTRODUCTION
3.2 THE ANAGEOMETRIC GRADIENT
3.3 THE ANAGEOMETRIC DERIVATIVE
3. 4 THE ANAGEOMETRIC AVERAGE
3.5 THE BASIC THEOREM OF ANAGEOMETRIC CALCULUS
3.6 THE ANAGEOMETRIC INTEGRAL
3.7 THE FUNDAMENTAL THEOREMS OF ANAGEOMETRIC CALCULUS
3.8 RELATIONSHIPS TO THE CLASSICAL CALCULUS
Chapter 4 THE BIGEOMETRIC CALCULUS
4.1 INTRODUCTION
4.2 THE BIGEOMETRIC GRADIENT
4.3 THE BIGEOMETRIC DERIVATIVE
4.4 THE BIGEOMETRIC AVERAGE
4.5 THE BASIC THEOREM OF BIGEOMETRIC CALCULUS
4.6 THE BIGEOMETRIC INTEGRAL
4.7 THE FUNDAMENTAL THEOREMS OF BIGEOMETRIC CALCULUS
4.8 RELATIONSHIPS TO THE CLASSICAL CALCULUS
Chapter 5 SYSTEMS OF ARITHMETIC
5.1 INTRODUCTION
5.2 ARITHMETICS
5. 3 a-ARITHMETIC
5.4 GEOMETRIC ARITHMETIC
Chapter 6 THE *-CALCULUS
6.1 INTRODUCTION
6.2 THE *-GRADIENT
6.3 THE *-DERIVATIVE
6.4 THE *-AVERAGE
6.5 THE BASIC THEOREM OF *-CALCULUS
6.6 THE *-INTEGRAL
6.7 THE FUNDAMENTAL THEOREMS OF *-CALCULUS
6.8 RELATIONSHIPS TO THE CLASSICAL CALCULUS
6.9 RELATIONSHIPS BETWEEN ANY TWO CALCULI
6.10 APPLICATIONS OF GEOMETRIC ARITHMETIC
6.11 GRAPHICAL INTERPRETATIONS
Chapter 7 THE QUADRATIC FAMILY OF CALCULI
7.1 THE QUADRATIC ARITHMETIC
7.2 THE QUADRATIC CALCULUS
7. 3 THE ANAQUADRATIC CALCULUS
7.4 THE BIQUADRATIC CALCULUS
Chapter 8 THE HARMONIC FAMILY OF CALCULI
8.1 THE HARMONIC ARITHMETIC
8.2 THE HARMONIC CALCULUS
8.3 THE ANAHARMONIC CALCULUS
8.4 THE BIHARMONIC CALCULUS
Chapter 9 H E U R I S T I C S
9.1 INTRODUCTION
9.2 CHOOSING GRADIENTS AND DERIVATIVES
9.3 CHOOSING INTEGRALS
9.4 CHOOSING AVERAGES
9.5 CONSTANTS AND SCIENTIFIC CONCEPTS
Chapter 10 COLLATERAL ISSUES
10.1 INTRODUCTION
10.2 •-SPACE
10.3 •-VECTORS
10.4 THE •-METHOD OF LEAST SQUARES
10.5 TRENDS
10.6 CALCULUS IN BANACH SPACES
10.7 CONCLUSION
N 0 T E S
Note 1 (to page 12)
Note 2 (to pa9e 13)
Note 3 (to page 19)
Note 4 (to page 49)
Note 5 (to pages 53 and 60)
Note 6 (to page 77)
Note 7 (to page 78)
LIST OF SYMBOLS
I N D E X
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