The First Systems Of Weighted Differential And Integral Calculus
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The First Systems of Weighted Differential and Integral Calculus
This book explains how each non-Newtonian calculus, as well as the classical calculus of Newton and Leibniz, can be 'weighted' in a natural way. In each of these weighted calculi, a weighted average (of functions) plays a central role. The weighted 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. It may well be that they can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.
Bigeometric Calculus
This book contains a detailed account of the bigeometric calculus, a non-Newtonian calculus in which the power 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 the bigeometric calculus can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.
Averages
This book concerns the averages of functions that arise in the development of non-Newtonian calculus and weighted non-Newtonian calculus, and an interesting family of means of two positive numbers. These averages and means provide a wide variety of mathematical tools for use in science, engineering, and mathematics. It may well be that they can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.