Details

Subject(s)

• Differential calculus—Early works to 1800 [Browse]

Translator

Blanton, John D. [Browse]

Summary note

What differential calculus, and, in general, analysis of the infinite, might be can hardly be explained to those innocent of any knowledge of it. Nor can we here offer a definition at the beginning of this dissertation as is sometimes done in other disciplines. It is not that there is no clear definition of this calculus; rather, the fact is that in order to understand the definition there are concepts that must first be understood. Besides those ideas in common usage, there are also others from finite analysis that are much less common and are usually explained in the course of the development of the differential calculus. For this reason, it is not possible to understand a definition before its principles are sufficiently clearly seen. In the first place, this calculus is concerned with variable quantities. Although every quantity can naturally be increased or decreased without limit, still, since calculus is directed to a certain purpose, we think of some quantities as being constantly the same magnitude, while others change through all the .stages of increasing and decreasing. We note this distinc­tion and call the former constant quantities and the latter variables. This characteristic difference is not required by the nature of things, but rather because of the special question addressed by the calculus.

Notes

Description based upon print version of record.

Bibliographic references

Includes bibliographical references and index.

Source of description

Description based on print version record.

Language note

English

Contents

• On Finite Differences
• On the Use of Differences in the Theory of Series
• On the Infinite and the Infinitely Small
• On the Nature of Differentials of Each Order
• On the Differentiation of Algebraic Functions of One Variable
• On the Differentiation of Transcendental Functions
• On the Differentiation of Functions of Two or More Variables
• On the Higher Differentiation of Differential Formulas
• On Differential Equations.

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ISBN

• 1-280-01037-1
• 9786610010370
• 0-387-22645-1

Doi

10.1007/b97699

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