A Treatise on the Integral Calculus Method of Rates by William Johnson
A Treatise on the Integral Calculus Method of Rates - Table of Contents
1. Elementary Methods of Integration
2. Methods of Integration
3. Geometrical Applications (Double and Triple Integrals)
4. Mean Values and Probabilities
5. Definite Integrals
6. Functions of the Complex Variable
What You Will Learn in A Treatise on the Integral Calculus Method of Rates
"A Treatise on the Integral Calculus Founded on Method of Rates" by "William Johnson" is a classic early 20th-century textbook that presents "integral calculus" using the traditional "method of rates". Instead of modern limit-based definitions, Johnson emphasizes Newton’s original concept of "fluxions" to explain derivatives and integrals, making complex ideas more intuitive for students. The book combines historical insight with practical instruction, bridging classical and modern approaches to calculus.
The text covers "definite and indefinite integrals", "multiple integrals", and a variety of applications including computing "volumes", "surfaces", and mean values. It also explores symbolic methods for integration and includes numerous worked examples, gradually increasing in complexity. Johnson integrates elements of "probability" and averages, demonstrating the broad utility of integral calculus in both geometry and applied mathematics. This approach highlights the versatility of calculus beyond pure theory.
Ideal for students, educators, and researchers, the book offers a unique perspective on the "history of calculus" while providing clear explanations and practical methods. Its focus on rates and classical techniques makes it a valuable resource for understanding how integration was taught before modern analytical methods. Johnson’s work remains significant for those studying the evolution of mathematical education and classical problem-solving techniques.
Book Details & Specifications
Title:
A Treatise on the Integral Calculus Method of Rates by William Johnson
Publisher:
J. Wiley & sons
Year:
1907
Pages:
466
Type:
PDF
Language:
English
ISBN-10 #:
1346837473
ISBN-13 #:
978-1346837475
License:
Public Domain Work
Amazon:
Amazon
About the Author: William Woolsey Johnson
The author William Woolsey Johnson
(1841–1927) was a prominent American mathematician and educator known for his innovative approach to teaching "calculus". He taught at the United States Naval Academy and contributed significantly to mathematical education in the U.S., emphasizing the "method of rates" over abstract limit-based approaches. Johnson authored influential textbooks that made "integral calculus" more accessible to students. His work bridged classical Newtonian ideas with modern teaching, covering "differential calculus", multiple integrals, and applications in "geometry" and "probability". As a founding figure of the American Mathematical Society, Johnson’s legacy endures in both pedagogy and the "history of mathematics".
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