An Elementary Treatise on the Integral Calculus by William Johnson
An Elementary Treatise on the Integral Calculus - Table of Contents
1. Functions, Rates, and Derivatives
2. The Differentiation of Algebraic Functions
3. The Differentiation of Transcendental Functions
4. The Logarithm
5. Successive Differentiation
6. The Evaluation of Indeterminate Forms
7. Maxima and Minima of Functions of a Single Variable
8. The Development of Functions in Series
9. Curve Tracing
10. Applications of the Differential Calculus to Plane Curves
11. Functions of Two or More Variables
What You Will Learn in An Elementary Treatise on the Integral Calculus
"An Elementary Treatise on the Integral Calculus Founded on the Method of Rates" by William Johnson is a classic guide to "Integral Calculus", providing a clear and structured introduction for students and mathematics enthusiasts. The book focuses on the foundational principles of integration, explaining concepts in a straightforward manner that emphasizes understanding rather than formalism. Johnson’s approach makes it easier for beginners to grasp the logic and techniques behind solving integrals.
The book covers a wide range of "Integration Techniques", from basic forms to more advanced methods, including rational fractions, reduction formulas, and definite integrals. Johnson also highlights practical "Applications" of calculus in geometry and mechanics, such as calculating areas, volumes, curve lengths, and moments of inertia. Each topic is illustrated with examples to reinforce learning and build problem-solving skills.
Rooted in the classical Newtonian perspective, Johnson teaches calculus through the method of "Fluxions", offering an alternative to modern limit-based approaches. His emphasis on "Classical Methods" provides students with a strong intuition for calculus, showing how integrals arise naturally from physical and geometric problems. This treatise remains a valuable resource for anyone seeking a clear, historical, and application-oriented understanding of integral calculus.
Book Details & Specifications
Title:
An Elementary Treatise on the Integral Calculus by William Johnson
Publisher:
J. Wiley & sons
Year:
1893
Pages:
459
Type:
PDF
Language:
English
ISBN-10 #:
B01BKH6HNA
ISBN-13 #:
License:
Public Domain Work
Amazon:
Amazon
About the Author: William Woolsey Johnson
The author William Woolsey Johnson
was a 19th-century mathematician and educator known for his clear and structured approach to teaching calculus. His work focused on making complex concepts accessible to students with a foundational knowledge of algebra and differential calculus. Johnson’s texts were widely used in British schools and universities, shaping the way calculus was taught during his time. His book, "An Elementary Treatise on the Integral Calculus", is a classic guide for understanding the fundamentals of integration. It covers "indefinite and definite integrals", techniques of integration, and practical applications in "geometry" and "physics".
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