An Elementary Treatise on the Calculus by George Gibson (Illustrations from Geometry)
An Elementary Treatise on the Calculus - Table of Contents
1. Coordinates; Functions
2. Graphs — Rational functions
3. Graphs — Algebraic and Transcendental functions; Conic sections
4. Rates; Limits
5. Continuity of functions; Special limits
6. Differentiation — Algebraic functions
7. Differentiation (continued) — Transcendental functions; Higher derivatives
8. Physical applications
9. Mean value theorems; Maxima and minima; Points of inflexion
10. Derived and integral curves; Integral function; Derivatives of area and volume of a surface of revolution; Polar formulae; Infinitesimals
11. Partial differentiation
12. Applications to the theory of equations
13. Integration
14. Definite integrals; Geometrical applications
15. Integral as limit of a sum; Double integrals
16. Curvature; Envelopes
17. Infinite series
18. Taylor’s theorem
19. Taylor’s theorem for functions of two or more variables; Applications
20. Differential equations
What You Will Learn in An Elementary Treatise on the Calculus
"An Elementary Treatise on the Calculus with illustrations from Geometry, Mechanics and Physics" by George Gibson is a foundational textbook aimed at introducing "calculus" to students. First published in the 19th century, it covers essential topics such as "differentiation", "integration", and "limits", offering clear explanations and practical examples. The book’s structured approach helps beginners build a strong understanding of key concepts like rates of change, areas under curves, and the fundamental theorems of calculus.
Gibson’s treatise focuses on the step-by-step development of each topic, making it accessible even to those with minimal mathematical background. The text includes numerous exercises designed to reinforce understanding and deepen comprehension, which is particularly useful for self-study or classroom instruction.
Though written with older mathematical notation and terminology, the book offers valuable insight into the "history" of "mathematics" education and the teaching of calculus. It provides an excellent foundation for anyone looking to understand how calculus was first introduced and how its basic principles were communicated to early learners. While more modern texts have updated the methods and language, Gibson’s work remains a solid resource for historical context or for those interested in classical approaches to teaching calculus.
Book Details & Specifications
Title:
An Elementary Treatise on the Calculus by George Gibson (Illustrations from Geometry)
Publisher:
MacMillan
Year:
1901
Pages:
488
Type:
PDF
Language:
English
ISBN-10 #:
1436770122
ISBN-13 #:
978-1436770125
License:
Public Domain Work
Amazon:
Amazon
About the Author: George Alexander Gibson
The author George Alexander Gibson
was a 19th-century Scottish "mathematician" and educator, known for his contributions to teaching "calculus". He focused on making complex mathematical concepts accessible to beginners, using clear explanations and step-by-step methods. His most famous work, "An Elementary Treatise on the Calculus", introduced students to "differentiation", "integration", and "limits", providing a structured approach with numerous exercises. While not as widely known as some other mathematicians, Gibson’s textbooks were influential in 19th-century "mathematics" education. His work helped shape how calculus was taught, making it a foundational subject in academic curricula.
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