Elements of the Differential Calculus by William Byerly
Differential Calculus, with Examples and Applications - Table of Contents
1. Introduction
2. Differentiation of Algebraic Functions
3. Applications (Tangents and Normals)
4. Transcendental Functions
5. Integration
6. Curvature
7. The Cycloid
8. Problems in Mechanics
9. Development of Series
10. Infinitesimals
11. Differentials
12. Functions of More Than One Variable (Partial Derivatives)
13. Change of Variables
14. Tangent Lines and Planes in Space
15. Development of a Function of Several Variables
16. Maxima and Minima of Functions of Two or More Variables
17. The Theory of Plane Curves
What You Will Learn in Differential Calculus, with Examples and Applications
"Elements of the Differential Calculus, with Examples and Applications" by "William Byerly" is a clear, practical introduction to early calculus, widely used in U.S. colleges during the late 19th century. Written with a straightforward teaching style, the book focuses on making core ideas understandable rather than overly formal. Byerly begins with the basic meaning of a "limit", the idea of continuity, and the derivative as a geometric and numerical tool.
The text moves smoothly into the main rules of differentiation, covering algebraic, trigonometric, and logarithmic functions. What sets the book apart is its strong emphasis on "examples", showing students exactly how to compute and apply derivatives step by step. Readers also encounter classic calculus problems such as finding tangents, determining "maxima and minima", solving simple "differential equations", and analyzing curves—skills that were essential for science and engineering studies of the time.
Byerly’s work stands out for its clarity, practical focus, and historical importance. Although less rigorous than modern textbooks, it remains valuable for understanding how calculus was taught and learned in earlier eras. The book’s accessible explanations, combined with its steady progression from concept to application, make it a noteworthy resource for students, educators, and anyone interested in the development of "calculus" education.
Book Details & Specifications
Title:
Elements of the Differential Calculus by William Byerly
Publisher:
Ginn & Co.
Year:
1879
Pages:
282
Type:
PDF
Language:
English
ISBN-10 #:
333781297X
ISBN-13 #:
978-3337812973
License:
Public Domain Work
Amazon:
Amazon
About the Author: William Elwood Byerly
The author William Elwood Byerly
(1849–1935) was a renowned American mathematician and educator, best known for his contributions to "calculus education". A Harvard University alumnus and professor, Byerly focused on making complex concepts in "differential calculus" clear and accessible. He emphasized step-by-step explanations and practical "examples", helping students bridge theory with application. Byerly authored influential textbooks, including "Elements of the Differential Calculus, with Examples and Applications", which shaped American mathematics teaching in the late 19th and early 20th centuries. His work greatly impacted "mathematics" pedagogy and remains significant for students and educators studying the history of mathematical learning.
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