Elements of the Differential Calculus By James McMahon, Virgil Snyder
Elements of the Differential Calculus - Table of Contents
0. Introduction
1. Fundamental Principles
2. Differentiation of the Elementary Forms
3. Successive Differentiation
4. Expansion of Functions
5. Indeterminate Forms
6. Mode of Variation of Functions of One Variable
7. Rates and Differentials
8. Differentiation of Functions of More Than One Variable
9. Successive Partial Differentiation
10. Maxima and Minima of Functions of Two Variables
11. Change of the Variable
12. Tangents and Normals
13. Derivative of an Arc, Area, Volume, and Surface of Revolution
14. Asymptotes
15. Direction of Bending. Points of Inflexion
16. Contact and Curvature
17. Singular Points
18. Curve Tracing
19. Envelopes
What You Will Learn in Elements of the Differential Calculus
"Elements of the Differential Calculus" by "James McMahon" and "Virgil Snyder" is a classic textbook that introduces the foundations of "differential calculus" for undergraduate students. First published in the late 19th century, the book provides a clear and rigorous treatment of "derivatives", limits, and infinitesimals. It is designed to balance accessibility with mathematical precision, making it suitable for students in engineering, mathematics, and related fields.
The book covers fundamental topics such as the definition and geometric interpretation of the derivative, "rules of differentiation", higher-order derivatives, and series expansions like Maclaurin and Taylor series. It also explores applications in "curve analysis", including maxima, minima, monotonicity, and concavity. While primarily focused on single-variable functions, it introduces some concepts for functions of multiple variables and implicit differentiation, maintaining clarity for first-year students.
Renowned for its classical approach, "Elements of the Differential Calculus" emphasizes understanding over rote computation. Its historical significance lies in providing a rigorous yet approachable foundation in calculus, bridging the gap between elementary textbooks and advanced treatises. Despite its traditional notation, it remains a valuable resource for students and enthusiasts seeking a deep conceptual grasp of "calculus principles".
Book Details & Specifications
Title:
Elements of the Differential Calculus By James McMahon, Virgil Snyder
Publisher:
American Book Company
Year:
1898
Pages:
368
Type:
PDF
Language:
English
ISBN-10 #:
1436833396
ISBN-13 #:
978-1436833394
License:
Public Domain Work
Amazon:
Amazon
About the Author: James McMahon, Virgil Snyder
The author James McMahon, Virgil Snyder
and "Virgil Snyder" were prominent American mathematicians associated with "Cornell University". McMahon specialized in "calculus" and geometry, known for making complex concepts clear and accessible for students. Snyder, a leading figure in "algebraic geometry", contributed his research expertise to ensure rigorous mathematical explanations. Together, they authored *Elements of the Differential Calculus*, blending educational clarity with scholarly precision. The book emphasizes "derivatives", limits, and proofs, providing a strong foundation in "mathematical principles".
Read or Downloadable Elements of the Differential Calculus
Free Differential Calculus Books PDF | Download Study Guides