A Treatise On The Differential Calculus by Isaac Todhunter
A Treatise On The Differential Calculus - Table of Contents
1. Definitions, Limit, Infinite
2. Definition of a Differential Coefficient, Differential Coefficient of a Sum, Product, and Quotient
3. Differential Coefficients of Simple Functions
4. Differential Coefficients of the Inverse Trigonometric Functions and of Complex Functions
5. Successive Differentiation
6. Expansion of Functions in Series
7. Examples of Expansion of Functions
8. Successive Differentiation; Differentiation of a Function of Two Variables
9. Lagrange's Theorem and Laplace's Theorem
10. Limiting Values of Functions Which Assume an Indeterminate Form
11. Differential Coefficient of a Function of Functions and of Implicit Functions
12. Change of the Independent Variable
13. Maxima and Minima Values of a Function of One Variable
14. Expansion of a Function of Two Independent Variables
15. Maxima and Minima Values of a Function of Two Independent Variables
16. Maxima and Minima Values of a Function of Several Variables
17. Elimination of Constants and Functions
18. Tangent and Normal to a Plane Curve
19. Asymptotes
20. Tangents and Asymptotes of Curves Referred to Polar Coordinates
21. Concavity and Convexity
22. Singular Points
23. Differential Coefficient of an Arc, an Area, a Volume, and a Surface
24. Contact, Curvature, Evolutes, and Involutes
25. Envelopes
26. Tracing of Curves
27. On Differentials
28. Miscellaneous Propositions
What You Will Learn in A Treatise On The Differential Calculus
"A Treatise on the Differential Calculus" by Isaac Todhunter is a classic 19th-century textbook that provides a clear and systematic introduction to "differential calculus". Designed for students and self-learners, it covers the fundamentals of derivatives, rules of differentiation, and applications to algebraic and trigonometric functions. Todhunter’s writing emphasizes clarity, making complex concepts like "higher-order derivatives" and implicit differentiation accessible through well-explained examples.
The book also explores advanced topics, including "Taylor and Maclaurin series", maxima and minima, concavity, and curve tracing. It bridges the gap between pure analysis and geometry by applying calculus to tangents, normals, areas, volumes, and surfaces. Readers benefit from its structured approach, which gradually introduces multivariable functions, limiting values, and indeterminate forms. Todhunter’s meticulous treatment of examples ensures that learners gain both theoretical understanding and practical problem-solving skills.
Widely regarded for its pedagogical clarity and historical significance, the book remains a valuable resource for mathematicians, educators, and enthusiasts of "classical calculus". Its comprehensive coverage, logical progression, and practical applications make it an enduring reference in mathematical education. Todhunter’s work not only teaches the mechanics of differential calculus but also nurtures analytical thinking and a deeper appreciation of mathematical structure.
Book Details & Specifications
Title:
A Treatise On The Differential Calculus by Isaac Todhunter
Publisher:
Macmillan
Year:
1871
Pages:
440
Type:
PDF
Language:
English
ISBN-10 #:
1145809774
ISBN-13 #:
978-1145809772
License:
Public Domain Work
Amazon:
Amazon
About the Author: Isaac Todhunter
The author Isaac Todhunter
(1820–1884) was a British mathematician and educator, famous for his clear and systematic textbooks on "calculus, algebra, and trigonometry". Educated at Cambridge University, he specialized in making complex mathematical concepts accessible through detailed explanations and practical examples. His works, including "A Treatise on the Differential Calculus", became standard references for students and teachers in the 19th century. Todhunter also wrote extensively on the "history of mathematics", combining rigorous theory with historical insights. His pedagogical approach emphasized logical structure, clarity, and application, making him a highly influential "mathematics author" whose legacy continues in classical "mathematical education".
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