A Treatise On The Differential Calculus by Isaac Todhunter - PDF

About this book :-
"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 Detail :-
Title: A Treatise On The Differential Calculus by Isaac Todhunter - PDF
Publisher: Macmillan
Year: 1871
Pages: 440
Type: PDF
Language: English
ISBN-10 #: 1145809774
ISBN-13 #: 978-1145809772
License: Public Domain Work
Amazon: Amazon

About Author :-
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".

Book 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

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