Differential & Integral Calculus and Variations by Thomas Hall
Differential & Integral Calculus and Variations - Table of Contents
Part-I Differential Calculus
1. Definitions and Principles
2. Differentiation of Circular Functions
3. Successive Differentiation
4. Taylor's Theorem
5. Failure of Taylor's Theorem—Explanation of the Term
6. PAGE Vanishing Fractions
7. Maxima and Minima defined
8. Functions of two or more Variables
9. Maxima and Minima of Functions of two Variables
10. Equations to Curves
11. Tangents to Curves—Equation to Tangent
12. I'Abh The Differentials of the Areas and Lengths of Curve?
13. Singular Points in Curves
14. Curvature and Osculating Curves
15. Envelopes to Curves
16. Change of the Independent Variable
Part-II Integral Calculus
1. Definition of Integration
2. Rational Fractions
3. Irrational Quantities
4. Integration of Logarithmic and Exponential Functions
5. Integration of Circular Functions
6. Methods of finding the Areas and Lengths of Curves, aiul the Volumes and Surfaces of Solids
7. Differential Equations, Order and Degree of
8. Calculus of Variations
What You Will Learn in Differential & Integral Calculus and Variations
The textbook A Treatise On the Differential and Integral Calculus: And the Calculus of Variations by Thomas Granger Hall is a classic mathematics book covering both fundamental and advanced topics in "calculus". It begins with clear explanations of "differential calculus" and "integral calculus", focusing on essential concepts like limits, derivatives, and integrals. This foundation prepares readers for deeper study and practical application.
The book progresses to the "calculus of variations", an important branch that deals with optimizing functionals—mathematical expressions depending on functions. This field has wide applications in physics, engineering, and optimization problems. Hall’s treatise helps readers understand these advanced concepts through a systematic and approachable style.
Though published in the 19th century, Hall’s work remains a valuable resource for students and scholars interested in the "historical development of calculus". Its logical structure and detailed explanations make complex mathematical ideas accessible. This treatise is ideal for those seeking both a strong foundation in classical calculus and an introduction to its advanced applications.
Book Details & Specifications
Title:
Differential & Integral Calculus and Variations by Thomas Hall
Publisher:
J. W. Parker, London
Year:
1846
Pages:
460
Type:
PDF
Language:
English
ISBN-10 #:
1022138545
ISBN-13 #:
978-1022138544
License:
Public Domain Work
Amazon:
Amazon
About the Author: Thomas Grainger Hall
The author
Thomas Grainger Hall
was a 19th-century mathematician and educator known for his contributions to the field of calculus. His most notable work is *A Treatise on the Differential and Integral Calculus: And the Calculus of Variations*, which offers a comprehensive exploration of both foundational and advanced topics in calculus. Published in the 19th century, this treatise has been recognized for its systematic approach and clarity in presenting complex mathematical concepts. Hall's life are limited but his academic influence is evident through his published works. His treatise has been republished in various formats, indicating its enduring value in the study of mathematics. His work remains a valuable resource for students and scholars interested in the historical development of calculus.
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