An Introduction to the Infinitesimal Calculus by Horatio Carslaw
An Introduction to the Infinitesimal Calculus - Table of Contents
1. Co-Ordinate Geometry
2. The Meaning Of Differentiation
3. Differentiation Of Algebraic Functions; And Some General Theorems In Differentiation
4. The Differentiation Of The Trigonometric Functions
5. The Exponential And Logarithmic Functions; Maxima And Minima; Partial Differentiation
6. The Conic Sections
7. The Integral Calculus, Integration
8. The Definite Integral And Its Applications
What You Will Learn in An Introduction to the Infinitesimal Calculus
"An Introduction to the Infinitesimal Calculus" by Horatio Scott Carslaw is a classic "introductory calculus" textbook designed for science and engineering students. First published in 1905, the book focuses on simplifying the core concepts of differentiation and integration for practical applications, rather than deep theoretical proofs. Carslaw’s approach ensures that students with only basic algebra and trigonometry can understand and apply calculus methods effectively.
The book is structured to balance theory with real-world "applications", providing numerous examples relevant to physics, engineering, and other scientific fields. While some proofs are outlined rather than fully detailed, this practical emphasis allows learners to quickly grasp essential techniques and apply them to problems in mechanics, geometry, and dynamics. Its concise format makes it ideal for a first course in calculus, especially in engineering programs where time is limited.
Historically, the text reflects early 20th-century efforts to make calculus accessible for non-mathematics majors. Its clear explanations and focus on practical use make it a valuable resource for both historical study and self-guided learning. Though modern textbooks may offer updated notation and expanded content, Carslaw’s work remains notable for its "educational clarity" and enduring influence in applied mathematics teaching.
Book Details & Specifications
Title:
An Introduction to the Infinitesimal Calculus by Horatio Carslaw
Publisher:
Longmans, Green
Year:
1905
Pages:
122
Type:
PDF
Language:
English
ISBN-10 #:
1436889170
ISBN-13 #:
978-1436889179
License:
Public Domain Work
Amazon:
Amazon
About the Author: Horatio Scott Carslaw
The author
Horatio Scott Carslaw
(1870–1954) was a Scottish-born mathematician and Professor of Mathematics at the "University of Sydney". Educated at the University of Glasgow and Cambridge, he excelled in mathematics and physics, earning a reputation for clarity and rigor. Carslaw specialized in "applied mathematics", particularly in the mathematical theory of heat conduction, and his textbooks, including "An Introduction to the Infinitesimal Calculus", aimed to make complex topics accessible for science and engineering students. Beyond research, Carslaw influenced mathematics education in Australia, shaping secondary school curricula and fostering a strong connection between "teaching" and practical applications. His legacy endures through his publications and contributions to applied mathematics.
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