A First Course in Infinitesimal Calculus by Daniel Murray
A First Course in Infinitesimal Calculus - Table of Contents
1. Introductory Problems
2. Algebraic Notions Which Are Frequently Used in the Calculus
3. Infinitesimals, Derivatives, Differentials, Anti-derivatives, and Anti-differentials
4. Differentiation of the Ordinary Functions, General Results in Differentiation
5. Some Geometrical, Physical, and Analytical Applications, Geometric Derivatives and Differentials
6. Successive Differentiation
7. Further Analytical and Geometrical Applications
8. Differentiation of Functions of Several Variables
9. Change of Variable
10. Integration
11. Elementary Integrals
12. Simple Geometrical Applications of Integration
13. Integration of Irrational and Trigonometric Functions
14. Approximate Integration, Mechanical Integration
15. Successive Integration, Multiple Integrals
16. Further Geometrical Applications of Integration
17. Concavity and Convexity, Contact and Curvature, Evolutes and Involutes
18. Special Topics Relating to Curves
19. Infinite Series
20. Taylor’s Theorem
21. Differential Equations
What You Will Learn in A First Course in Infinitesimal Calculus
"A First Course in Infinitesimal Calculus" by Daniel Alexander Murray is a classic introductory "calculus" textbook aimed at beginners in mathematics and applied sciences. It provides a clear and systematic approach to learning the fundamentals of "differential calculus" and "integral calculus", making complex concepts accessible. Murray focuses on real functions, rates of change, and the practical understanding of derivatives, helping students build a solid foundation in calculus.
The book covers essential topics including "derivatives", tangents, maxima and minima, definite and indefinite "integrals", and series expansions. It also demonstrates applications in "geometry", such as calculating areas, volumes, and curves. Numerous worked examples and exercises allow students to practice problem-solving while understanding the reasoning behind each method. Murray emphasizes step-by-step explanations to foster comprehension and build mathematical intuition.
Ideal for beginners, Murray’s textbook balances theory and practical application. Its structured layout and focus on foundational concepts make it a valuable resource for students seeking to master the core principles of calculus. By combining clarity, examples, and applications, "A First Course in Infinitesimal Calculus" remains a timeless introduction to the subject, bridging historical methods with modern learning.
Book Details & Specifications
Title:
A First Course in Infinitesimal Calculus by Daniel Murray
Publisher:
Green & Co.
Year:
1903
Pages:
466
Type:
PDF
Language:
English
ISBN-10 #:
1163633968
ISBN-13 #:
978-1163633960
License:
Public Domain Work
Amazon:
Amazon
About the Author: Daniel Alexander Murray
The author Daniel Alexander Murray
(1862–1934) was a Canadian mathematician and educator known for his contributions to "calculus" and mathematical education. He served as a professor at McGill University, teaching applied mathematics and developing clear, structured textbooks for students learning "differential calculus" and "integral calculus". Murray authored several influential works, including "A First Course in Infinitesimal Calculus", aimed at making complex mathematical concepts accessible. His books emphasized logical progression, worked examples, and applications in "geometry", helping generations of students build a solid foundation in mathematics. His legacy remains significant in the "history of mathematics".
Read or Downloadable A First Course in Infinitesimal Calculus
Free Calculus Books PDF | Download Textbooks & Solutions