Elements of the Infinitesimal Calculus by George Chandler
Elements of the Infinitesimal Calculus - Table of Contents
1. Limits. Infinitesimals
2. Functions. Derivatives. Differentials
3. Differential of a Power, a Product, and a Quotient
4. Tangents and Normals
5. Differentials of Exponentials and Logarithms
6. Differentials of Direct Circular Functions
7. Differentials of Inverse Circular Functions
8. Differentials of Hyperbolic Functions
9. Differentials as Infinitesimals
10. Functions of More Than One Variable
11. Small Differences
12. Multiple Points
13. Asymptotes
14. Tangent Planes. Tangents to Curves in Space
15. Successive Differentiation
16. Rates
17. Maxima and Minima
18. Curvature
19. Integration. Elementary Illustrations
20. Fundamental Integrals I
21. Fundamental Integrals II
22. Fundamental Integrals III
23. Fundamental Integrals IV
24. Integration of Rational Fractions
25. Integration by Substitution
26. Integration by Parts
27. Successive Reduction
28. Certain Definite Integrals
29. Areas and Lengths of Plane Curves. Surfaces and Volumes of Solids of Revolution
30. Simpson's Rule. Volumes from Parallel Sections. The Prismoidal Formula. Length of a Curve in Space
31. Polar Coordinates
32. Associated Curves
33. Centres of Gravity
34. Moments of Inertia
35. Successive Integration
36. Mean Values
37. Intrinsic Equation of a Curve. The Tractrix. The Catenary
38. Infinite Series
39. Taylor's Theorem
40. Fourier's Series
41. Approximate Integration. Elliptic Integrals
42. Singular Forms
43. Successive Differentials of Functions of More Than One Variable. Extension of Taylor's Theorem. Maxima and Minima from Taylor's Theorem
44. Differential Equations of the First Order
45. Differential Equations of the Second Order
A. Partial Fractions
B. Curve Tracing
C. Hyperbolic Functions
D. Mechanical Integration
TABLE
1. Powers, Napierian Logarithms, etc.
2. Circular Functions I
3. Circular Functions II
4. Hyperbolic Functions
5. Lambda Function
6. Gamma Function
7. First Elliptic Integral
8. Second Elliptic Integral
What You Will Learn in Elements of the Infinitesimal Calculus
"Elements of the Infinitesimal Calculus" by "George Chandler" is a classic textbook that introduces the fundamentals of "infinitesimal calculus" for students and self-learners. Designed for beginners, it emphasizes the conceptual foundations of calculus, focusing on "limits", infinitesimals, and the logical development of mathematical ideas. The book balances clarity with rigor, making complex topics accessible without sacrificing depth.
The text covers essential topics including "differentiation", the rules of derivatives, and basic integration, with detailed examples and explanations. Chandler presents these concepts step by step, helping students understand the reasoning behind each method rather than just memorizing formulas. Applications to functions, curves, and practical problems are included to illustrate the relevance of calculus in "engineering" and applied sciences.
Chandler’s book remains a valuable resource for anyone seeking a strong conceptual grounding in calculus. Its classical approach provides historical insight into how infinitesimal calculus was taught while still offering a solid foundation for modern learning. By focusing on core "calculus principles" and problem-solving techniques, the book helps readers develop both understanding and confidence in applying calculus to real-world situations.
Book Details & Specifications
Title:
Elements of the Infinitesimal Calculus by George Chandler
Publisher:
J. Wiley & sons
Year:
1907
Pages:
359
Type:
PDF
Language:
English
ISBN-10 #:
0526038438
ISBN-13 #:
978-0526038435
License:
Public Domain Work
Amazon:
Amazon
About the Author: George Henry Chandler
The author George Henry Chandler
was a mathematician and educator, known for his work on "infinitesimal calculus". He authored "Elements of the Infinitesimal Calculus" to provide a clear, logical introduction to "limits", "differentiation", and fundamental "calculus principles" for beginners. Chandler’s book was designed for students in "engineering" and applied sciences, emphasizing understanding over rote memorization. By systematically presenting calculus concepts and practical applications, he made complex topics accessible.
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