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.
- TABLE 2. Circular Functions I
- TABLE 3. Circular Functions II
- TABLE 4. Hyperbolic Functions
- TABLE 5. Lambda Function
- TABLE 6. Gamma Function
- TABLE 7. First Elliptic Integral
- TABLE 8. Second Elliptic Integral
What You Will Learn in Elements of the Infinitesimal Calculus
Elements of the Infinitesimal Calculus by George Chandler is an enduring classical treatise carefully structured to guide university scholars through the fundamental mechanics of calculus. Designed for academic mathematics programs, this volume functions as an ideal guide for infinitesimal calculus Chandler differential equations practice.
The book systematically investigates limits, differentiation rules, transcendental functions, indefinite integration, and geometric applications. By balancing theoretical proofs with direct physical applications, Chandler empowers students to perform essential calculus mathematical proof derivations with complete analytical precision and clarity.
Widely valued by educators for its direct explanations and structured problem sets, this foundational work remains an excellent text for self-guided instruction. Chandler’s clear instructional methodology delivers essential logical frameworks required for mastering modern infinitesimal calculus principles across mathematical disciplines.
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 dedicated 19th-century educator and author known for his impactful contributions to introductory calculus and mathematical pedagogy.
Throughout his teaching career, Chandler focused on simplifying complex analytical tools for undergraduate students. His clear, methodical writing style provided lasting foundational references for educators seeking classical college calculus study materials.
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