Elements of the Infinitesimal Calculus by George Chandler - PDF

Elements of the Infinitesimal Calculus by George Chandler - PDF - 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 by George Chandler - PDF

"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 - PDF
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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