Elements of the Infinitesimal Calculus: With Numerous Examples and Applications to Analysis (Classic Reprint) - Hardcover

James Gregory Clark

9780331981629: Elements of the Infinitesimal Calculus: With Numerous Examples and Applications to Analysis (Classic Reprint)

Hardcover

ISBN 10: 0331981629 ISBN 13: 9780331981629

Publisher: Forgotten Books, 2017

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Master the ideas of limits and the calculus tools that power analysis.

This classic treatment introduces the method of limits as the foundation for both differential and integral calculus, with clear explanations and many worked examples. It emphasizes a sound, educational philosophy and offers numerous applications to real problems in analysis.

The book surveys how quantities approach limits, defines infinitesimals, and builds up the rules of differentiation and integration through rigorous development and practical illustrations. It connects theory to practice with chapters on functions, series, maxima and minima, tangents and normals, curvature, and envelopes of curves, among others.

Foundations of limits and infinitesimals, with emphasis on a solid underlying philosophy
Differential calculus topics: functions, differentiation, and applications to curves
Integral calculus topics: direct integration, substitutions, and quadrature
Worked examples and discussions of geometric and analytic properties of curves

Ideal for students and readers seeking a thorough, classroom-ready presentation of the infinitesimal calculus and its applications to analysis.

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