On a New Method of Obtaining the Differentials of Functions With Especial Reference to the Newtonian Conception of Rates or Velocities (Classic Reprint) - Tapa blanda

Sinopsis

This book delves into the fascinating history of calculus, offering a fresh perspective on the influential Newtonian method of fluxions. The author takes a unique approach, challenging the prevailing methods of the time that relied on limits and infinitesimals. By advocating for a return to Newton's original framework, the book argues for the clarity and accessibility of fluxions, especially for those new to the subject. It examines the objections raised against Newton's method, demonstrating their lack of merit when applied to the author's proposed approach. The book offers a thorough exploration of the concepts of differentials and rates, using clear definitions and notation. It delves into the calculation of differentials for a range of functions, from algebraic expressions to transcendental functions like logarithms and trigonometric functions. The author skillfully uses the method of rates to derive formulas for areas and volumes, showcasing the applicability of the approach beyond theoretical calculations. The book concludes by advocating for the continued relevance of the fluxional method, highlighting its potential for illuminating the foundational concepts of calculus in a way that is both rigorous and easily understood.

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