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Calculus Reordered

Auteurs

David M. Bressoud

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Calculus Reordered takes readers on a journey through the history of calculus, tracing its development over centuries. David Bressoud explores how calculus is attributed to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure emerged from nineteenth-century advancements. He advocates for a teaching approach informed by this historical context, which he believes enhances student understanding of this complex field. The book delves into the origins of calculus in the Hellenistic Eastern Mediterranean, particularly in Syracuse and Alexandria, as well as its development in India and the Islamic Middle East. Bressoud examines how calculus evolved in response to key questions in engineering and astronomy, highlighting the contributions of figures like Galileo Galilei. In discussing the evolution of calculus, Bressoud critiques the traditional curriculum sequence of limits, differentiation, integration, and series. He proposes that a historical ordering—beginning with integration as accumulation, followed by differentiation as ratios of change, then series as sequences of partial sums, and concluding with limits derived from algebraic inequalities—better serves the classroom environment. By exploring the motivations behind calculus's discovery, the book emphasizes the significance of this mathematical tool.