## Free textbook downloads Calculus Reordered: A History of the Big Ideas by David M. Bressoud iBook 9780691181318 in English

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## Calculus Reordered: A History of the Big Ideas by David M. Bressoud

- Calculus Reordered: A History of the Big Ideas
- David M. Bressoud
- Page: 242
- Format: pdf, ePub, mobi, fb2
- ISBN: 9780691181318
- Publisher: Princeton University Press

Download Calculus Reordered: A History of the Big Ideas

### Free textbook downloads Calculus Reordered: A History of the Big Ideas by David M. Bressoud iBook 9780691181318 in English

How our understanding of calculus has evolved over more than three centuries, how this has shaped the way it is taught in the classroom, and why calculus pedagogy needs to change Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus’s birth in the Hellenistic Eastern Mediterranean—particularly in Syracuse, Sicily and Alexandria, Egypt—as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus’s evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order—integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities—makes more sense in the classroom environment. Exploring the motivations behind calculus’s discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.

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The standard order of the four big ideas of calculus—limits then derivatives then integrals then series—is historically and pedagogically problematic. Drawing on
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Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of
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This article explores the history of calculus before Newton and Leibniz: the people, known by the Latinized form of his name: Alhazen) was one of the great Arab . The idea is to approximate the area using ever-smaller pieces whose area . We reorder the last sum, putting the fourth powers together and regrouping so
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