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

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ISBN: 9780691181318 | 242 pages | 7 Mb

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

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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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Fractional Calculus: History, Definitions and Applications for the reader to the concepts, applicable definitions, and execution of fractional calculus (including a discussion .. Algebraically, we can reorder the result in (40) into one of two forms. ˜u(s) = sα . Consider the value of Γ(z) for large values of z. At. David Bressoud - Macalester College
Characteristics of Successful Programs in College Calculus (NSF #0910240) A five-year NSF-sponsored study Calculus Reordered: A History of the Big Ideas. Calculus Reordered: A History of the Big Ideas, David M. Bressoud
Editorial Reviews. Review. “I wish David Bressoud's beautifully and accessibly written book had been available to me back when I was a mathematics student.

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