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Calculus reordered : a history of the big ideas

Author: David M Bressoud
Publisher: Princeton, New Jersey : Princeton University Press, [2019]
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical  Read more...
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Genre/Form: Electronic books
History
Additional Physical Format: Print version:
BRESSOUD, DAVID M.
CALCULUS REORDERED.
[Place of publication not identified], PRINCETON University PRES, 2019
(OCoLC)1059262130
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David M Bressoud
ISBN: 9780691189161 0691189161
OCLC Number: 1091029414
Description: 1 online resource (xvi, 224 pages) : illustrations
Contents: Cover; Contents; Preface; Chapter 1. Accumulation; 1.1. Archimedes and the Volume of the Sphere; 1.2. The Area of the Circle and the Archimedean Principle; 1.3. Islamic Contributions; 1.4. The Binomial Theorem; 1.5. Western Europe; 1.6. Cavalieri and the Integral Formula; 1.7. Fermat's Integral and Torricelli's Impossible Solid; 1.8. Velocity and Distance; 1.9. Isaac Beeckman; 1.10. Galileo Galilei and the Problem of Celestial Motion; 1.11. Solving the Problem of Celestial Motion; 1.12. Kepler's Second Law; 1.13. Newton's Principia; Chapter 2. Ratios of Change; 2.1. Interpolation 2.2. Napier and the Natural Logarithm; 2.3. The Emergence of Algebra; 2.4. Cartesian Geometry; 2.5. Pierre de Fermat; 2.6. Wallis's Arithmetic of Infinitesimals; 2.7. Newton and the Fundamental Theorem; 2.8. Leibniz and the Bernoullis; 2.9. Functions and Differential Equations; 2.10. The Vibrating String; 2.11. The Power of Potentials; 2.12. The Mathematics of Electricity and Magnetism; Chapter 3. Sequences of Partial Sums; 3.1. Series in the Seventeenth Century; 3.2. Taylor Series; 3.3. Euler's Influence; 3.4. D'Alembert and the Problem of Convergence; 3.5. Lagrange Remainder Theorem Teaching Series as Sequences of Partial Sums; Teaching Limits as the Algebra of Inequalities; The Last Word; Notes; Bibliography; Index; Image Credits
Responsibility: David M. Bressoud.

Abstract:

Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, 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 presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in 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 instead that the historical order--which follows first 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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"In an orderly sense, the writer introduces the context and then proceeds to state exactly what was the major draw back in the context during the relevant period of time. . . The progression, as well Read more...

 
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