Calculus Reordered (eBook)

A History of the Big Ideas

David M. Bressoud (Autor)

eBook Download: PDF

2019
242 Seiten
Princeton University Press (Verlag)
978-0-691-18916-1 (ISBN)

Infos

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 changeCalculus 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.

Autor

David M. Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and Director of the Conference Board of the Mathematical Sciences. His many books include Second Year Calculus and A Radical Approach to Lebesgue’s Theory of Integration. He lives in St. Paul, Minnesota.

Produkt-Details

• Erscheint lt. Verlag: 16.7.2019
• Zusatzinfo: 74 b/w illus. 1 table.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Naturwissenschaften
• Schlagworte: Addition • Adequality • Algebra • algebraic equation • analytic geometry • Antiderivative • Approximation • arc length • Area of a circle • arithmetic • Astronomy • Basel problem • Bernhard Riemann • Binomial series • Calculation • Cardinality • Carl Friedrich Gauss • Cartesian coordinate system • Cauchy Sequence • circumference • coefficient • complex plane • continuous function • Continuous function (set theory) • Continuum Hypothesis • counterexample • Cours d'analyse • David Hilbert • Derivative • Differential Calculus • differential equation • elliptic function • Equation • error • Euler's formula • exponential function • For All Practical Purposes • Fourier • Fourier series • Function (mathematics) • fundamental theorem • Geometric series • Geometry • Georg Cantor • hilbert space • Horologium Oscillatorium • Hyperbolic function • Inequality (mathematics) • Infinitesimal • Instant • Interval (mathematics) • Isaac Barrow • Jacob Bernoulli • Karl Weierstrass • Lebesgue integration • Leonhard Euler • Liber Abaci • Lipman Bers • logarithm • Marin Mersenne • mathematician • Mathematics • Maxima and minima • mean value theorem • Method of exhaustion • natural logarithm • Natural number • Newton's method • Nicole Oresme • Notation • On the Sphere and Cylinder • parallelogram • partial differential equation • Pierre de Fermat • polynomial • power series • Proportionality (mathematics) • Quadratic equation • Quantity • Ratio • Rational number • ratio test • real number • rectangle • Riemann integral • scientific notation • Series (mathematics) • Special case • Srinivasa Ramanujan • Subset • Summation • Tangent • Taylor series • Taylor's theorem • Theorem • The Whetstone of Witte • Trigonometric Functions • Variable (mathematics) • Velocity • Zermelo–Fraenkel set theory
• ISBN-10: 0-691-18916-1 / 0691189161
• ISBN-13: 978-0-691-18916-1 / 9780691189161