Leseprobe
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
Calculus Reordered
David M. Bressoud
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Variable (mathematics), Hyperbolic function, Elliptic function, The Whetstone of Witte, Cardinality, Natural number, Algebra, Differential equation, Geometry, Fundamental theorem, Antiderivative, Summation, Coefficient, Error, Natural logarithm, Tangent, Lebesgue integration, Scientific notation, Calculation, Bernhard Riemann, Infinitesimal, Instant, Maxima and minima, Geometric series, Function (mathematics), Mathematics, Mathematician, Mean value theorem, Rectangle, Velocity, Approximation, Fourier series, Ratio test, Complex plane, Quadratic equation, Equation, Addition, Trigonometric functions, Isaac Barrow, Taylor series, Arc length, Power series, Interval (mathematics), Differential calculus, Cauchy sequence, Derivative, Newton's method, Series (mathematics), Proportionality (mathematics), Exponential function, Horologium Oscillatorium, Continuous function, Area of a circle, Cartesian coordinate system, Basel problem, Special case, Rational number, Continuum hypothesis, Partial differential equation, Subset, Karl Weierstrass, Jacob Bernoulli, Zermelo–Fraenkel set theory, Real number, Circumference, Logarithm, Notation, Polynomial, Theorem, Quantity