Analysis by Its HistorySpringer Science & Business Media, 2 jun 2008 - 382 pagina's . . . that departed from the traditional dry-as-dust mathematics textbook. (M. Kline, from the Preface to the paperback edition of Kline 1972) Also for this reason, I have taken the trouble to make a great number of drawings. (Brieskom & Knorrer, Plane algebraic curves, p. ii) . . . I should like to bring up again for emphasis . . . points, in which my exposition differs especially from the customary presentation in the text books: 1. Illustration of abstract considerations by means of figures. 2. Emphasis upon its relation to neighboring fields, such as calculus of dif ferences and interpolation . . . 3. Emphasis upon historical growth. It seems to me extremely important that precisely the prospective teacher should take account of all of these. (F. Klein 1908, Eng\. ed. p. 236) Traditionally, a rigorous first course in Analysis progresses (more or less) in the following order: limits, sets, '* continuous '* derivatives '* integration. mappings functions On the other hand, the historical development of these subjects occurred in reverse order: Archimedes Cantor 1875 Cauchy 1821 Newton 1665 . ;::: Kepler 1615 Dedekind . ;::: Weierstrass . ;::: Leibniz 1675 Fermat 1638 In this book, with the four chapters Chapter I. Introduction to Analysis of the Infinite Chapter II. Differential and Integral Calculus Chapter III. Foundations of Classical Analysis Chapter IV. Calculus in Several Variables, we attempt to restore the historical order, and begin in Chapter I with Cardano, Descartes, Newton, and Euler's famous Introductio. |
Inhoudsopgave
Gedeelte 1 | 1 |
Gedeelte 2 | 80 |
Gedeelte 3 | 105 |
Gedeelte 4 | 106 |
Gedeelte 5 | 142 |
Gedeelte 6 | 155 |
Gedeelte 7 | 170 |
Gedeelte 8 | 225 |
Gedeelte 11 | 279 |
Gedeelte 12 | 281 |
Gedeelte 13 | 301 |
Gedeelte 14 | 305 |
Gedeelte 15 | 312 |
Gedeelte 16 | 313 |
Gedeelte 17 | 314 |
Gedeelte 18 | 332 |
Overige edities - Alles bekijken
Veelvoorkomende woorden en zinsdelen
a² f Algebra apply arctan Bernoulli bounded calculus Cauchy product Cauchy sequence coefficients compute consider the function constant continuous at xo continuous function convergence cos² counterexample curve Darboux sums defined Definition denote Descartes differentiable at xo differential equation Euler example Exercise exists f(xo FIGURE fn(x formula fraction function f(x geometric given ɛ grad Hence infinite series integral interval inverse Lagrange Leibniz Lemma Let f limit linear logarithms Math mathematics Newton norm null set obtain Oeuvres partial derivatives Peano permission of Bibl polynomial Proof prove radius of convergence real number Reproduced with permission Riemann roots satisfying Sect Show sin² solution Taylor series Theorem triangle inequality uniform convergence uniformly continuous variables vector Weierstrass მყ
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Mathematics Teaching Practice: Guide for University and College Lecturers J H Mason Geen voorbeeld beschikbaar - 2002 |