A History of Mathematics: An IntroductionA History of Mathematics, Third Edition, provides students with a solid background in the history of mathematics and focuses on the most important topics for today's elementary, high school, and college curricula. Students will gain a deeper understanding of mathematical concepts in their historical context, and future teachers will find this book a valuable resource in developing lesson plans based on the history of each topic. This book is ideal for a junior or senior level course in the history of mathematics for mathematics majors intending to become teachers. |
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Page 782
... function . " Fourier next investigated the representation of various functions by series of trigonometric functions , the most general being the series of the form co + c1 cos x + c2 cos 2x + ··· + dj sin x + d2 sin 2x + .... Usually ...
... function . " Fourier next investigated the representation of various functions by series of trigonometric functions , the most general being the series of the form co + c1 cos x + c2 cos 2x + ··· + dj sin x + d2 sin 2x + .... Usually ...
Page 783
... function of Figure 22.4 over the entire real line . Abel realized not only that this function violated Cauchy's result on the sum of a series of continuous functions , but also that Fourier's attempts at a proof that the Fourier series ...
... function of Figure 22.4 over the entire real line . Abel realized not only that this function violated Cauchy's result on the sum of a series of continuous functions , but also that Fourier's attempts at a proof that the Fourier series ...
Page 785
... function integrable and in what cases not ? Cauchy himself had only shown that a certain class of functions was integrable , but had not tried to find all such functions . Riemann , on the other hand , formulated a necessary and ...
... function integrable and in what cases not ? Cauchy himself had only shown that a certain class of functions was integrable , but had not tried to find all such functions . Riemann , on the other hand , formulated a necessary and ...
Contents
PART ONE Ancient Mathematics | 1 |
3 | 43 |
References and Notes | 49 |
Copyright | |
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al-Khwarizmi algebra algorithm Almagest angle Apollonius Archimedes arithmetic astronomical axis Babylonian basic Bernoulli Book Brahmagupta calculate century chapter Chinese Chinese Mathematics chord circle coefficients conic sections consider construction cube cubic equation curve derived Descartes determine diameter difference differential Diophantus discussed distance divided Elements ellipse equal Euclid Euclid's Elements Euler example Fermat FIGURE fluxion formula fractions function geometric given number Greek mathematics Hipparchus hyperbola Ibid ideas Indian infinite integral intersection Islamic known Leibniz length logarithm mathematicians method modern notation motion multiplied Newton noted parabola parallel perpendicular plane polynomial positive probably problem procedure proof proportion Proposition proved Ptolemy Ptolemy's Pythagorean Theorem quadratic equation quantities radius ratio rectangle represent result right triangle rule side sine solution solve sphere square root straight line subtract tangent theorem translated treatise trigonometry velocity