The Mathematical Experience |
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Page 257
... series ? These questions , raised by the practical demands of Fourier analysis , have taxed the efforts of every great ana- lyst since Euler and Bernoulli ; they are still receiving new answers today . One new answer , a very practical ...
... series ? These questions , raised by the practical demands of Fourier analysis , have taxed the efforts of every great ana- lyst since Euler and Bernoulli ; they are still receiving new answers today . One new answer , a very practical ...
Page 262
... Fourier series ! No wonder Lagrange , the eighteenth century analyst par excellence , found Fourier's claim hard to swallow . How Fourier Calculated Of course an essential step in Fourier's work was to find the formula for the coefficients ...
... Fourier series ! No wonder Lagrange , the eighteenth century analyst par excellence , found Fourier's claim hard to swallow . How Fourier Calculated Of course an essential step in Fourier's work was to find the formula for the coefficients ...
Page 265
... Fourier series . Indeed , since the area under such a " curve " is undefined , and since the Euler coefficients are obtained by integrating ( i.e. , computing an area ) , Fourier could not have found even a single term of the Fourier ...
... Fourier series . Indeed , since the area under such a " curve " is undefined , and since the Euler coefficients are obtained by integrating ( i.e. , computing an area ) , Fourier could not have found even a single term of the Fourier ...
Other editions - View all
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience: Study Edition Philip J. Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 1995 |
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abstract aesthetic algebra algorithmic analysis analytic answer applications argument arithmetic asserts axiom of choice Bibliography calculus called century circle complex conjecture construct continuum hypothesis course definition differential equations elements ematics Euclid Euclidean geometry Euler example existence experience fact figure finite formal language formalist formula Fourier Fourier series function Further Readings G. H. Hardy Hilbert human hypercube hypersquares idea ideal infinite set infinitesimal infinity integers intuition knowledge Lakatos logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers non-Euclidean geometry non-Riemannian nonstandard notion number theory parallel postulate philosophy of mathematics physical Platonism Platonist possible postulate prime number prime number theorem problem proof proved question real numbers reason restricted set theory result rigorous sense solution square statement straight line symbols theorem thing tion triangle true truth universe words zero