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The Analytical Theory Of Heat (1878) | 
| Author: Joseph Fourier
Creator: Alexander Freeman
Publisher: Kessinger Publishing, LLC
Category: Book
List Price: $53.95
Buy New: $35.99
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Avg. Customer Rating:  1 reviews
Sales Rank: 1058789
Media: Hardcover
Number Of Items: 1
Pages: 494
Shipping Weight (lbs): 1.7
Dimensions (in): 9 x 6.1 x 1.4
ISBN: 054896730X
EAN: 9780548967300
ASIN: 054896730X
Publication Date: June 2, 2008
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Product Description
This unabridged republication of Fourier's Theorie Analytique de la Chaleur offers modern readers access to a landmark of modern science. With this work, the great mathematician first showed how any discontinuous function could be represented by a trigonometric series and advanced other concepts of modern mathematical physics. 1878 English translation.
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| Customer Reviews:
A dry classic January 14, 2006
3 out of 4 found this review helpful
The book opens with a long preface and introduction in excellent 19th century style. Chapter 1 also gives the basic principles of heat, such as what we call "Newton's law of cooling" (sec. 3). From here we derive the heat equation (chapter 2, esp. 142). In chapter 3 we solve the heat equation for an infinite rectangle with given boundary conditions. This of course calls for the principles of Fourier analysis, which are explained in full generality (sec. 6). Then in chapters 4-8 we do the same thing for other bodies (rings, spheres, infinite cylinders, infinite rectangular prisms, cubes). In the case of cylinders, Fourier series are not appropriate to solve the corresponding heat equation in polar coordinates, so we must introduce Bessel functions. In chapter 9 we study the diffusion of heat in bodies with no boundary influence. The simplest example is the isolated, infinite line. This leads to Fourier integrals. Throughout, the theory is essentially identical to the modern one, except that Fourier couldn't care less about about convergence and such. It is understandable that Fourier wished to devote an entire book to the rudiments of Fourier analysis. I still think it's a pity that he didn't find it appropriate to include his favourite application: "The problem of the terrestrial temperatures presents one of the most beautiful applications of the theory of heat", he says (12), but does not treat this problem further here.
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