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The Analytical Theory of Heat (Unabridged) Paperback – March 1, 2007

5.0 out of 5 stars 1 customer review

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Editorial Reviews

Language Notes

Text: English (translation)
Original Language: French --This text refers to an out of print or unavailable edition of this title.

Book Description

Translated by Alexander Freeman in 1878, with additional footnotes, 20 figures and an extensive bibliography, this book presents Fourier's theories of the mathematical laws governing the diffusion of heat in solids. Originally published in French in 1822, Fourier's work changed the way scientists perceived mathematical functions. --This text refers to an alternate Paperback edition.
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Product Details

  • Paperback: 492 pages
  • Publisher: Cosimo Classics; Unabridged edition (March 1, 2007)
  • Language: English
  • ISBN-10: 1602061076
  • ISBN-13: 978-1602061071
  • Product Dimensions: 5.5 x 1.1 x 8.5 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #4,272,135 in Books (See Top 100 in Books)

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Format: Hardcover
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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