The Analytical Theory of Heat (Classic Reprint), by Joseph Fourier
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The Analytical Theory of Heat (Classic Reprint), by Joseph Fourier
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Excerpt from The Analytical Theory of HeatStatement of the Object of the Work: Object of the theoretical researches; Different examples, ring, cube, sphere, infinite prism; the variable temperature at any point whatever is a function of the coordinates and of the time. The quantity of heat, which during unit of time crosses a given surface in the interior of the solid, is also a function of the time elapsed, and of quantities which determine the form and position of the surface. The object of the theory is to discover these functions; The three specific elements which must be observed, are the capacity, the conductibility proper or permeability, and the external conductibility or penetrability. The coefficients which express them may be regarded at first as constant numbers, independent of the temperatures; First statement of the problem of terrestrial temperatures; Conditions necessary to applications of the theory. Object of the experiments; The rays of heat which escape from the same point of a surface have not the same intensity. The intensity of each ray is proportionalAbout the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
The Analytical Theory of Heat (Classic Reprint), by Joseph Fourier- Amazon Sales Rank: #6368700 in Books
- Published on: 2015-09-27
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x 1.04" w x 5.98" l, 1.51 pounds
- Binding: Paperback
- 518 pages
Language Notes Text: English (translation) Original Language: French
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Most helpful customer reviews
8 of 9 people found the following review helpful. A dry classic By Viktor Blasjo 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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