First published in 1878, The Analytical Theory of Heat is Alexander Freeman's English translation of French mathematician Joseph Fourier's Théorie Analytique de la Chaleur, originally published in French in 1822. In this groundbreaking study, arguing that previous theories of mechanics advanced by such scientific greats as Archimedes, Galileo, Newton and their successors did not explain the laws of heat, Fourier set out to study the mathematical laws governing heat diffusion and proposed that an infinite mathematical series may be used to analyse the conduction of heat in solids. Known in scientific circles as the 'Fourier Series', this work paved the way for modern mathematical physics. This translation, now reissued, contains footnotes that cross-reference other writings by Fourier and his contemporaries, along with 20 figures and an extensive bibliography. This book will be especially useful for mathematicians who are interested in trigonometric series and their applications.
Author(s): Fourier J.B.
Series: Cambridge Library Collection - Mathematics
Publisher: CUP
Year: 2009
Language: English
Pages: 495
Tags: Математика;Математическая физика;
Cover......Page Cover
Frontmatter......Page i
PREFACE......Page iii
Contents......Page v
PRELIMINARY DISCOURSE......Page 1
SECTION I. STATEMENT OF THE OBJECT OF THE WORK......Page 14
SECTION II. GENERAL NOTIONS AND PRELIMINARY DEFINITIONS......Page 26
SECTION III. PRINCIPLE OF THE COMMUNICATION OF HEAT......Page 41
SECTION IV. OF THE UNIFORM AND LINEAR MOVEMENT OF HEAT......Page 45
SECTION V. LAW OF THE PERMANENT TEMPERATURES IN A PRISM OF SMALL THICKNESS......Page 56
SECTION VI. THE HEATING OF CLOSED SPACES......Page 62
SECTION VII. OF THE UNIFORM MOVEMENT OF HEAT IN THREE DIMENSIONS......Page 73
SECTION VIII. MEASURE OF THE MOVEMENT OF HEAT AT A GIVEN POINT OF A GIVEN SOLID......Page 78
SECTION I. EQUATION OF THE VARIED MOVEMENT OF HEAT IN A RING......Page 85
SECTION II. EQUATION OF THE VARIED MOVEMENT OF HEAT IN A SOLID SPHERE......Page 90
SECTION III. EQUATION OF THE VARIED MOVEMENT OF HEAT IN A SOLID CYLINDER......Page 95
SECTION IV. EQUATIONS OF THE VARIED MOVEMENT OF HEAT IN A SOLID PRISM OF INFINITE LENGTH......Page 97
SECTION V. EQUATIONS OF THE VARIED MOVEMENT OF HEAT IN A SOLID CUBE......Page 101
SECTION VI. GENERAL EQUATION OF THE PROPAGATION OF HEAT IN THE INTERIOR OF SOLIDS......Page 104
SECTION VII. GENERAL EQUATION BELATIVE TO THE SURFACE......Page 115
SECTION VIII. APPLICATION OF THE GENERAL EQUATIONS......Page 123
SECTION IX. GENERAL REMARKS......Page 126
SECTION I. STATEMENT OF THE PROBLEM......Page 131
SECTION II. FIRST EXAMPLE OF THE USE OF TRIGONOMETRIC SERIES IN THE THEORY OF HEAT......Page 137
SECTION III. REMARKS ON THESE SERIES......Page 145
SECTION IV. GENERAL SOLUTION......Page 154
SECTION V. FINITE EXPRESSION OF THE RESULT OF THE SOLUTION......Page 166
SECTION VI. DEVELOPMENT OF AN ARBITRARY FUNCTION IN TRIGONOMETRIC SERIES......Page 168
SECTION VII. APPLICATION TO THE ACTUAL PROBLEM......Page 209
SECTION I. GENERAL SOLUTION OF THE PROBLEM......Page 213
SECTION II. OF THE COMMUNICATION OF HEAT BETWEEN SEPARATE MASSES......Page 225
SECTION I. GENERAL SOLUTION......Page 268
SECTION II. DIFFERENT REMARKS ON THIS SOLUTION......Page 279
CHAPTER VI - Of the Movement of Heat in a solid cylinder......Page 291
CHAPTER VII - Propagation of Heat in a rectangular prism......Page 311
CHAPTER VIII - Of the Movement of Heat in a solid cube......Page 323
SECTION I. OF THE FREE MOVEMENT OF HEAT IN AN INFINITE LINE......Page 333
SECTION II. OF THE FREE MOVEMENT OF HEAT IN AN INFINITE SOLID......Page 368
SECTION III. THE HIGHEST TEMPERATURES IN AN INFINITE SOLID......Page 385
SECTION IV. COMPARISON OF THE INTEGRALS......Page 396
