The Analytical Theory of Heat |
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Page xiii
... ARBITRARY FUNCTION IN TRIGONOMETRIC SERIES . 207-214 . The development obtained by determining the values of the un- known coefficients in the following equations infinite in number : A = a + 2b + 3c + 4d + & c . , B = a + 236 + 33c + ...
... ARBITRARY FUNCTION IN TRIGONOMETRIC SERIES . 207-214 . The development obtained by determining the values of the un- known coefficients in the following equations infinite in number : A = a + 2b + 3c + 4d + & c . , B = a + 236 + 33c + ...
Page xiv
... arbitrary . We may also choose any limits whatever for x 235. Divers remarks on the use of developments in trigonometric series • • • • 204 · 206 SECTION VII . APPLICATION TO THE ACTUAL PROBLEM . 236 , 237. Expression of the permanent ...
... arbitrary . We may also choose any limits whatever for x 235. Divers remarks on the use of developments in trigonometric series • • • • 204 · 206 SECTION VII . APPLICATION TO THE ACTUAL PROBLEM . 236 , 237. Expression of the permanent ...
Page xv
... arbitrary 256 , 257. Remarkable consequences of this solution 221 225 • 228 236 237 258. Application to the case in which the number of masses is infinite . 259-266 . Of the communication of heat between n separate masses arranged ...
... arbitrary 256 , 257. Remarkable consequences of this solution 221 225 • 228 236 237 258. Application to the case in which the number of masses is infinite . 259-266 . Of the communication of heat between n separate masses arranged ...
Page xxi
... arbitrary function of t 401. Notation appropriate to the representation of these developments . The analysis which is derived from it dispenses with effecting the develop , ment in series 402. Application to the equations : dev d2v d2v ...
... arbitrary function of t 401. Notation appropriate to the representation of these developments . The analysis which is derived from it dispenses with effecting the develop , ment in series 402. Application to the equations : dev d2v d2v ...
Page xxii
... arbitrary functions of t 414. The expressions change form when we use other limits of the definite • . • • • • integrals 415 , 416. Construction which serves to prove the general equation 1 2T +00 f ( x ) = 1 daƒ ( a ) + dp cos ( px ...
... arbitrary functions of t 414. The expressions change form when we use other limits of the definite • . • • • • integrals 415 , 416. Construction which serves to prove the general equation 1 2T +00 f ( x ) = 1 daƒ ( a ) + dp cos ( px ...
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Common terms and phrases
a₁ abscissa action actual temperature analysis arbitrary axis b₁ body chaleur co-ordinates coefficients conducibility consider constant temperature convergent series cooling corresponding cosines curve d'v d'v definite integrals denoting determine different points differential equations dimensions distance dv dv dv dx dv dz dx dy dx² dy dz dy² enclosure equa equation dv expressed fixed temperature give given heat equal heat which escapes heat which flows Hence hypothesis infinitely small initial temperatures instant dt integral interior maintained mass mathematical analysis molecule movement of heat multiple arcs multiply ordinates parallel partial differential equations perature permanent temperature perpendicular plane prism problem propagation of heat quantity of heat radius ratio rays represented result satisfies second member sin x sines solution source of heat substitute suppose theorems theory of heat thermometer tion unknowns variable vary versin
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