The Analytical Theory of Heat |
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Results 1-5 of 79
Page xiii
... 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 + 43d + & c . , C = a + 2b + 3 ° c + 43d + & c . , D = a + 2b + 37c + 47d ...
... 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 + 43d + & c . , C = a + 2b + 3 ° c + 43d + & c . , D = a + 2b + 37c + 47d ...
Page xvi
... obtain the solution relative to a solid ring , set forth in Article 241 , and the theorem of Article 234. We thus ascertain the origin of the analysis which we have employed to solve the equation relating to con- tinuous bodies . . 279 ...
... obtain the solution relative to a solid ring , set forth in Article 241 , and the theorem of Article 234. We thus ascertain the origin of the analysis which we have employed to solve the equation relating to con- tinuous bodies . . 279 ...
Page xx
... obtained is founded upon the following proposition , which may be regarded as self - evident . Two functions of the variables x , y , z , t are necessarily identical , if they satisfy the differential equation dv dev d2v dev + + dt dx ...
... obtained is founded upon the following proposition , which may be regarded as self - evident . Two functions of the variables x , y , z , t are necessarily identical , if they satisfy the differential equation dv dev d2v dev + + dt dx ...
Page xxii
... obtain the integrals , by summing the series which represent them . Application to the equation dv d2v = dt dz2 ... obtained by this method ex- press either the variable state , or the initial state of masses of infinite dimensions . The ...
... obtain the integrals , by summing the series which represent them . Application to the equation dv d2v = dt dz2 ... obtained by this method ex- press either the variable state , or the initial state of masses of infinite dimensions . The ...
Page 6
... obtained ; this process consists in passing from a common expression to a particular solution subject to all the given con- ditions . This difficult investigation requires a special analysis founded on new theorems , whose object we ...
... obtained ; this process consists in passing from a common expression to a particular solution subject to all the given con- ditions . This difficult investigation requires a special analysis founded on new theorems , whose object we ...
Contents
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470 | |
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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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