The Analytical Theory of Heat |
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Results 1-5 of 76
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 + 45d + & 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 + 45d + & 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 dt = d2v d2v + + dav 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 dt = d2v d2v + + dav dx ...
Page xxii
... obtain the integrals , by summing the series which represent them . Application to the equation dv dav = 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 dav = 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
2kt versin a₁ abscissa action actual temperature analysis arbitrary function axis b₁ b₂ body chaleur co-ordinates coefficient conducibility consider constant temperature convergent series cooling corresponding cosines curve d'v d'v d²v definite integrals denoting determine different points differential equations distance dv dv dv dx dx² enclosure equation dv expressed fixed temperature function f(x give given heat equal heat which escapes heat which flows Hence hypothesis infinitely small initial temperatures instant dt integral interior layers maintained mass mathematical analysis molecules movement of heat 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 source of heat sphere substitute suppose theorems theory of heat thermometer unit of surface unknown variable vary
Popular passages
Page 470 - Bible, an edition such as, to use the words of the Editor, 'would have been executed long ago had this version been nothing more than the greatest and best known of English classics.' Falling at a time when the formal revision of this version, has been undertaken by a distinguished company of scholars and divines, the publication of this edition must be considered most opportune.