The Analytical Theory of Heat |
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Page xi
... infinite rectangular solid . SECTION I. STATEMENT OF THE PROBLEM . 163-166 . The constant temperatures of a rectangular plate included be- tween two parallel infinite sides , maintained at the temperature 0 , are d2v d2v = 0 . dx dy ...
... infinite rectangular solid . SECTION I. STATEMENT OF THE PROBLEM . 163-166 . The constant temperatures of a rectangular plate included be- tween two parallel infinite sides , maintained at the temperature 0 , are d2v d2v = 0 . dx dy ...
Page xii
... infinite • · 145 • • 147 182-184 . The same process is applied to several other series 185-188 . In the preceding development , which gives the value of the function of x and m , we determine rigorously the limits within which the sum ...
... infinite • · 145 • • 147 182-184 . The same process is applied to several other series 185-188 . In the preceding development , which gives the value of the function of x and m , we determine rigorously the limits within which the sum ...
Page xiii
... 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 + & c . , & c . , & c . To solve these equations , we first suppose the number of 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 + & c . , & c . , & c . To solve these equations , we first suppose the number of equations ...
Page xvi
... infinite . We 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 ...
... infinite . We 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 ...
Page xviii
... INFINITE LINE . We consider the linear movement of heat in an infinite line , a part of which has been heated ; the initial state is represented by v = F ( x ) . The following theorem is proved : π F ( x ) = dq cos da F ( a ) cos qa ...
... INFINITE LINE . We consider the linear movement of heat in an infinite line , a part of which has been heated ; the initial state is represented by v = F ( x ) . The following theorem is proved : π F ( x ) = dq cos da F ( a ) cos qa ...
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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
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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.