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 xix
... arbitrary function 355-358 . The developments of functions in sines or cosines of multiple arcs are transformed into definite integrals 359. The following theorem is proved : f ( x ) = dq sinqe [ " daƒ ( a ) sin qa . 338 339 340 ib ...
... arbitrary function 355-358 . The developments of functions in sines or cosines of multiple arcs are transformed into definite integrals 359. The following theorem is proved : f ( x ) = dq sinqe [ " daƒ ( a ) sin qa . 338 339 340 ib ...
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 : d2v d2v = dt ...
... 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 : d2v d2v = dt ...
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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.