The Analytical Theory of Heat |
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Page xii
... function of a and m . This function is developed according to powers of the reciprocal of m , and m is made infinite . 182-184 . The same process is applied to several other series • • 145 • • 147 185-188 . In the preceding development ...
... function of a and m . This function is developed according to powers of the reciprocal of m , and m is made infinite . 182-184 . The same process is applied to several other series • • 145 • • 147 185-188 . In the preceding development ...
Page xiii
... 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 + 43d + & c ...
... 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 + 43d + & c ...
Page xiv
... function whatever , F ( x ) , may be developed in the form a cos x + a , cos 2x + α cos 3x + & c . , F ( x ) = 4+ { cinx + b2 sin 2x + b , sin 3x + & c . Each of the coefficients is a definite integral . We have in general and 2πA ...
... function whatever , F ( x ) , may be developed in the form a cos x + a , cos 2x + α cos 3x + & c . , F ( x ) = 4+ { cinx + b2 sin 2x + b , sin 3x + & c . Each of the coefficients is a definite integral . We have in general and 2πA ...
Page xvii
... function of x which is one of the factors of this expression is given by a differential equation of the second order . A number g enters into this function , and must satisfy a definite equation · • 291 · . 294 308 , 309. Analysis of ...
... function of x which is one of the factors of this expression is given by a differential equation of the second order . A number g enters into this function , and must satisfy a definite equation · • 291 · . 294 308 , 309. Analysis of ...
Page xix
... 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 : п f ( x ) = [ " dq sin qa daf ( a ) sin qa . 340 ib . • 343 345 The ...
... 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 : п f ( x ) = [ " dq sin qa daf ( a ) sin qa . 340 ib . • 343 345 The ...
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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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Page 469 - Greek and English Testament, in parallel columns on the same page. Edited by J. SCHOLEFIELD, MA late Regius Professor of Greek in the University. New Edition, with the marginal references as arranged and revised by DR SCRIvENER, js.