The Analytical Theory of Heat |
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Page ix
... represented by the terms of a recurring series . temperatures v1 , v2 , v3 of three consecutive points gives the measure of the ratio h : we have ' = q , w3 - qw + 1 = 0 , and v 1 + v z V2 h S / log w 2 1 1/2 = 5 ( 1086 ) 2 . K The ...
... represented by the terms of a recurring series . temperatures v1 , v2 , v3 of three consecutive points gives the measure of the ratio h : we have ' = q , w3 - qw + 1 = 0 , and v 1 + v z V2 h S / log w 2 1 1/2 = 5 ( 1086 ) 2 . K The ...
Page xiv
... 237. Expression of the permanent temperature in the infinite rectangular slab , the state of the transverse edge being represented by an arbitrary function . 209 ART . CHAPTER IV . Of the linear and varied xiv TABLE OF CONTENTS .
... 237. Expression of the permanent temperature in the infinite rectangular slab , the state of the transverse edge being represented by an arbitrary function . 209 ART . CHAPTER IV . Of the linear and varied xiv TABLE OF CONTENTS .
Page xvii
... represented by a + b + c + d + & c . , 2.3 the value of the series ct ets gto a + 22 + + & c . , 22.42 22.42.62 is #s " dup ( t sin u ) . 0 Remark on this use of definite integrals 298 313. Expression of the function u of the variable x ...
... represented by a + b + c + d + & c . , 2.3 the value of the series ct ets gto a + 22 + + & c . , 22.42 22.42.62 is #s " dup ( t sin u ) . 0 Remark on this use of definite integrals 298 313. Expression of the function u of the variable x ...
Page xviii
... of which has been heated ; the initial state is represented by v = F ( x ) . The following theorem is proved : | ; F ( x ) = dq cos qx fo da F ( a ) cos qa . 0 ART . The function F ( x ) satisfies the xviii TABLE OF CONTENTS .
... of which has been heated ; the initial state is represented by v = F ( x ) . The following theorem is proved : | ; F ( x ) = dq cos qx fo da F ( a ) cos qa . 0 ART . The function F ( x ) satisfies the xviii TABLE OF CONTENTS .
Page xix
... represented by v = f ( x ) at the distance x to the right of the origin , and by v = -ƒ ( x ) at the distance x to the left of the origin . Expression of the variable temperature at any point . The solution derived from the analysis ...
... represented by v = f ( x ) at the distance x to the right of the origin , and by v = -ƒ ( x ) at the distance x to the left of the origin . Expression of the variable temperature at any point . The solution derived from the analysis ...
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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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