Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page x
... derivatives of the expanded functions 237 239 271 . SECTION III . - On the discontinuity of the sums of infinite series , and of the values of integrals taken between infinite limits SECTION IV . - Examples of the application of the ...
... derivatives of the expanded functions 237 239 271 . SECTION III . - On the discontinuity of the sums of infinite series , and of the values of integrals taken between infinite limits SECTION IV . - Examples of the application of the ...
Page 236
... derivative restricted to vanish at the limits 0 and a . Although however the possibility of the expansion of an arbitrary function in a series of sines , for instance , when the function does not vanish at the limits 0 and a , cannot ...
... derivative restricted to vanish at the limits 0 and a . Although however the possibility of the expansion of an arbitrary function in a series of sines , for instance , when the function does not vanish at the limits 0 and a , cannot ...
Page 260
... of 1 / n , and rejecting the terms which would render the series contained in the uth derived equation divergent . The reason of this is the same as before . 17. The direct expansions of the derivatives of f ( 260 ON THE CRITICAL VALUES OF.
... of 1 / n , and rejecting the terms which would render the series contained in the uth derived equation divergent . The reason of this is the same as before . 17. The direct expansions of the derivatives of f ( 260 ON THE CRITICAL VALUES OF.
Page 261
... derivatives is discontinuous . In what follows , a will be taken to denote a value of x for which f ( x ) or any one of its derivatives of the orders considered is discontinuous ; Q , Q1 , ... Qu will denote the quantities by which f ...
... derivatives is discontinuous . In what follows , a will be taken to denote a value of x for which f ( x ) or any one of its derivatives of the orders considered is discontinuous ; Q , Q1 , ... Qu will denote the quantities by which f ...
Page 263
... derivatives is discontinuous , and likewise the quantity by which the function or derivative is suddenly increased . This remark will apply to the extreme values 0 and a of x if we con- tinue to denote the sum of the series by f ( x ) ...
... derivatives is discontinuous , and likewise the quantity by which the function or derivative is suddenly increased . This remark will apply to the extreme values 0 and a of x if we con- tinue to denote the sum of the series by f ( x ) ...
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Common terms and phrases
according angle apply approximation arbitrary axes axis become infinite Cambridge Philosophical Society canal centre co-ordinates condition Consequently considered constant convergent series corresponding cosines cylinder Demy Octavo denote depth determined direction discontinuous divergent series dx dy elastic equal equation essentially convergent ether exact differential expansion expression finite force formula friction function given h vanishes Hence homogeneous function horizontal increases inertia integral length limit molecules moment of inertia observed obtained Octavo order of approximation oscillation oscillatory waves paper parallel parallelepiped particles perpendicular plane Poisson positive pressure quantities ratio rectangular refracting respect result satisfied shew shewn sines solid solitary wave sphere St John's College suppose surface tangential theorem theory tion variables velocity of propagation wave motion whence zero ηπα аф
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