A Treatise on Infinitesimal Calculus ... |
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Page xxiii
... effected .. .. 218. The differentiation of the same , when one definite integra- 297 298 CHAP . IX . QUADRATURE OF SURFACES , PLANE AND CURVED . SECTION 1. - Quadrature of Plane Surfaces ; Cartesian Coordinates . 219. Investigation of ...
... effected .. .. 218. The differentiation of the same , when one definite integra- 297 298 CHAP . IX . QUADRATURE OF SURFACES , PLANE AND CURVED . SECTION 1. - Quadrature of Plane Surfaces ; Cartesian Coordinates . 219. Investigation of ...
Page xxvi
... effected by means of the Gamma - function when the limits are given by an inequality .. 392 280. Extension of the theorem by Lejeune Dirichlet 393 281. Further extension by Liouville .. 396 282. Liouville's theorem , when the limits are ...
... effected by means of the Gamma - function when the limits are given by an inequality .. 392 280. Extension of the theorem by Lejeune Dirichlet 393 281. Further extension by Liouville .. 396 282. Liouville's theorem , when the limits are ...
Page 93
... effected , to be divided into n finite parts ; and to the several points of partition let x1 , x2 , ... X - 1 refer ; so that we have the identity , + . ( 29 ) xx 。= ( x1 − xo ) + ( X2 − X1 ) + ... + ( xn − Xn - 1 ) . Also let the ...
... effected , to be divided into n finite parts ; and to the several points of partition let x1 , x2 , ... X - 1 refer ; so that we have the identity , + . ( 29 ) xx 。= ( x1 − xo ) + ( X2 − X1 ) + ... + ( xn − Xn - 1 ) . Also let the ...
Page 111
... effected as they are with respect to different variables , and thus independent of each other , may be interchanged without any alteration of the result . The process of differentiating a definite integral with respect to a variable ...
... effected as they are with respect to different variables , and thus independent of each other , may be interchanged without any alteration of the result . The process of differentiating a definite integral with respect to a variable ...
Page 114
... effected as they are with respect to vari- ables independent of each other , may be interchanged without alteration of the result . This theorem is called the inversion of the order of integrations ; and the members of ( 102 ) are ...
... effected as they are with respect to vari- ables independent of each other , may be interchanged without alteration of the result . This theorem is called the inversion of the order of integrations ; and the members of ( 102 ) are ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ a₂ angle application axis Beta-function bx dx consequently convergent series coordinates cosec cx² cycloid definite integral denoted determined differential double integral dx a² dx dx dx dy dx Ex dx² dy dx dy² e-ax element-function ellipse equal evaluation expressed find the area finite and continuous fraction function Gamma-function geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation involute left-hand member length let us suppose limits of integration multiple integrals plane curve polar coordinates preceding proper fraction radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variable x-integration x₁ x²)¹ x²)³ αξ πα