A Treatise on Infinitesimal Calculus ... |
From inside the book
Page xvii
... substitution .. 80. Reason why the number of indefinite integrals is so small CHAP . IV . ON DEFINITE INTEGRATION AND ON DEFINITE INTEGRALS . SECTION 1. - Definite Integrals determined by Indefinite Integration . 81. Great importance of ...
... substitution .. 80. Reason why the number of indefinite integrals is so small CHAP . IV . ON DEFINITE INTEGRATION AND ON DEFINITE INTEGRALS . SECTION 1. - Definite Integrals determined by Indefinite Integration . 81. Great importance of ...
Page xxiv
... substitution SECTION 2. - Quadrature of Plane Surfaces ; Polar Coordinates . 226. The differential expression of a surface - element 227. Examples illustrative of it .. 312 313 228. The order of integrations inverted 315 229. Cases of ...
... substitution SECTION 2. - Quadrature of Plane Surfaces ; Polar Coordinates . 226. The differential expression of a surface - element 227. Examples illustrative of it .. 312 313 228. The order of integrations inverted 315 229. Cases of ...
Page xxx
... substitution required for separation of the variables shewn to be equivalent to multiplication by an inte- grating factor .. .. 380. An a posteriori proof that a homogeneous equation when thus modified is an exact differential .. 381 ...
... substitution required for separation of the variables shewn to be equivalent to multiplication by an inte- grating factor .. .. 380. An a posteriori proof that a homogeneous equation when thus modified is an exact differential .. 381 ...
Page xxxi
... substitution , and examples .. 383. Bernoulli's equation SECTION 5. - Partial Differential Equations of the First Order and First Degree . 384. Method of integrating partial differential equations , and of introducing an arbitrary ...
... substitution , and examples .. 383. Bernoulli's equation SECTION 5. - Partial Differential Equations of the First Order and First Degree . 384. Method of integrating partial differential equations , and of introducing an arbitrary ...
Page xxxii
... substitution .. 420. Substitution by means of polar coordinates 597 597 .. 421. The integral of Euler's differential equation 422. Determination of functions by means of integration 423. Riccati's equation 599 601 602 424 , 425. Other ...
... substitution .. 420. Substitution by means of polar coordinates 597 597 .. 421. The integral of Euler's differential equation 422. Determination of functions by means of integration 423. Riccati's equation 599 601 602 424 , 425. Other ...
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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