A Treatise on Infinitesimal Calculus ... |
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Page xxvii
... Difference as to operations and symbols between the dif- ferential calculus and the calculus of variations .. 293. Further differences and coincidences .. 294. Our ignorance limits the calculus of variations to certain forms of definite ...
... Difference as to operations and symbols between the dif- ferential calculus and the calculus of variations .. 293. Further differences and coincidences .. 294. Our ignorance limits the calculus of variations to certain forms of definite ...
Page 1
... difference between two con- secutive terms being an infinitesimal of an order higher than that of each term . Thus , according to the doctrine of infinitesimals and infinities , which has been established in Vol . I , if relatively to a ...
... difference between two con- secutive terms being an infinitesimal of an order higher than that of each term . Thus , according to the doctrine of infinitesimals and infinities , which has been established in Vol . I , if relatively to a ...
Page 2
... difference between the values of the variables at the limits will be a finite quantity ; so that the problem is definite as to its limits , and the distance between the limits is finite . The process by which such sums are found is ...
... difference between the values of the variables at the limits will be a finite quantity ; so that the problem is definite as to its limits , and the distance between the limits is finite . The process by which such sums are found is ...
Page 3
... F ( x ) be a function of a finite and continuous for all values of a between a and r ; and let the difference x - xo be divided into n equal and = finite parts each of which is equal to ax , B 2 2. ] 3 A SUMMATION - PROCESS .
... F ( x ) be a function of a finite and continuous for all values of a between a and r ; and let the difference x - xo be divided into n equal and = finite parts each of which is equal to ax , B 2 2. ] 3 A SUMMATION - PROCESS .
Page 11
... differences between vo , v1 , v2 , ... v , are infinitesimal , as are also the differences between u 。, u1 , if we take i to be the general symbol of an infinitesimal , we have ... Un v1 = v2 + i1 , u1 = u2 + i2 , V2 = V1 + iq , Ug ...
... differences between vo , v1 , v2 , ... v , are infinitesimal , as are also the differences between u 。, u1 , if we take i to be the general symbol of an infinitesimal , we have ... Un v1 = v2 + i1 , u1 = u2 + i2 , V2 = V1 + iq , Ug ...
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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