A Treatise on Infinitesimal Calculus ... |
From inside the book
Results 6-10 of 75
Page 25
... convenience of reference , we shall symbolize by F ( x ) f ( x ) ( 20 ) ( 21 ) Suppose then roots of f ( x ) to be a1 , a ,, ... a ,, which may be either real or impossible ; and all may be unequal , or there may be one or more systems ...
... convenience of reference , we shall symbolize by F ( x ) f ( x ) ( 20 ) ( 21 ) Suppose then roots of f ( x ) to be a1 , a ,, ... a ,, which may be either real or impossible ; and all may be unequal , or there may be one or more systems ...
Page 27
Bartholomew Price. which form is , when a is real , as convenient as the result admits of : but if a is impossible , then , to avoid the Logarithms of impossible quantities , we reduce as follows : Let a + BV - 1 , a - B - 1 be a pair of ...
Bartholomew Price. which form is , when a is real , as convenient as the result admits of : but if a is impossible , then , to avoid the Logarithms of impossible quantities , we reduce as follows : Let a + BV - 1 , a - B - 1 be a pair of ...
Page 30
... convenient , and it is allowable , to assume the numerator of the first partial frac- tion in the form M1 + M2 ( x - a1 ) + M3 ( x − a1 ) 2 + - + Mm ( x − α1 ) TM −1 ; ( 33 ) so that = M1 ( x — a1 ) m M2 Mm + + + + ( x — a1 ) m −1 x ...
... convenient , and it is allowable , to assume the numerator of the first partial frac- tion in the form M1 + M2 ( x - a1 ) + M3 ( x − a1 ) 2 + - + Mm ( x − α1 ) TM −1 ; ( 33 ) so that = M1 ( x — a1 ) m M2 Mm + + + + ( x — a1 ) m −1 x ...
Page 42
... convenient , and better suited in most cases for finding the definite integral . Integration of dx ( x2 + a2 ) " In the formula , fudv = UV- let u = 42 [ 27 . INTEGRATION OF RATIONAL FUNCTIONS . (a2 + x2) (a + bx + cx2) Examples in ...
... convenient , and better suited in most cases for finding the definite integral . Integration of dx ( x2 + a2 ) " In the formula , fudv = UV- let u = 42 [ 27 . INTEGRATION OF RATIONAL FUNCTIONS . (a2 + x2) (a + bx + cx2) Examples in ...
Page 49
... convenient to employ the method of inte- gration by parts given by the formula , Judv dv = uv To determine f ( a2 — x2 ) 1 dx . Let u = ( a2 — x2 ) , --- -xdx – Svdu . dvdx ; ( 78 ) ... du = ( a2 — x2 ) PRICE , VOL . II . v = x . H ...
... convenient to employ the method of inte- gration by parts given by the formula , Judv dv = uv To determine f ( a2 — x2 ) 1 dx . Let u = ( a2 — x2 ) , --- -xdx – Svdu . dvdx ; ( 78 ) ... du = ( a2 — x2 ) PRICE , VOL . II . v = x . H ...
Contents
1 | |
4 | |
18 | |
41 | |
48 | |
53 | |
71 | |
83 | |
322 | |
323 | |
324 | |
326 | |
327 | |
328 | |
330 | |
332 | |
85 | |
98 | |
104 | |
105 | |
108 | |
111 | |
117 | |
121 | |
123 | |
130 | |
134 | |
144 | |
150 | |
154 | |
155 | |
161 | |
169 | |
177 | |
184 | |
190 | |
197 | |
206 | |
210 | |
217 | |
222 | |
224 | |
231 | |
240 | |
249 | |
255 | |
256 | |
267 | |
279 | |
283 | |
287 | |
290 | |
302 | |
307 | |
308 | |
310 | |
311 | |
312 | |
313 | |
315 | |
316 | |
317 | |
319 | |
321 | |
333 | |
335 | |
337 | |
338 | |
339 | |
354 | |
366 | |
372 | |
376 | |
382 | |
388 | |
389 | |
395 | |
396 | |
403 | |
405 | |
411 | |
414 | |
420 | |
426 | |
427 | |
430 | |
436 | |
461 | |
482 | |
491 | |
511 | |
513 | |
520 | |
528 | |
556 | |
569 | |
589 | |
597 | |
606 | |
614 | |
615 | |
622 | |
629 | |
643 | |
651 | |
663 | |
666 | |
673 | |
680 | |
687 | |
693 | |
Other editions - View all
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