A Treatise on Infinitesimal Calculus ... |
From inside the book
Results 6-10 of 100
Page xxxiv
... equation of the nth order , the order of the equation may be diminished by unity 449. If n particular integrals of a differential equation , which is without the second member , are known , the coefficients of the several terms are ...
... equation of the nth order , the order of the equation may be diminished by unity 449. If n particular integrals of a differential equation , which is without the second member , are known , the coefficients of the several terms are ...
Page xxxv
... equation whose coefficients are the successive powers of a binomial SECTION 2. - The Solution of Partial Differential Equations by Symbolical Methods . 475. The process applied to equations which have constant co- efficients .. 476. The ...
... equation whose coefficients are the successive powers of a binomial SECTION 2. - The Solution of Partial Differential Equations by Symbolical Methods . 475. The process applied to equations which have constant co- efficients .. 476. The ...
Page 123
... equation . Let u = f ( z ) , where z = p ( x , y ) ; then ( du ) = ƒ ' ( z ) d2u d S = dz du dz dx ' = f ' ( z ) dy dy d2 u dy dx d dz ) = dx ; ( da dy ހ { f ( z ) da dz dy S dz ) ( 2 ) dy's ( 125 ) dy dx dz S d { red } = Z { red } ...
... equation . Let u = f ( z ) , where z = p ( x , y ) ; then ( du ) = ƒ ' ( z ) d2u d S = dz du dz dx ' = f ' ( z ) dy dy d2 u dy dx d dz ) = dx ; ( da dy ހ { f ( z ) da dz dy S dz ) ( 2 ) dy's ( 125 ) dy dx dz S d { red } = Z { red } ...
Page 202
... equation is x + y3 = a3 , see fig . 10 , is equal to 6a . e * + 1 e - 1 prove that Ex . 9. The equation to a curve being e " = the length of the arc between ( xo , yo ) and ( x , y ) = exn ― e - xn log exo - e - xo 156. ] The process of ...
... equation is x + y3 = a3 , see fig . 10 , is equal to 6a . e * + 1 e - 1 prove that Ex . 9. The equation to a curve being e " = the length of the arc between ( xo , yo ) and ( x , y ) = exn ― e - xn log exo - e - xo 156. ] The process of ...
Page 211
... equation is r = a ( 1+ cos 0 ) , is 8a . Ex . 5. If the equation to the lemniscata is r2 = a2 cos 20 , and s the length of a loop , 8 = 2a2 a2 [ ° 0 dr ( a + — r4 ) 3 = α S # de . - ( cos 20 ) This last value may be expressed in terms ...
... equation is r = a ( 1+ cos 0 ) , is 8a . Ex . 5. If the equation to the lemniscata is r2 = a2 cos 20 , and s the length of a loop , 8 = 2a2 a2 [ ° 0 dr ( a + — r4 ) 3 = α S # de . - ( cos 20 ) This last value may be expressed in terms ...
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