A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page viii
... coefficients of the terms of a series ; they are not considered in that relation at their first admission , and it is only by a course of reasoning that they afterwards become so . Expansion in a series has been admitted fundamentally ...
... coefficients of the terms of a series ; they are not considered in that relation at their first admission , and it is only by a course of reasoning that they afterwards become so . Expansion in a series has been admitted fundamentally ...
Page 2
... coefficients of y and z be equal to zero ; so that b112 + b2λ2 + b3λg = 0 , whence by elimination , λι = λε C1λ1 + Cgλq + Cgλg = 0 ; λο = b2C3 - C2b3 bgc , — c3b1 b1c2 - ci b2 But thus the ratio only of the multipliers has been ...
... coefficients of y and z be equal to zero ; so that b112 + b2λ2 + b3λg = 0 , whence by elimination , λι = λε C1λ1 + Cgλq + Cgλg = 0 ; λο = b2C3 - C2b3 bgc , — c3b1 b1c2 - ci b2 But thus the ratio only of the multipliers has been ...
Page 3
... coefficients of x and y had been equated to zero , 2 = dı ( ɑ2b3 — b2α3 ) + d2 ( ɑ3b1 − b3α1 ) + dз ( α1b2 — b1ɑ2 ) C1 ( α2b3 — b2α3 ) + C2 ( a3b1 − b3α1 ) + C3 ( α1b2 — b1α2 ) ' This method of elimination is generally known by the ...
... coefficients of x and y had been equated to zero , 2 = dı ( ɑ2b3 — b2α3 ) + d2 ( ɑ3b1 − b3α1 ) + dз ( α1b2 — b1ɑ2 ) C1 ( α2b3 — b2α3 ) + C2 ( a3b1 − b3α1 ) + C3 ( α1b2 — b1α2 ) ' This method of elimination is generally known by the ...
Page 4
... coefficients of the three pre- ceding equations , when they coexist . This theorem is one of the simplest in the method of Deter- minants the general principles of which are explained in Mr. Spottiswoode's " Elementary Theorems relating ...
... coefficients of the three pre- ceding equations , when they coexist . This theorem is one of the simplest in the method of Deter- minants the general principles of which are explained in Mr. Spottiswoode's " Elementary Theorems relating ...
Page 23
... coefficients ; and the difference is an infinity or infinitesimal of the same order , except when the coefficients are equal , in which case it is absolutely zero . Thus ai " + bi " = ( a + b ) in , ain — bi ” = ( a — b ) i ” , ain ...
... coefficients ; and the difference is an infinity or infinitesimal of the same order , except when the coefficients are equal , in which case it is absolutely zero . Thus ai " + bi " = ( a + b ) in , ain — bi ” = ( a — b ) i ” , ain ...
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Common terms and phrases
a₁ algebraical ascending powers b₁ becomes calculated change of sign changes sign coefficients constant curve d²u d²x d²y d2y dx2 d³u d³y denominator determine differential equation dr dr dr dx dx dr dx dx dx dy dx dz dx² dx2 dy2 dy d2u dy dx dy dy dy dz dy² dy³ dz dx dz dz equal equicrescent Evaluate explicit function expression F(xo F(xo+h factor finite quantity fraction given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity logarithm loge maxima and minima minimum value negative partial derived-functions particular values positive primitive equation proper fraction replaced result roots Similarly sin x singular value substituting suppose symbols Taylor's Series tion total differentials vanish variation whence x+▲x zero
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