The Analyst: A Monthly Journal of Pure and Applied Mathematics, Volumes 3-4Pierson & Blair, 1876 |
From inside the book
Results 1-5 of 84
Page 1
... values of the ordinates we are obliged to resort to approximate quadrature . The simplest method is this : divide ... value Sydt = = 1 n 4. ( yo + y1 + Y2 + .... + Yn − 1 + Yn ) . This method is obvious and must be very ancient ...
... values of the ordinates we are obliged to resort to approximate quadrature . The simplest method is this : divide ... value Sydt = = 1 n 4. ( yo + y1 + Y2 + .... + Yn − 1 + Yn ) . This method is obvious and must be very ancient ...
Page 3
... values for the other sections . Adding these integrals and ob- serving that Ayo + Ay1 + ... + Ayn - 1 = Y1 - Yo + Y2 - Y1 + ... + Yn - Ym1 = Ya - Yo Byo + By + ... + Syn - 1 = Ay , Ay 。 + & c . , — we have for the value of the integral ...
... values for the other sections . Adding these integrals and ob- serving that Ayo + Ay1 + ... + Ayn - 1 = Y1 - Yo + Y2 - Y1 + ... + Yn - Ym1 = Ya - Yo Byo + By + ... + Syn - 1 = Ay , Ay 。 + & c . , — we have for the value of the integral ...
Page 4
... values of y . If nt ( nt — 1 ) ( nt — 2 ) ( nt — 3 ) . . . . ( nt — n ) I'm = - - - nt - m Mm the value of T for nt = m , = M . the function m = x Tm Σ.um Μη • m = 0 reduces to ym for the value nt = m , and has n + 1 values common with ...
... values of y . If nt ( nt — 1 ) ( nt — 2 ) ( nt — 3 ) . . . . ( nt — n ) I'm = - - - nt - m Mm the value of T for nt = m , = M . the function m = x Tm Σ.um Μη • m = 0 reduces to ym for the value nt = m , and has n + 1 values common with ...
Page 5
... values of the seven equidistant ordinates are , YoY6 = 1/3 = 0.8660254 Уо Y1 = y = 1/8 Y1 - Y5 - = 0.9428090 Y2 = Y4 = { √35 0.9860133 Y3 The exact value of this area is = 1 . 1/35 = 2ƒ31√ ( 1 − x2 ) dx = [ xv ( 1 − x2 ) + sin − 1x ...
... values of the seven equidistant ordinates are , YoY6 = 1/3 = 0.8660254 Уо Y1 = y = 1/8 Y1 - Y5 - = 0.9428090 Y2 = Y4 = { √35 0.9860133 Y3 The exact value of this area is = 1 . 1/35 = 2ƒ31√ ( 1 − x2 ) dx = [ xv ( 1 − x2 ) + sin − 1x ...
Page 6
... values of y when x has certain values . The form which Lagrange employs in his method of interpolation gives , denoting by a , a1 , a2 , & c . the given values of x , y = yo · - ( xa1 ) ( x - a2 ) ( x — α3 ) 1 - ( a — a1 ) ( a — a2 ) ...
... values of y when x has certain values . The form which Lagrange employs in his method of interpolation gives , denoting by a , a1 , a2 , & c . the given values of x , y = yo · - ( xa1 ) ( x - a2 ) ( x — α3 ) 1 - ( a — a1 ) ( a — a2 ) ...
Other editions - View all
Common terms and phrases
5th degree a₁ algebraic ANALYST angle ARTEMAS MARTIN assumed axis b₁ C₁ circular coefficients common logarithms constant curve denote determine differential distance E. B. SEITZ ellipse Elliptic Functions equal equation expression factor formula function given circle gives hence hyperbola integral intersection inverse Lagrange's Theorem locus logarithms method multiply observations orbital orbital force ORSON PRATT oxen parabola parallel perpendicular plane points at infinity position probable error quadrics quadrilateral radius ratio reduce represent result roots sides SOLUTION BY PROF SOLUTIONS of problems sphere square substitution surface tangent Taylor's Theorem Theorem tion triangle UNION SPRINGS unknown quantities values velocity whence zero