Mathematical Handbook: Containing the Chief Formulas of Algebra, Trigonometry, Circular and Hyperbolic Functions, Differential and Integral Calculus, and Analytical Geometry, Together with Mathematical Tables
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1907 Excerpt: ...h and height equal to the ordinate on the left-hand side of it. The areas of the strips are hy0, hylt hy2, ... hyn, and their sum, A, is approximately the area of the given space. 1181. A-h(y0+ yt+ y2+.., +y). (ii) Each strip regarded as a trapezoid the areas of which are 2' 2' 2' 2 and their sum 1182. A = h (iy0 + yl ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1907 Excerpt: ...h and height equal to the ordinate on the left-hand side of it. The areas of the strips are hy0, hylt hy2, ... hyn, and their sum, A, is approximately the area of the given space. 1181. A-h(y0+ yt+ y2+.., +y). (ii) Each strip regarded as a trapezoid the areas of which are 2' 2' 2' 2 and their sum 1182. A = h (iy0 + yl + y2 +... +yn_i + %yn). This approximation is closer than that given by 1181. (iii) A still closer approximation is obtained by regarding the curve passing through the ends of each set of three successive ordinates as being approximately the arc of a parabola having its axis parallel to the ordinates. For this purpose, make n an even number. The area of the two strips lying between the ordinates Vo Vv 2/2 is $h (y0 + 4yt+ y2). The area of the next two strips lying between the ordinates Z/2 2/s V is ih (y2 + 42/3+ yt). And so on, the area of the last two strips being ih (yn-2 + 42/, -! + yn). The sum of these n double strips is 1183. A-ih y0+ 4 (y, + y3 +yt +... + t/n-i) + 2 (y2 + yt + % +... + yn-2) + ttJ This formula is known under the name of Simpson's Ride. Simpson's Rule may be used for computing the value of the definite integral 6 J f (x) dx, provided / (x) and its derivatives /' (x), f (x), and /"' (x) remain finite and continuous in the interval from x = a to x = 6, and provided further that /iv (x) undergo no change of sign in the same interval. Under these conditions b 1184. Jj (x) dx-ih y0 + 4 (y, + j/s + ys +... + j/"_, ) + 2 (y2 + yt +ye +... + j/"_2) + yn + tt p K w" (b)-r m The last term represents E, the error of Simpson's Rule, that is 1185. i-ihTW-f'(4 In this expression p is no further known than that it is a positive or negative proper fraction, -1 P + 1; therefore the limits of the error are found by subs...
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Add this copy of Mathematical Handbook: Containing the Chief Formulas of to cart. $19.72, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Mathematical Handbook: Containing the Chief Formulas of to cart. $29.16, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
All Editions of Mathematical Handbook: Containing the Chief Formulas of Algebra, Trigonometry, Circular and Hyperbolic Functions, Differential and Integral Calculus, and Analytical Geometry, Together with Mathematical Tables
