«TAYLOR'S SERIES» 관련 영어 책
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1
Optimization: Foundations and Applications
The results in Taylor's series are essential for these definitions. 3.3.1 Taylor's
Series for/(,v) Taylor's (Brook Taylor, English, 1685-1731) series for/U) says that
an approximation to the value of the function in the neighborhood of a particular ...
2
Analysis of Aircraft Structures: An Introduction
The question of exactly when a Taylor's series is valid is not a simple one. The
use of Taylor's series to represent the exceptionally smooth functions that
generally describe stresses, strains, displacements, and the derivatives of these ...
3
Calculus: Problems and Solutions
1234) in which convergent power series serve as Taylor's series of a given
function /(x), (i.e. they are obtained from/(x) by Taylo(s procedure), but their sum S
(x) differs from /(x). Only the fact that lim A„+i(x0) = 0 ensures that the s— ,s sum S
(x0) ...
4
Advanced Engineering Mathematics
Linear Taylor's series approximation is /(x0 + Ji, y0 + fc) «/(x0, y0) + [fx(xQ, y0) +/y
(x0, y0)]. Substituting the values, we get In [(1.03)1/3 + (0.98)1/4 - 1] = 0 + (.03) (1/
3) - (.02) (1/4) = .01 - .005 = .005 (approx.) EXERCISE 4.7 1. Express x2 + 3y2 ...
5
Optimization: Foundations and Applications
3.3 TAYLOR'S SERIES, CONCAVITY, AND CONVEXITY OF f (x) Second-order
conditions at a point x* establish the shape of f(x) at that point. The definitions of
concavity and convexity of f(x) are also descriptions of shape, and they are easily
...
6
Mathematics for Electrical Technicians 4/5: Level 4-5
This equation is called Taylor's theorem or Taylor's series. If a is made zero in
Taylor's series given in equation (6), then: f(x) =f(0) + xf'(0) +%f”(()) + . .. i.e.
Maclaurin's series is a special case of Taylor's series when a is equal to 0. Some
of the ...
J. O. Bird, A. J. C. May, 2014
7
Engineering Thermofluids: Thermodynamics, Fluid Mechanics, ...
Numerical Solutions of Ordinary Differential Equations There are several
methods for numerically solving the initial value problems of ordinary differential
equations among which we mention such method as Taylor's series, Euler,
Adams, ...
8
A Course in Pure Mathematics
Margaret M. Gow. 11.3.
Taylor's series Taylor's series gives the expansion of /(*)
in powers olx — a, a being a constant. Suppose that /(*) = b0+b1(x-a) + bi(x-a)* +
b3(x - a)3 + . . . + bn(x - a)» + . . . (ii) when a— l<x<a+l. Then by successive ...
9
Advanced Mathematical Methods with Maple
For functions that possess a Taylor's series the command series (f ,x=c,N+l)
produces the same result. A.-L. Cauchy Cauchy noted that the series 4.26 may
converge, but not necessarily to the original (1789-1857) function f(x). for
example if fix.
Equation (9) which expands f(x, y) in infinite power series in powers (terms) of (x -
a)and(;y — b) is known as Taylor's series or Taylor's expansion or Taylor's series
expansion of /(.v, y) about the point Introducing the operator notation, .3 .3 so ...
