[미적분]다항식의 추정값(polynomial appoximation to functions)
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- 2008.06.16
- 최종 저작일
- 2007.04
- 3페이지/ 한컴오피스
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다항식의 추정값을 구하는 것으로
대부분 테일러 시리즈에 대한 내용으로
영문자료임.
시험 전에 정리해서 보기 좋은 자료.
목차
Theorem 7.1.
Theorem. 7.2. The Taylor operator Tn has the following properties:
Theorem. 7.3. Substitution Property.
Theorem. 7.4
Theorem 7.5
Theorem 7.6
Theorem. 7.7.
등..
본문내용
Theorem 7.1. Let f be a function with derivatives of order n at the point x=0. Then there exists one and only one polynomial P of degree ≤ n which satisfies the n+1 conditions p(0) = f(0), P`(0) = f`(0), ....., P(n)(0) = f(n)(0). This polynomial is given by the formula P(x) = Tn f(x).
Point. point x = a, P(x) = Tn f(x;a).
Point. T2n+1(sinx) = x - x3/3! + x5/5! - x7/7! + ... + (-1)n x2n+1/(2n+1)!
Point. T2n(cosx) = 1 - x2/2! + x4/4! - x6/6! + .... + (-1)n x2n/(2n)!
Theorem. 7.2. The Taylor operator Tn has the following properties:
(a) Linearity property. If c1 and c2 are constants, then Tn(c1f + c2g) = c1Tn(f) + c2Tn(g)
(b) Differentiation property. The derivative of a Taylor polynomial of f is a Taylor polynomial of f`; in fact, we have (Tnf)` = Tn-1(f`).
(c) Integration property. An indefinite integral of a Taylor polynomial of f is a Taylor polynomial of an indefinite integral of f. More precisely, if g(x) = , then we have Tn+1g(x) = .
Theorem. 7.3. Substitution Property. Let g(x) = f(cx), where c is a constant. Then we have Tng(x;a) = Tnf(cx;ca).
참고 자료
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