[A+] [미적분]다항식의 추정값(polynomial appoximation to functions)
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작성일 20-03-20 14:40
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다항식의 추정값을 구하는 것으로
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[미적분]다항식의 추정값(polynomial appoximation to functions)
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Download : 7_Polynomial_Approximations_to_Functions.hwp( 26 )
시험 전에 정리(arrangement)해서 보기 좋은 자료.
영문자료임.
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`).
7. Polynomial Approximations to Functions.
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) = , …(skip)
다항식의 추정값을 구하는 것으로대부분 테일러 시리즈에 대한 내용으로영문자료임.시험 전에 정리해서 보기 좋은 자료. , [미적분]다항식의 추정값(polynomial appoximation to functions)시험자료전문자료 , 테일러 전개 급수 시리즈 다항식 태일러
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