Taylor Series 테일러 급수 문서 자료 및 동영상 강의

Taylor Series
functions can be approximated by series

Comprehensive notes on Taylor Series 테일러 급수 포괄적 자료
University of Washington Math 126 자료
http://www.math.washington.edu/~m126/TaylorNotes.pdf

Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

 

Taylor series (물리과학)

임의의 함수를 점 x＝ a 부근에서 다항식으로 근사하는 방법.

Taylor series (수리과학)

특정 함수식을 다항식으로 표현하는 방법.

 

http://alldic.daum.net/dic/search_result_total.do?eq=&LAYOUT_URL_PREFIX=&nil_profile=vsearch&nil_src=dic&type=all&q=taylor+series

 

"As the degree of the Taylor polynomial rises, it approaches the correct function. This image shows sin x (in black) and Taylor approximations, polynomials of degree 1, 3, 5, 7, 9, 11 and 13."


"The exponential function (in blue), and the sum of the first n+1 terms of its Taylor series at 0 (in red)."


Definition

The Taylor series of a real or complex function ƒ(x) that is infinitely differentiable in a neighborhood of a real or complex number a is the power series

which can be written in the more compact sigma notation as

where n! denotes the factorial of n and ƒ ⁽ⁿ⁾(a) denotes the nth derivative of ƒ evaluated at the point a. The zeroth derivative of ƒ is defined to be ƒ itself and (x − a)⁰ and 0! are both defined to be 1. In the case that a = 0, the series is also called a Maclaurin series.




Fundamentals of Physics (PHYS 200) 16. The Taylor Series and Other Mathematical Concepts
무표정으로 재미있는 교수 my 이상형 쿸 ah 공부가 필요하다






http://www.youtube.com/watch?v=KzrdZD4EPXY
http://en.wikipedia.org/wiki/Taylor_series