Investigation in Taylor series
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"Investigation in Taylor series"에 대한 내용입니다.
목차
I. Introduction
II. The general formula for the Taylor series:
III. Taylor’s theorem
IV. Approximation error
V. Convergence of Taylor series
VI. A better approximation method taking error into consideration
VII. Real-life implications of results
VIII. Conclusion and Reflection
IX. Works Cited
본문내용
My interest in Taylor series arose when I became curious of how our graphic display calculators actually calculate a value when we plug-in an value into a function. As a calculator would not be able to have every single value for any function, there must be an algorithm that the calculator uses to calculate functional values. I searched up what kind of calculations our graphic calculators are actually doing, and what I have found was the marvelous series – Taylor series.
A Taylor series is “a series expansion of a function about a point” (Abramowitz). What our calculators do to calculate a functional value is that, they approximate a function into this Taylor series give approximate values when we input a value. I became curious of the explicit process ‘how’ this Taylor series is actually used and how reliable it is to use to calculate any functional value on the calculator. Therefore I developed my aims of this exploration: 1) Investigate in how Taylor series is used in graphic display calculators through its proof and applications and 2) investigate in the approximation error produced by Taylor series.
참고 자료
Abramowitz, Milton. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Martino Publishing, 2014.
“Calculus: an Intuitive and Physical Approach (2nd Edition), by Morris Kline. Pp Xvi, 943. £14·60. 1977.
SBN 0 471 49116 0 (Wiley).” The Mathematical Gazette, vol. 61, no. 417, 1977, p. 240., doi:10.1017/s0025557200085132.
Genocchi, Angelo. Calcolo differenziale e principii di calcolo integrale. Fratelli Bocca ed, 1884.
Mastragostino, Robert. “What Are the Practical Applications of the Taylor Series?” Mathematics Stack Exchange, math.stackexchange.com/questions/218421/what-are-the-practical-applications-of-thetaylor-series.
Smith, Steven W. “The Scientist and Engineer's Guide To Digital Signal Processing By Steven W. Smith,
Ph.D.” The Scientist and Engineer's Guide to Digital Signal Processing,
www.dspguide.com/ch13/4.htm.
