Investigation in Taylor series

소개

"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.

참고자료

· 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.