Taylor Series

George McCarty
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George McCarty: University of California

Chapter 13 in Calculator Calculus, 1982, pp 184-201 from Springer

Abstract: Abstract After the Fundamental Theorem of the Calculus, Taylor’s theorem and the Taylor series form the most important theoretical and practical tool of the calculus. They certainly comprise the central concept of numerical analysis. In the last chapter we developed many familiar functions in series and acquired some facility in their use. We shall now study some applications of this theory. A first Example develops a series that approximates the logarithm function at x=2, even though the function is not defined at all at x=0. Next we describe Newton’s method and give Examples of its use and misuse for the functions e x -2x-1 and (x-1)/x2. Then series integration is explored with the Sine and Fresnel integrals as Examples. In the Example of 1/(1-x2) we discuss and then analyze the error in series integration.

Keywords: Taylor Series; Tangent Line; Decimal Place; Remainder Term; Iteration Function (search for similar items in EconPapers)
Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4684-6484-9_13

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DOI: 10.1007/978-1-4684-6484-9_13

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