Results 221 to 230 of about 2,019,730 (284)
Some of the next articles are maybe not open access.
2020
This chapter focuses on the Taylor series. It points out that, Wwhen dealing with a complicated function, it can be useful to approximate the functionit with one of a simpler form. While the latter may not represent a complete and accurate description of the situation at hand, it frequently provides the only means of making analytical progress.
D.S. Sivia, J.L. Rhodes, S.G. Rawlings
openaire +1 more source
This chapter focuses on the Taylor series. It points out that, Wwhen dealing with a complicated function, it can be useful to approximate the functionit with one of a simpler form. While the latter may not represent a complete and accurate description of the situation at hand, it frequently provides the only means of making analytical progress.
D.S. Sivia, J.L. Rhodes, S.G. Rawlings
openaire +1 more source
2011
In this lecture, we shall prove Taylor’s Theorem, which expands a given analytic function in an infinite power series at each of its points of analyticity. The novelty of the proof comes from the fact that it requires only Cauchy’s integral formula for derivatives.
Ravi P. Agarwal +2 more
openaire +1 more source
In this lecture, we shall prove Taylor’s Theorem, which expands a given analytic function in an infinite power series at each of its points of analyticity. The novelty of the proof comes from the fact that it requires only Cauchy’s integral formula for derivatives.
Ravi P. Agarwal +2 more
openaire +1 more source
Taylor Polynomials and Taylor Series
2015Taylor polynomials are used to approximate values of functions at specified points. The error incurred is investigated by means of Taylor’s theorem. A method for ensuring that the approximation is accurate to within a specified error tolerance is illustrated. Taylor polynomials are then used to define Taylor series. Several techniques for finding these
Charles H. C. Little +2 more
openaire +1 more source
Some Taylor Series without Taylor's Theorem
Mathematics Magazine, 2018The Taylor series for ex, sin (x), and cos (x) are perhaps the most frequently used in all of mathematics (and give a nice proof of Euler's formula), but rigorously deriving them is nontrivial and ...
openaire +1 more source
From Taylor series to Taylor models
AIP Conference Proceedings, 1997An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way.
openaire +1 more source
Taylor Series and Power Series
2009In Chap. 5 we showed that the sum of a geometric series is given by $$1+x+x^{2}+x^{3}+\cdots=\frac{1}{1-x}$$ This formula holds true for ...
Klaus Weltner +3 more
openaire +1 more source