Taylor polynomial meaning: definition, quotations

Taylor polynomial

noun

Mathematical analysis, Mathematics, Sciences A truncated Taylor series; the sum of the first n terms of a Taylor series.

For example, if Mⁿ#61;#92;mathbb#123;R#125;ⁿ and Nᵏ#61;#92;mathbb#123;R#125;, a singularity means the vanishing of the gradient, or equivalently, the linear terms of the Taylor's polynomial of some degree greater than 1. If one has a singularity, one may look at the second-order terms in the Taylor's polynomial.1980, Donald W. Kahn, Introduction to Global Analysis, Academic Press, page 314:
The polynomial approximation above for exp(x) is an example of a Taylor polynomial of degree 2 and in fact the polynomial approximations to sin(x) and cos(x) that we wrote down in Chapter 3 are also Taylor polynomials.1989, J. Berry, John Stephen Berry, A. Norcliffe, S. Humble, Introductory Mathematics Through Science Applications, Cambridge University Press, page 211:

1 more example

Then, we introduce and investigate the Taylor polynomials and we prove suitable versions of the Lagrange mean value theorem and of the Taylor formula.2007, Andrea Bonfiglioli, Ermanno Lanconelli, Francesco Uguzzoni, Stratified Lie Groups and Potential Theory for their Sub-Laplacians, Springer, page 733: