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2 results

  • 6 - Taylor Series Expansion and Application in Error Estimate

  • Chunyan Li, Louisiana State University
  • Book:
    Time Series Data Analysis in Oceanography
    Published online:
    21 April 2022
    Print publication:
    05 May 2022, pp 110-129

  • Summary

    The objective of this chapter is to review the Taylor series expansion and discuss its usage in error estimation. The unique value of Taylor series expansion is often neglected. The major assumption is that a function must be infinitely differentiable to use the Taylor series expansion. In real applications in oceanography, however, hardly there is a need to worry about a derivative higher than the 3rd order, although one may think of some exceptions. The point is, there is rarely a need in oceanography and other environmental sciences to actually consider calculating a very high order derivative, unless for theoretical investigations or under special situations. So the application of Taylor series expansion usually only involves the first two derivatives. In this chapter, some simple examples are included for a better understanding of the applications.

  • Multialgebras, universal algebras and identities

  • Part of
  • Cosmin Pelea, Ioan Purdea
  • Journal:
    Journal of the Australian Mathematical Society / Volume 81 / Issue 1 / August 2006
    Published online by Cambridge University Press:
    09 April 2009, pp. 121-140
    Print publication:
    August 2006
    • Article
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  • In this paper we determine the smallest equivalence relation on a multialgebra for which the factor multialgebra is a universal algebra satisfying a given identity. We also establish an important property for the factor multialgebra (of a multialgebra) modulo this relation.