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The mathematical study of how given quantities can be approximated by other (usually simpler) ones under appropriate conditions. Approximation theory also studies the size and properties of the Error introduced by approximation. Approximations are often obtained by Power Series expansions in which the higher order terms are dropped.
See also Lagrange Remainder
References
Achieser, N. I. Theory of Approximation. New York: Dover, 1992.
Cheney, E. W. Introduction to Approximation Theory. New York: McGraw-Hill, 1966.
Golomb, M. Lectures on Theory of Approximation. Argonne, IL: Argonne National Laboratory, 1962.
Jackson, D. The Theory of Approximation. New York: Amer. Math. Soc., 1930.
Natanson, I. P. Constructive Function Theory, Vol. 1: Uniform Approximation. New York: Ungar, 1964.
Petrushev, P. P. and Popov, V. A. Rational Approximation of Real Functions. New York: Cambridge University Press, 1987.
Rivlin, T. J. An Introduction to the Approximation of Functions. New York: Dover, 1981.
Timan, A. F. Theory of Approximation of Functions of a Real Variable. New York: Dover, 1994.
Approximation Theory