Abstract
Mathematica usually works with exact numbers, either symbolic (π, e) or rational, and derives exact analytical results. However, it can also perform approximate numerical calculations. Many problems cannot be solved analytically, but numerical solution is possible. On the other side, an analytical result can depend on symbolic parameters; in order to do a numerical calculation, you have to substitute some numerical values for all parameters. It is often useful to check the correctness of a complicated analytical derivation by a direct numerical calculation for a few sets of values of the parameters.
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Grozin, A. (2014). Numerical Calculations. In: Introduction to Mathematica® for Physicists. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-00894-3_9
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