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Precise Numerical Differentiation of Thermodynamic Functions with
 Multicomplex Variables

The multicomplex finite-step method for numerical differentiation is an extension
 of the popular Squire–Trapp method, which uses complex arithmetics to compute
 first-order derivatives with almost machine precision. In contrast to this, the
 multicomplex method can be applied to higher-order derivatives. Furthermore, it can be
 applied to functions of more than one variable and obtain mixed derivatives. It is
 possible to compute various derivatives at the same time. This work demonstrates the
 numerical differentiation with multicomplex variables for some thermodynamic problems.
 The method can be easily implemented into existing computer programs, applied to
 equations of state of arbitrary complexity, and achieves almost machine precision for
 the derivatives. Alternative methods based on complex integration are discussed,
 too.