Theory of functions of complex variables, a branch of classical mathematics, has been applied to research the properties and performance of concrete materials. To study the stability of the system, dispersion relation and theory of conformal mapping, whicth are based on Cauchy's theorem, are to be used effectively. Inverse Laplace transform has been used to transform the impedance function from frequency domain into time domain. The research of the hydration dynamics of cement paste is a typical example of its application.