Taylor and Maclaurin series

Taylor s theorem permits the expansion of certain functions, often in the form of a polynomial. Only the terms which contribute in a significant way to the response are utilized, in this way facilitating the mathematical 

The theorem covers continuous functions which have continuous and unique value derivatives within the range considered. The expansion for f(a+x) is 

Hyperbolic functions are combinations of exponentials. They are given in Table A1.4, and these functions are plotted in Fig. A1.4. Since they are continuous functions, with continuous derivatives obtained in the same way as normal trigonometric functions, that is 

Hyperbolic functions frequently appear in electrochemical problems, for instance in the inversion of Laplace transforms. An important example of the use of the cosh function is in the expression for the differential capacity of the electrolyte double layer following the Gouy-Chapman model (Chapter 3) which has a minimum value and is symmetric around this minimum—compare Fig. 3.6 with the cosh function in Fig. A1.4. 

Abramowitz and I. A. Stegun (ed.), Handbook of mathematical functions, Dover, New York, 1965. 

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