Taylor s expansion theorem

The linearisation of the non-linear component and energy balance equations, based on the use of Taylor s expansion theorem, leads to two, simultaneous, first-order, linear differential equations with constant coefficients of the form... 

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... 

Taylor s theorem determines the law for the expansion of a function of the sum, or difference of two variables into a series of ascending powers of one of the variables. Now let... 

Taylor s theorem may be extended so as to include the expansion of functions of two or more independent variables. Let... 

This result is known as Taylor s theorem, and the expansion is a Taylor series. The case xq = 0, given by Eq. (7.40), is sometimes called a Maclaurin series. 

The first derivatives in a Taylor expansion, similar to Eqn (28), of the energy E with respect to the occupation numbers rii provide the KS-eigenvalues, as stated by Janak s theorem, and the second derivatives ... 

On the other hand, the Taylor expansion of Y gives the coefficient ak with de Moivre s theorem in the form48,49 ... 

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