Discrete Calculus By Analogy

Preliminary Concepts

Author(s): F. A. Izadi

Pp: 1-19 (19)

Doi: 10.2174/978160805086410901010001

* (Excluding Mailing and Handling)

Abstract

For the purpose of being self-contained, the book starts with some elementary topics. These include the definition of various standard sets, some basic combinatorial definitions and identities, introducing complex numbers and their arithmetic properties, in particular de Moivre formula and the nth roots of a complex number. The case of square root gives rise to an elegant formula for the root of the real number of the form a± √b. The next two sections are devoted to the definitions and properties of matrices and determinants, the solutions of the linear system of equations as well as the formulas for some special determinants, in particular the Vandermonde determinant. Finally, the closing remark of the chapter is the definition of a function which plays an important role in discrete calculus. Because of its relation to the arrangement formula it is called "the arrangement power function".

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