12

Preliminaries

In this chapter, we present some basic mathematical concepts and definitions which shall be frequently used in the forthcoming chapters. The knowledge of these concepts is essential due to their extensive use in the study of Fourier series and various integral transforms. For example, knowledge of real- and complex-valued functions—along with their continuity, differentiability, and integrability, and sequences, series, and special functions—is required time and again in this study.

12.1 SETS AND FUNCTIONS

According to Georg Cantor, a set may be viewed as a well-defined collection of objects, called the elements or members of the set.

The sets are denoted by capital letters such A, B, and C whereas its elements are denoted by ...

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