ABSTRACT
Mathematics has its roots embedded within various streams of engineering and sciences. The concepts of the famous Fourier series were originated from the field of physics. The fundamental problem is not that number theorists bring in additional concepts like number fields, Galois groups, and modular forms. They do, but the issue arises even when working with purely elementary statements like the four-square theorem. J. Willard Gibbs, an American physicist, studied the peculiar manner of Fourier series. He stated that near the discontinuity manifested, due to lack of development in the approximations, there is a continual presence of the overshoot or undershoot. A major portion of the study of theory of signals is concerned with the connections between the structural properties of a function and its degree of approximation. In mathematical physics, the wave equations can be represented in the form of the trigonometric Fourier series.
