Mathematical Method in Physics

Mathematical Physics is a significant discipline, concerned with the interface of mathematics and physics. There are several distinct branches of Mathematical Physics and these roughly corresponded to particular historical periods. Mathematics and physics have interacted fruitfully for centuries. Physics has been a constant source of interesting mathematical problems, and these problems have often required new mathematics for their solution. Conversely, advances in mathematics have found surprising and impressive applications in physics. Mathematics may be considered as a logical relationship language developed upon the concept / definition of one. From this one, we can logically define two, three, etc. which we call numbers. Hence a number is some relationship to one. Once we have whole numbers then we can define add, subtract, multiply and divide. Fractions, squares, cubes, etc, all became possible, as more and more complexly defined relationships between numbers evolved. Ordinary differential equations are equations to be solved in which the unknown element is a function, rather than a number, and in which the known information relates that function to its derivatives. Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. There are many important classes of differential equations for which detailed information is available. Fourier series are used extensively in engineering, especially for processing images and other signals. Finding the coefficients of a Fourier series is the same as doing a spectral analysis of a function. The Fourier series is a mathematical tool used for analyzing an arbitrary periodic function by decomposing it into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. This book is intended partly to serve as a textbook cum reference for the course Engineering Physics taught at the undergraduate level in engineering colleges all over the country. The other purpose of the book is to serve as a reference book for research workers in theoretical physics and signal processing.