Introduction to Laplace Transforms and Fourier Series (ePub)

This book is an outcome of my teaching Mathematical Physics to the Final Year B. Sc. Physics (Hons.) students at Gargi College, Delhi University for about two decades. Over the years, my experience has been that there is a requirement of a book which dicusses the applications of Fourier series, Laplace transforms, Fourier transforms and Dirac delta function. These are topics which have several applications in Physics and Engineering namely in Mechanics, Sound, Optics, Electrical circuits. While excellent General Mathematical Physics books are available, the present textbook is an effort towards a simplified presentation of the most common integral transforms that the students of physics, mathematics and engineering learn. The book deals with a diverse set of applications from physics and engineering. It has a chapter dedicated to Dirac delta function which has several engineering oriented applications. Salient Features: Presentation of the Mathematics of these transforms with step wise derivations. Application of these Mathematical concepts to Physics and Engineering problems namely (a) mechanical oscillations (b) sound (c) optics (d) electrical circuits (e) quantum mechanics. Simple MATLAB codes have been written for determining the Laplace transforms, Inverse Laplace transforms, Fourier transforms and Inverse Fourier transforms which can be used by the students for verifying their answers. Solutions of the Exercises have been provided at the end of the book for a detailed understanding of each problem. Solutions to University examination questions on Fourier Series, Fourier Transforms, Laplace Transforms and Dirac delta functions have been included in the book.