Signal Processing

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In signals and systems, we are taught how to model systems using linear ordinary differential and differences equations with constant coefficients. This book extends this circle of ideas by introducing systems in physics that are modeled using partial differential equations, and nonlinear differential equations having possibly time varying coefficients and also stochastic differential equations involving nonlinear systems with random inputs. The physical systems that are modeled using nonlinear ordinary differential equations are those arising in classical mechanics, namely the Newtonian laws of motion. The systems involving the use of partial differential equations are those arising in electrodynamics, fluid dynamics quantum mechanics and general relativity. The systems involving the use of stochastic differential equations are primarily mechanical systems perturbed by noise. Numerical techniques developed for the solution of nonlinear ordinary and partial differential equations lead to difference equations. The undergraduate student after attending the course on signals and systems will be in a position to read this book and embar upon research in this wide field. The book can be used even by applied mathematicians who are looking for problems in physics where they can apply the theory of differential equations.

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