Description
Taylor & Francis Introduction To Fourier Analysis by Russell L. Herman
This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering._x000D__x000D__x000D__x000D__x000D__x000D_This introductory textbook was written with mathematics, science, and engineering students with a background in calculus and basic linear algebra in mind. It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A number of examples and exercises are provided including implementations of Maple, MATLAB, and Python for computing series expansions and transforms. _x000D__x000D__x000D__x000D__x000D__x000D_After reading this book, students will be familiar with:_x000D__x000D__x000D__x000D__x000D__x000D_* Convergence and summation of infinite series_x000D__x000D__x000D_* Representation of functions by infinite series_x000D__x000D__x000D_* Trigonometric and Generalized Fourier series_x000D__x000D__x000D_* Legendre, Bessel, gamma, and delta functions_x000D__x000D__x000D_* Complex numbers and functions_x000D__x000D__x000D_* Analytic functions and integration in the complex plane_x000D__x000D__x000D_* Fourier and Laplace transforms._x000D__x000D__x000D_* The relationship between analog and digital signals_x000D__x000D__x000D__x000D__x000D__x000D_Dr. Russell L. Herman is a professor of Mathematics and Professor of Physics at the University of North Carolina Wilmington. A recipient of several teaching awards, he has taught introductory through graduate courses in several areas including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests include topics in nonlinear wave equations, soliton perturbation theory, fluid dynamics, relativity, chaos and dynamical systems._x000D_ _x000D_
Review of Sequences and Infinite Series. Fourier Trigonometric Series. Generalized Fourier Series and Function Spaces. Complex Analysis. Fourier and Laplace Transforms. From Analog to Discrete Signals. Signal Analysis._x000D_