Midlands State University Library
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An introduction to Fourier analysis / created by Russell Leland Herman.

By: Material type: TextTextPublisher: Taylor & Francis, 2017Description: xv, 386 pages: coloured illustrations; 28 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9781498773706
Subject(s): LOC classification:
  • QA403.5 HER
Contents:
Review of sequences of infinite series Fourier trigonometric series Generalized Fourier series and function spaces From continuous to discrete signals Signal analysis
Summary: This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. 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. After reading this book, students will be familiar with: " Convergence and summation of infinite series " Representation of functions by infinite series " Trigonometric and Generalized Fourier series " Legendre, Bessel, gamma, and delta functions " Complex numbers and functions " Analytic functions and integration in the complex plane " Fourier and Laplace transforms." The relationship between analog and digital signals 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
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Includes bibliographical references and index.

Review of sequences of infinite series
Fourier trigonometric series
Generalized Fourier series and function spaces
From continuous to discrete signals
Signal analysis

This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. 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. After reading this book, students will be familiar with: " Convergence and summation of infinite series " Representation of functions by infinite series " Trigonometric and Generalized Fourier series " Legendre, Bessel, gamma, and delta functions " Complex numbers and functions " Analytic functions and integration in the complex plane " Fourier and Laplace transforms." The relationship between analog and digital signals 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

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