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An Introduction to Fourier Analysis (Paperback)
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An Introduction to Fourier Analysis (Paperback)
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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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