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 provides 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.
• Relationship between analog and digital signals.
Dr. Russell L. Herman is Professor of Mathematics and Professor of Physics at
UNC 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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