English | 2017 | PDF | 11 MB | 805 Pages
by Kenneth B. Howell
Fourier analysis is one of the most useful and widely employed
sets of tools for the engineer, the scientist, and the applied
mathematician. As such, students and practitioners in these disciplines
need a practical and mathematically solid introduction to its
principles. They need straightforward verifications of its results and
formulas, and they need clear indications of the limitations of those
results and formulas.
Principles of Fourier Analysis furnishes
all this and more. It provides a comprehensive overview of the
mathematical theory of Fourier analysis, including the development of
Fourier series, "classical" Fourier transforms, generalized Fourier
transforms and analysis, and the discrete theory. Much of the author's
development is strikingly different from typical presentations. His
approach to defining the classical Fourier transform results in a much
cleaner, more coherent theory that leads naturally to a starting point
for the generalized theory. He also introduces a new generalized theory
based on the use of Gaussian test functions that yields an even more
general -yet simpler -theory than usually presented.
Principles
of Fourier Analysis stimulates the appreciation and understanding of the
fundamental concepts and serves both beginning students who have seen
little or no Fourier analysis as well as the more advanced students who
need a deeper understanding. Insightful, non-rigorous derivations
motivate much of the material, and thought-provoking examples illustrate
what can go wrong when formulas are misused. With clear, engaging
exposition, readers develop the ability to intelligently handle the more
sophisticated mathematics that Fourier analysis ultimately requires.
ISBNs: 1032477008, 1498734138, 9781032477008, 9781498734134, 9780849382758, 9781498734097, 9781315181493, 9781351722520, 9781498734080, 978-1032477008, 978-1498734134, 978-0849382758, 978-1498734097, 978-1315181493, 978-1351722520, 9781498734080
