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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.
The Second Edition of Ordinary Differential Equations: An
Introduction to the Fundamentals builds on the successful First
Edition. It is unique in its approach to motivation, precision,
explanation and method. Its layered approach offers the instructor
opportunity for greater flexibility in coverage and depth. Students
will appreciate the author's approach and engaging style. Reasoning
behind concepts and computations motivates readers. New topics are
introduced in an easily accessible manner before being further
developed later. The author emphasizes a basic understanding of the
principles as well as modeling, computation procedures and the use
of technology. The students will further appreciate the guides for
carrying out the lengthier computational procedures with
illustrative examples integrated into the discussion. Features of
the Second Edition: Emphasizes motivation, a basic understanding of
the mathematics, modeling and use of technology A layered approach
that allows for a flexible presentation based on instructor's
preferences and students' abilities An instructor's guide
suggesting how the text can be applied to different courses New
chapters on more advanced numerical methods and systems (including
the Runge-Kutta method and the numerical solution of second- and
higher-order equations) Many additional exercises, including two
"chapters" of review exercises for first- and higher-order
differential equations An extensive on-line solution manual About
the author: Kenneth B. Howell earned bachelor's degrees in both
mathematics and physics from Rose-Hulman Institute of Technology,
and master's and doctoral degrees in mathematics from Indiana
University. For more than thirty years, he was a professor in the
Department of Mathematical Sciences of the University of Alabama in
Huntsville. Dr. Howell published numerous research articles in
applied and theoretical mathematics in prestigious journals, served
as a consulting research scientist for various companies and
federal agencies in the space and defense industries, and received
awards from the College and University for outstanding teaching. He
is also the author of Principles of Fourier Analysis, Second
Edition (Chapman & Hall/CRC, 2016).
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.
The Second Edition of Ordinary Differential Equations: An
Introduction to the Fundamentals builds on the successful First
Edition. It is unique in its approach to motivation, precision,
explanation and method. Its layered approach offers the instructor
opportunity for greater flexibility in coverage and depth. Students
will appreciate the author's approach and engaging style. Reasoning
behind concepts and computations motivates readers. New topics are
introduced in an easily accessible manner before being further
developed later. The author emphasizes a basic understanding of the
principles as well as modeling, computation procedures and the use
of technology. The students will further appreciate the guides for
carrying out the lengthier computational procedures with
illustrative examples integrated into the discussion. Features of
the Second Edition: Emphasizes motivation, a basic understanding of
the mathematics, modeling and use of technology A layered approach
that allows for a flexible presentation based on instructor's
preferences and students' abilities An instructor's guide
suggesting how the text can be applied to different courses New
chapters on more advanced numerical methods and systems (including
the Runge-Kutta method and the numerical solution of second- and
higher-order equations) Many additional exercises, including two
"chapters" of review exercises for first- and higher-order
differential equations An extensive on-line solution manual About
the author: Kenneth B. Howell earned bachelor's degrees in both
mathematics and physics from Rose-Hulman Institute of Technology,
and master's and doctoral degrees in mathematics from Indiana
University. For more than thirty years, he was a professor in the
Department of Mathematical Sciences of the University of Alabama in
Huntsville. Dr. Howell published numerous research articles in
applied and theoretical mathematics in prestigious journals, served
as a consulting research scientist for various companies and
federal agencies in the space and defense industries, and received
awards from the College and University for outstanding teaching. He
is also the author of Principles of Fourier Analysis, Second
Edition (Chapman & Hall/CRC, 2016).
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