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\[CloseCurlyQuote]s one of the main tools available for solving differential \
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This book focuses exclusively on the Laplace transform and its inverse in \
both everyday words and mathematical terms. We avoid presenting sophisticated \
proofs and focus instead on explaining essential concepts in detail. A large \
number of examples and exercises are included to help the reader digest the \
material and to highlight the practical side of Laplace transform theory. \
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The 25 chapters presented here are organized into three sections. The first \
and second sections introduce the Laplace transform and its inverse \
respectively, covering essential properties such as linearity, scaling, \
translation theorems and the convolution theorem. We also explain methods for \
evaluating Laplace and inverse Laplace transforms, including the Bromwich \
inversion formula for the inverse transform, asymptotic expansion methods, \
numerical methods and more. The third section is dedicated to applications of \
the Laplace transform in differential equations (e.g. ODEs, PDEs, integral \
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physics and engineering. Engineers will find this section useful for studying \
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A wide range of readers will benefit from this material. Primarily, it is \
designed to be used by undergraduates as a textbook for a formal course on \
Laplace transforms or as supplementary material for such a course. The book \
also contains more advanced material (e.g. chapters on asymptotic expansions \
of the Laplace transform and numerical inverse Laplace transforms), which can \
be beneficial for both graduate students and researchers. We have tried to \
keep the book self-contained; however, some prior knowledge of calculus and \
complex analysis is required for a better understanding of the book.\
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Hrachya Khachatryan,
Wolfram Research, Inc.\
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