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This book is the very first one in the English language entirely
dedicated to the Lambert W function, its generalizations, and its
applications. One goal is to promote future research on the topic.
The book contains all the information one needs when trying to find
a result. The most important formulas and results are framed. The
Lambert W function is a multi-valued inverse function with plenty
of applications in areas like molecular physics, relativity theory,
fuel consumption models, plasma physics, analysis of epidemics,
bacterial growth models, delay differential equations, fluid
mechanics, game theory, statistics, study of magnetic materials,
and so on. The first part of the book gives a full treatise of the
W function from theoretical point of view. The second part presents
generalizations of this function which have been introduced by the
need of applications where the classical W function is
insufficient. The third part presents a large number of
applications from physics, biology, game theory, bacterial cell
growth models, and so on. The second part presents the generalized
Lambert functions based on the tools we had developed in the first
part. In the third part familiarity with Newtonian physics will be
useful. The text is written to be accessible for everyone with only
basic knowledge on calculus and complex numbers. Additional
features include the Further Notes sections offering interesting
research problems and information for further studies. Mathematica
codes are included. The Lambert function is arguably the simplest
non-elementary transcendental function out of the standard set of
sin, cos, log, etc., therefore students who would like to deepen
their understanding of real and complex analysis can see a new
"almost elementary" function on which they can practice their
knowledge.
Combinatorics and Number Theory of Counting Sequences is an
introduction to the theory of finite set partitions and to the
enumeration of cycle decompositions of permutations. The
presentation prioritizes elementary enumerative proofs. Therefore,
parts of the book are designed so that even those high school
students and teachers who are interested in combinatorics can have
the benefit of them. Still, the book collects vast, up-to-date
information for many counting sequences (especially, related to set
partitions and permutations), so it is a must-have piece for those
mathematicians who do research on enumerative combinatorics. In
addition, the book contains number theoretical results on counting
sequences of set partitions and permutations, so number theorists
who would like to see nice applications of their area of interest
in combinatorics will enjoy the book, too. Features The Outlook
sections at the end of each chapter guide the reader towards topics
not covered in the book, and many of the Outlook items point
towards new research problems. An extensive bibliography and tables
at the end make the book usable as a standard reference. Citations
to results which were scattered in the literature now become easy,
because huge parts of the book (especially in parts II and III)
appear in book form for the first time.
Combinatorics and Number Theory of Counting Sequences is an
introduction to the theory of finite set partitions and to the
enumeration of cycle decompositions of permutations. The
presentation prioritizes elementary enumerative proofs. Therefore,
parts of the book are designed so that even those high school
students and teachers who are interested in combinatorics can have
the benefit of them. Still, the book collects vast, up-to-date
information for many counting sequences (especially, related to set
partitions and permutations), so it is a must-have piece for those
mathematicians who do research on enumerative combinatorics. In
addition, the book contains number theoretical results on counting
sequences of set partitions and permutations, so number theorists
who would like to see nice applications of their area of interest
in combinatorics will enjoy the book, too. Features The Outlook
sections at the end of each chapter guide the reader towards topics
not covered in the book, and many of the Outlook items point
towards new research problems. An extensive bibliography and tables
at the end make the book usable as a standard reference. Citations
to results which were scattered in the literature now become easy,
because huge parts of the book (especially in parts II and III)
appear in book form for the first time.
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