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Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is... more...

Vector calculus is the foundation stone on which a vast amount of applied mathematics is based. Topics such as fluid dynamics, solid mechanics and electromagnetism depend heavily on the calculus of vector quantities in three dimensions. This book covers the material in a comprehensive but concise manner, combining mathematical rigour with physical insight. There are many diagrams to illustrate the physical meaning of the mathematical concepts, which is... more...

The eighth edition of the classic Gradshteyn and Ryzhik is an
updated completely revised edition of what is acknowledged
universally by mathematical and applied science users as the key
reference work concerning the integrals and special functions.
The book is valued by users of previous editions of the work both
for its comprehensive coverage of integrals and special
functions, and also for its accuracy and valuable updates. Since
the... more...

Are you looking for new lectures for your course on algorithms,
combinatorial optimization, or algorithmic game theory?
Maybe you need a convenient source of relevant, current topics
for a graduate student or advanced undergraduate student
seminar? Or perhaps you just want an enjoyable look at some
beautiful mathematical and algorithmic results, ideas, proofs,
concepts, and techniques in discrete mathematics and theoretical... more...

Over 1500 problems on theory of functions of the complex
variable; coverage of nearly every branch of classical function
theory. Topics include conformal mappings, integrals and power
series, Laurent series, parametric integrals, integrals of the
Cauchy type, analytic continuation, Riemann surfaces, much
more. Answers and solutions at end of text. Bibliographical
references. 1965 edition.

This commemorative volume honors mathematician Paul R. Halmos,
whose research, unparalleled mathematical exposition, and
dedication to service made a major impact on the mathematics
community. Various articles discuss his contributions to the
operator theory.

Using a contemporary approach and a lively style, Gelbaum combines
real and complex analysis, covering all major topics. He discusses
topology in three ways: via open sets, nets and filters. Features a
detailed exploration of the link between measure as derived from a
Daniell functional and classical Lebesgue-Caratheodory measure.
Includes complete definitions of all mathematical concepts as well
as numerous exercises and illustrations.

This book covers the material of a one year course in real
analysis. It includes an original axiomatic approach to
Lebesgue integration which the authors have found to be effective
in the classroom. Each chapter contains numerous examples
and an extensive problem set which expands considerably the
breadth of the material covered in the text. Hints are
included for some of the more difficult problems.

This book is intended for graduate students and research
mathematicians.

A systematic, unified treatment of orthogonal transform methods for
signal processing, data analysis and communications, this book
guides the reader from mathematical theory to problem solving in
practice. It examines each transform method in depth, emphasizing
the common mathematical principles and essential properties of each
method in terms of signal decorrelation and energy compaction. The
different forms of Fourier transform, as well as the... more...