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This book presents an introduction to the key topics in Real
Analysis and makes the subject easily understood by the learners.
The book is primarily useful for students of mathematics and
engineering studying the subject of Real Analysis. It includes many
examples and exercises at the end of chapters. This book is very
authentic for students, instructors, as well as those doing
research in areas demanding a basic knowledge of Real Analysis. It
describes several useful topics in Real Analysis such as sets and
functions, completeness, ordered and field, neighborhoods, limit
points of a set, open sets, closed sets, countable and uncountable
sets, sequences of real numbers, limit, continuity and
differentiability of real functions, uniform continuity, point-wise
and uniform convergence of sequences and series of real functions,
Riemann integration, improper integrals and metric spaces.
The volume will consist of about 40 articles written by some very
influential mathematicians of our time and will expose the latest
achievements in the broad area of nonlinear analysis and its
various interdisciplinary applications.
One service mathematics has rendered the 'Et moi .... si favait su
comment en revenir, je human race. It has put common sense back n'y
serais point a1l6.' lules Verne where it belongs, on the topmost
shelf next to the dusty eanister labelled 'discarded nonsense' .
Erie T. Bell The series is divergent; therefore we may be able to
do something with it O. Heaviside Mathematics is a tool for
thought. A highly necessary tool in a world where both feedback and
nonlineari ties abound. Similarly, all kinds of parts of
mathematics serve as tools for other parts and for other sci ences.
Applying a simple rewriting rule to the quote on the right above
one finds such statements as: 'One ser vice topology has rendered
mathematical physics .. .'; 'One service logic has rendered
computer science .. .'; 'One service category theory has rendered
mathematics .. .'. All arguably true. And all statements obtainable
this way form part of the raison d'etre of this series. This
series, Mathematics and Its Applications, started in 1977. Now that
over one hundred volumes have appeared it seems opportune to
reexamine its scope. At the time I wrote "Growing specia1ization
and diversification have brought a host of monographs and textbooks
on increasingly specialized topics. However, the 'tree' of
knowledge of mathematics and It also happens, quite often in
related fields does not grow only by putting forth new branches."
This book features selected papers from The Seventh International
Conference on Research and Education in Mathematics that was held
in Kuala Lumpur, Malaysia from 25 - 27th August 2015. With chapters
devoted to the most recent discoveries in mathematics and
statistics and serve as a platform for knowledge and information
exchange between experts from academic and industrial sectors, it
covers a wide range of topics, including numerical analysis, fluid
mechanics, operation research, optimization, statistics and game
theory. It is a valuable resource for pure and applied
mathematicians, statisticians, engineers and scientists, and
provides an excellent overview of the latest research in
mathematical sciences.
The book is devoted to recent developments in the theory of
fractional calculus and its applications. Particular attention is
paid to the applicability of this currently popular research field
in various branches of pure and applied mathematics. In particular,
the book focuses on the more recent results in mathematical
physics, engineering applications, theoretical and applied physics
as quantum mechanics, signal analysis, and in those relevant
research fields where nonlinear dynamics occurs and several tools
of nonlinear analysis are required. Dynamical processes and
dynamical systems of fractional order attract researchers from many
areas of sciences and technologies, ranging from mathematics and
physics to computer science.
This book explores several important aspects of recent developments
in the interdisciplinary applications of mathematical analysis
(MA), and highlights how MA is now being employed in many areas of
scientific research. Each of the 23 carefully reviewed chapters was
written by experienced expert(s) in respective field, and will
enrich readers' understanding of the respective research problems,
providing them with sufficient background to understand the
theories, methods and applications discussed. The book's main goal
is to highlight the latest trends and advances, equipping
interested readers to pursue further research of their own. Given
its scope, the book will especially benefit graduate and PhD
students, researchers in the applied sciences, educators, and
engineers with an interest in recent developments in the
interdisciplinary applications of mathematical analysis.
This book presents a collection of original research papers from
the 2nd International Conference on Mathematical and Related
Sciences, held in Antalya, Turkey, on 27 - 30 April 2019 and
sponsored/supported by Duzce University, Turkey; the University of
Jordan; and the Institute of Applied Mathematics, Baku State
University, Azerbaijan. The book focuses on various types of
mathematical methods and models in applied sciences; new
mathematical tools, techniques and algorithms related to various
branches of applied sciences; and important aspects of applied
mathematical analysis. It covers mathematical models and modelling
methods related to areas such as networks, intelligent systems,
population dynamics, medical science and engineering, as well as a
wide variety of analytical and numerical methods. The conference
aimed to foster cooperation among students, researchers and experts
from diverse areas of mathematics and related sciences and to
promote fruitful exchanges on crucial research in the field. This
book is a valuable resource for graduate students, researchers and
educators interested in applied mathematics and interactions of
mathematics with other branches of science to provide insights into
analysing, modelling and solving various scientific problems in
applied sciences.
This book features selected papers from The Seventh International
Conference on Research and Education in Mathematics that was held
in Kuala Lumpur, Malaysia from 25 - 27th August 2015. With chapters
devoted to the most recent discoveries in mathematics and
statistics and serve as a platform for knowledge and information
exchange between experts from academic and industrial sectors, it
covers a wide range of topics, including numerical analysis, fluid
mechanics, operation research, optimization, statistics and game
theory. It is a valuable resource for pure and applied
mathematicians, statisticians, engineers and scientists, and
provides an excellent overview of the latest research in
mathematical sciences.
The volume will consist of about 40 articles written by some very
influential mathematicians of our time and will expose the latest
achievements in the broad area of nonlinear analysis and its
various interdisciplinary applications.
In recent years there has been an increasing interest in problems
involving closed form evaluations of (and representations of the
Riemann Zeta function at positive integer arguments as) various
families of series associated with the Riemann Zeta function ((s),
the Hurwitz Zeta function ((s, a), and their such extensions and
generalizations as (for example) Lerch's transcendent (or the
Hurwitz-Lerch Zeta function) iI>(z, s, a). Some of these
developments have apparently stemmed from an over two-century-old
theorem of Christian Goldbach (1690-1764), which was stated in a
letter dated 1729 from Goldbach to Daniel Bernoulli (1700-1782),
from recent rediscoveries of a fairly rapidly convergent series
representation for ((3), which is actually contained in a 1772
paper by Leonhard Euler (1707-1783), and from another known series
representation for ((3), which was used by Roger Apery (1916-1994)
in 1978 in his celebrated proof of the irrationality of ((3). This
book is motivated essentially by the fact that the theories and
applications of the various methods and techniques used in dealing
with many different families of series associated with the Riemann
Zeta function and its aforementioned relatives are to be found so
far only"in widely scattered journal articles. Thus our systematic
(and unified) presentation of these results on the evaluation and
representation of the Zeta and related functions is expected to
fill a conspicuous gap in the existing books dealing exclusively
with these Zeta functions."
Analytic and Geometric Inequalities and Applications is devoted to
recent advances in a variety of inequalities of Mathematical
Analysis and Geo metry. Subjects dealt with in this volume include:
Fractional order inequalities of Hardy type, differential and
integral inequalities with initial time differ ence,
multi-dimensional integral inequalities, Opial type inequalities,
Gruss' inequality, Furuta inequality, Laguerre-Samuelson inequality
with extensions and applications in statistics and matrix theory,
distortion inequalities for ana lytic and univalent functions
associated with certain fractional calculus and other linear
operators, problem of infimum in the positive cone, alpha-quasi
convex functions defined by convolution with incomplete beta
functions, Chebyshev polynomials with integer coefficients,
extremal problems for poly nomials, Bernstein's inequality and
Gauss-Lucas theorem, numerical radii of some companion matrices and
bounds for the zeros of polynomials, degree of convergence for a
class of linear operators, open problems on eigenvalues of the
Laplacian, fourth order obstacle boundary value problems, bounds on
entropy measures for mixed populations as well as controlling the
velocity of Brownian motion by its terminal value. A wealth of
applications of the above is also included. We wish to express our
appreciation to the distinguished mathematicians who contributed to
this volume. Finally, it is our pleasure to acknowledge the fine
cooperation and assistance provided by the staff of Kluwer Academic
Publishers. June 1999 Themistocles M. Rassias Hari M."
One service mathematics has rendered the 'Et moi .... si favait su
comment en revenir, je human race. It has put common sense back n'y
serais point a1l6.' lules Verne where it belongs, on the topmost
shelf next to the dusty eanister labelled 'discarded nonsense' .
Erie T. Bell The series is divergent; therefore we may be able to
do something with it O. Heaviside Mathematics is a tool for
thought. A highly necessary tool in a world where both feedback and
nonlineari ties abound. Similarly, all kinds of parts of
mathematics serve as tools for other parts and for other sci ences.
Applying a simple rewriting rule to the quote on the right above
one finds such statements as: 'One ser vice topology has rendered
mathematical physics .. .'; 'One service logic has rendered
computer science .. .'; 'One service category theory has rendered
mathematics .. .'. All arguably true. And all statements obtainable
this way form part of the raison d'etre of this series. This
series, Mathematics and Its Applications, started in 1977. Now that
over one hundred volumes have appeared it seems opportune to
reexamine its scope. At the time I wrote "Growing specia1ization
and diversification have brought a host of monographs and textbooks
on increasingly specialized topics. However, the 'tree' of
knowledge of mathematics and It also happens, quite often in
related fields does not grow only by putting forth new branches."
This book explores several important aspects of recent developments
in the interdisciplinary applications of mathematical analysis
(MA), and highlights how MA is now being employed in many areas of
scientific research. Each of the 23 carefully reviewed chapters was
written by experienced expert(s) in respective field, and will
enrich readers' understanding of the respective research problems,
providing them with sufficient background to understand the
theories, methods and applications discussed. The book's main goal
is to highlight the latest trends and advances, equipping
interested readers to pursue further research of their own. Given
its scope, the book will especially benefit graduate and PhD
students, researchers in the applied sciences, educators, and
engineers with an interest in recent developments in the
interdisciplinary applications of mathematical analysis.
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