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Fractional calculus in terms of mathematics and statistics and its
applications to problems in natural sciences is NOT yet part of
university teaching curricula. This book is one attempt to provide
an approach to include topics of fractional calculus into
university curricula. Additionally the material is useful for
people who do research work in the areas of special functions,
fractional calculus, applications of fractional calculus, and
mathematical statistics.
This book offers an introduction to concepts of probability theory,
probability distributions relevant in the applied sciences, as well
as basics of sampling distributions, estimation and hypothesis
testing. As a companion for classes for engineers and scientists,
the book also covers applied topics such as model building and
experiment design. Contents Random phenomena Probability Random
variables Expected values Commonly used discrete distributions
Commonly used density functions Joint distributions Some
multivariate distributions Collection of random variables Sampling
distributions Estimation Interval estimation Tests of statistical
hypotheses Model building and regression Design of experiments and
analysis of variance Questions and answers
In order not to intimidate students by a too abstract approach,
this textbook on linear algebra is written to be easy to digest by
non-mathematicians. It introduces the concepts of vector spaces and
mappings between them without dwelling on statements such as
theorems and proofs too much. It is also designed to be
self-contained, so no other material is required for an
understanding of the topics covered. As the basis for courses on
space and atmospheric science, remote sensing, geographic
information systems, meteorology, climate and satellite
communications at UN-affiliated regional centers, various
applications of the formal theory are discussed as well. These
include differential equations, statistics, optimization and some
engineering-motivated problems in physics. Contents Vectors
Matrices Determinants Eigenvalues and eigenvectors Some
applications of matrices and determinants Matrix series and
additional properties of matrices
The book deals with bilinear forms in real random vectors and their
generalizations as well as zonal polynomials and their applications
in handling generalized quadratic and bilinear forms. The book is
mostly self-contained. It starts from basic principles and brings
the readers to the current research level in these areas. It is
developed with detailed proofs and illustrative examples for easy
readability and self-study. Several exercises are proposed at the
end of the chapters. The complicated topic of zonal polynomials is
explained in detail in this book. The book concentrates on the
theoretical developments in all the topics covered. Some
applications are pointed out but no detailed application to any
particular field is attempted. This book can be used as a textbook
for a one-semester graduate course on quadratic and bilinear forms
and/or on zonal polynomials. It is hoped that this book will be a
valuable reference source for graduate students and research
workers in the areas of mathematical statistics, quadratic and
bilinear forms and their generalizations, zonal polynomials,
invariant polynomials and related topics, and will benefit
statisticians, mathematicians and other theoretical and applied
scientists who use any of the above topics in their areas. Chapter
1 gives the preliminaries needed in later chapters, including some
Jacobians of matrix transformations. Chapter 2 is devoted to
bilinear forms in Gaussian real ran dom vectors, their properties,
and techniques specially developed to deal with bilinear forms
where the standard methods for handling quadratic forms become
complicated."
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