"This is an intermediate level text, with exercises, whose avowed
purpose is to provide the science and engineering graduate student
with an appropriate modern mathematical (analysis and algebra)
background in a succinct, but nontrivial, manner.... [T]he book is
quite thorough and can serve as a text, for self-study, or as a
reference." a "Mathematical Reviews
Written for graduate and advanced undergraduate students in
engineering and science, this classic book focuses primarily on set
theory, algebra, and analysis. Useful as a course textbook, for
self-study, or as a reference, the work is intended to:
* provide readers with appropriate mathematical background for
graduate study in engineering or science;
* allow students in engineering or science to become familiar
with a great deal of pertinent mathematics in a rapid and efficient
manner without sacrificing rigor;
* give readers a unified overview of applicable mathematics,
enabling them to choose additional, advanced topical courses in
mathematics more intelligently.
Whereas these objectives for writing this book were certainly
pertinent over twenty years ago when the work was first published,
they are even more compelling now. Todaya (TM)s graduate students
in engineering or science are expected to be more knowledgeable and
sophisticated in mathematics than students in the past. Moreover,
todaya (TM)s graduate students in engineering or science are
expected to be familiar with a great deal of ancillary material
(primarily in the computer science area), acquired in courses that
did not even exist a couple of decades ago.
The book is divided into three parts: set theory (Chapter 1),
algebra (Chapters 2a "4), andanalysis (Chapters 5a "7). The first
two chapters deal with the fundamental concepts of sets, functions,
relations and equivalence relations, and algebraic structures.
Chapters 3 and 4 cover vector spaces and linear transformations,
and finite-dimensional vector spaces and matrices. The last three
chapters investigate metric spaces, normed and inner product
spaces, and linear operators. Because of its flexible structure,
Algebra and Analysis for Engineers and Scientists may be used
either in a one- or two-semester course by deleting appropriate
sections, taking into account the studentsa (TM) backgrounds and
interests.
A generous number of exercises have been integrated into the
text, and a section of references and notes is provided at the end
of each chapter. Applications of algebra and analysis having a
broad appeal are also featured, including topics dealing with
ordinary differential equations, integral equations, applications
of the contraction mapping principle, minimization of functionals,
an example from optimal control, and estimation of random
variables.
Supplementary material for students and instructors is available
at http: //Michel.Herget.net.
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