Mathematics Textbooks for Science and Engineering volumeI-II

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收藏 2015-04-03

Mathematics Textbooks for Science and Engineering系列目前出到volume4，现在分享最新的volume1-2，volume3,4论坛上已有，先看一下本系列高大上的Editorial

Recent years have witnessed an extraordinarily rapid advance in the direction of
information technology within the scientific, engineering, and other disciplines, in
which mathematics play a crucial role. To meet such urgent demands, effective
mathematical models as well as innovative mathematical theory, methods, and
algorithms have to be developed for data information manipulation, understanding,
visualization, communication, and other applications.
The Atlantis book series, ‘‘Mathematics Textbooks for Science and Engineering
(MTSE)’’, is founded to meet the need of textbooks on the fundamental and core of
such mathematical development, as well as their applications, that can be used for
classroom teaching at the college level and beyond. For the benefit of students and
readers from the interdisciplinary areas of mathematics, economics, computer
science, physical and biological sciences, and various engineering specialties,
contributing authors are requested to keep in mind that the writings for the MTSE
book series should be elementary and relatively easy to read, with sufficient
examples and exercises. We welcome submission of such book manuscripts from
all who agree with us on this point of view.
This third volume, authored by Prof. Shapoor Vali, on the principles of
mathematical economics, with emphasis on non-linear mathematical models, is a
very valuable contribution to the MTSE series. Written for students in economics,
business, management, and related fields, this textbook is self sufficient and self
contained for the reader with only a basic knowledge of pre-college algebra as well
as introductory micro- and macro-economics. A distinct and important feature of
this nicely written textbook is the connection of the mathematical models,
developed and formulated in each chapter, to specific real-world problems. We
welcome this textbook to the MTSE book series.
Menlo Park, CA Charles K. Chui

Mathematics of Approximation.pdf
大小:(4.81 MB)
只需: 5 个论坛币马上下载

Applied Mathematics.pdf
大小:(6.01 MB)
只需: 5 个论坛币马上下载

补充点详细介绍：
This book is an elementary and yet comprehensive textbook that covers most of
the standard topics in Applied Mathematics, with a unified theme of applications to
data analysis, data manipulation, and data compression. It is a suitable textbook,
not only for most undergraduate and graduate Applied Mathematics courses, but
also for a variety of Special Topics courses or seminars. The objective of this guide
is to suggest several samples of such courses.
(1) A general ‘‘Applied Mathematics’’ course: Linear Spaces, Linear Analysis,
Fourier Series, Fourier Transform, Partial Differential Equations, and
Applications
(2) Applied Mathematics: with emphasis on computations and data compression
(3) Applied Mathematics: with emphasis on data analysis and representation
(4) Applied Mathematics: with emphasis on time-frequency analysis
(5) Applied Mathematics: with emphasis on time-frequency and multi-scale
methods
(6) Applied Linear Algebra
(7) Applied Fourier Analysis
(8) Applied and Computational Wavelet Analysis
(9) Fourier and Wavelet Analyses

Mathematics of approximation plays a key role in bridging the gap between abstract mathematical theory and numerical implementation. With the recent exponential increase of
available data that are easily accessible andrelevant to our daily lives, understanding of
such data often requires sophisticated mathematical manipulation by taking advantage of
the continuing rapid technological advancement of computational capability. However,
without assurance of accuracy in mathematical manipulation, results from simply number
crunching by the powerful computer might be meaningless. In addition, for those data
governed by certain physical phenomena or biological models, approximate solutions of
the associated complex systems in terms of commonly used basis functions must guarantee
accurate representation within a given tolerance.
This book by a leading expert in the field is intended to meet the need of such mathematical contents for classroom teaching, particularly for the undergraduate college level.
Approximation and interpolation by algebraic and trigonometric polynomials for global
representation, and spline functions for local analysis, are discussed from first principles
with examples and full sets of carefully prepared exercises for each chapter. Convergence
results are derived to assure meaningful mathematical manipulation, and error estimates are
developed for data representation, with a guarantee of accuracy within a given tolerance.
On the other hand, in contrast with the vast literature on Approximation Theory and Computational Mathematics, Professor De Villiers has taken great care to avoid using powerful
advanced mathematics from Real Analysis and Functional Analysis, in that only elementary theory and methods from Linear Algebra and basic Advanced Calculus are applied in
the derivations and discussions throughout the entire presentation. As a result, the writing
is elementary and self-contained.