Matrix Analysis for Scientists and Engineers provides a blend
of undergraduate- and graduate-level topics in matrix theory and
linear algebra that relieves instructors of the burden of
reviewing such material in subsequent courses that depend heavily
on the language of matrices. Consequently, the text provides an
often-needed bridge between undergraduate-level matrix theory and
linear algebra and the level of matrix analysis required for
graduate-level study and research. The text is sufficiently
compact that the material can be taught comfortably in a one-quarter
or one-semester course.
Throughout the book, the author emphasizes the concept of matrix
factorization to provide a foundation for a later course in
numerical linear algebra. The author addresses connections to
differential and difference equations as well as to linear system
theory and encourages instructors to augment these examples with
other applications of their own choosing.
Audience
Because the tools of matrix analysis are applied on a daily basis
to problems in biology, chemistry, econometrics, engineering,
physics, statistics, and a wide variety of other fields, the text
can serve a rather diverse audience. The book is primarily
intended to be used as a text for senior undergraduate or
beginning graduate students in engineering, the sciences,
mathematics, computer science, or computational science who wish
to be familiar enough with matrix analysis and linear algebra
that they can effectively use the tools and ideas of these
fundamental subjects in a variety of applications. However,
individual engineers and scientists who need a concise reference
or a text for self-study will also find this book useful.
Prerequisites for using this text are knowledge of calculus and
some previous exposure to matrices and linear algebra, including,
for example, a basic knowledge of determinants, singularity of
matrices, eigenvalues and eigenvectors, and positive definite
matrices. There are exercises at the end of each chapter.
Contents
Preface; Chapter 1: Introduction and Review; Chapter 2: Vector
Spaces; Chapter 3: Linear Transformations; Chapter 4:
Introduction to the Moore-Penrose Pseudoinverse; Chapter 5:
Introduction to the Singular Value Decomposition; Chapter 6:
Linear Equations; Chapter 7: Projections, Inner Product Spaces,
and Norms; Chapter 8: Linear Least Squares Problems; Chapter 9:
Eigenvalues and Eigenvectors; Chapter 10: Canonical Forms;
Chapter 11: Linear Differential and Difference Equations; Chapter
12: Generalized Eigenvalue Problems; Chapter 13. Kronecker
Products; Bibliography; Index.
December 2004 / Approx. xiv + 157 pages / Softcover / ISBN 0-89871-576-8
SIAM Classics in Applied Mathematics 46
Mathematical Models in Biology is an introductory book for
readers interested in biological applications of mathematics and
modeling in biology. A favorite in the mathematical biology
community, it shows how relatively simple mathematics can be
applied to a variety of models to draw interesting conclusions.
Connections are made between diverse biological examples linked
by common mathematical themes. A variety of discrete and
continuous ordinary and partial differential equation models are
explored. Although great advances have taken place in many of the
topics covered, the simple lessons contained in Mathematical
Models in Biology are still important and informative.
Shortly after the publication of Mathematical Models in Biology,
the genomics revolution turned Mathematical Biology into a
prominent area of interdisciplinary research. With this new
millennium, biologists have discovered that mathematics is not
only useful, but indispensable! As a result, there has been much
resurgent interest in, and a huge expansion of, the fields
collectively called mathematical biology. This book serves as a
basic introduction to concepts in deterministic biological
modeling.
Audience
Mathematical Models in Biology does not assume too much
background knowledge?essentially some calculus and high-school
algebra. It was originally written with third- and fourth-year
undergraduate mathematical-biology majors in mind; however, it
was picked up by beginning graduate students as well as a number
of researchers in math (and some in biology) who wanted to learn
about this field.
Contents
Acknowledgments; Part 1: Discrete Process in Biology; Chapter 1:
The Theory of Linear Difference Equations Applied to Population
Growth; Chapter 2: Nonlinear Difference Equations; Chapter 3:
Applications of Nonlinear Difference Equations to Population
Biology; Part 2: Continuous Processes and Ordinary Differential
Equations; Chapter 4: An Introduction to Continuous Models;
Chapter 5: Phase-Plane Methods and Qualitative Solutions; Chapter
6: Applications of Continuous Models to Population Dynamics;
Chapter 7: Models for Molecular Events; Chapter 8: Limit Cycles,
Oscillations, and Excitable Systems; Part 3: Spatially
Distributed Systems and Partial Differential Equation Models;
Chapter 9: An Introduction to Partial Differential Equations and
Diffusion in Biological Settings; Chapter 10: Partial
Differential Equation Models in Biology; Chapter 11: Models for
Development and Pattern Formation in Biological Systems; Selected
Answers; Author Index; Subject Index
December 2004 | xlii + 586 pages | Softcover | ISBN 0-89871-554-7
"An accessible presentation of statistical methods and analysis to deal with imperfect data in real data mining applications."
--Joydeep Ghosh, University of Texas at Austin.
"An appealing feature of this book is the use of fresh
datasets that are much larger than those currently found in
standard books on outliers and statistical diagnostics."
--Anthony Atkinson, London School of Economics.
Data mining is concerned with the analysis of databases large
enough that various anomalies, including outliers, incomplete
data records, and more subtle phenomena such as misalignment
errors, are virtually certain to be present. Mining Imperfect
Data describes in detail a number of these problems, as well as
their sources, their consequences, their detection, and their
treatment. Specific strategies for data pretreatment and
analytical validation that are broadly applicable are described,
making them useful in conjunction with most data mining analysis
methods. Examples are presented to illustrate the performance of
the pretreatment and validation methods in a variety of
situations, both simulation based, where "correct"
results are known unambiguously, and real data examples that
illustrate typical cases met in practice.
Mining Imperfect Data, which deals with a wider range of data
anomalies than are usually treated in one book, includes a
discussion of detecting anomalies through generalized sensitivity
analysis (GSA), a process of identifying inconsistencies using of
systematic and extensive comparisons of results obtained by
analysis of exchangeable datasets. The book makes extensive use
of real data, both in the form of a detailed analysis of a few
real datasets and various published examples. Also included is a
succinct introduction to functional equations that illustrates
their utility in describing various forms of qualitative behavior
for useful data characterizations.
Audience
Industrial and academic researchers will be interested in this
book to learn how to develop strategies and tactics for dealing
with a number of critically important data imperfections that
must be addressed before obtaining useful analysis results from
large databases.
Contents
Preface; Chapter 1: Introduction; Chapter 2: Imperfect Datasets:
Characters, Consequences, and Causes; Chapter 3: Univariate
Outlier Detection; Chapter 4: Data Pretreatment; Chapter 5: What
Is a "Good" Data Characterization?; Chapter 6:
Generalized Sensitivity Analysis; Chapter 7: Sampling Schemes for
a Fixed Dataset; Chapter 8: Concluding Remarks and Open
Questions; Bibliography; Index
Available April 2005 / Approx. vi + 312 pages / Softcover / ISBN
0-89871-582-2
Series: Undergraduate Texts in Mathematics,
2005, Approx. 400 p., Softcover
ISBN: 0-387-23234-6
About this textbook
Difference equations are models of the world around us. From
clocks to computers to chromosomes, processing discrete objects
in discrete steps is a common theme. Difference equations arise
naturally from such discrete descriptions and allow us to pose
and answer such questions as: How much? How many? How long?
Difference equations are a necessary part of the mathematical
repertoire of all modern scientists and engineers.
In this new text, designed for sophomores studying mathematics
and computer science, the authors cover the basics of difference
equations and some of their applications in computing and in
population biology. Each chapter leads to techniques that can be
applied by hand to small examples or programmed for larger
problems. Along the way, the reader will use linear algebra and
graph theory, develop formal power series, solve combinatorial
problems, visit Perron?Frobenius theory, discuss pseudorandom
number generation and integer factorization, and apply the Fast
Fourier Transform to multiply polynomials quickly.
The book contains many worked examples and over 250 exercises.
While these exercises are accessible to students and have been
class-tested, they also suggest further problems and possible
research topics.
Paul Cull is a professor of Computer Science at Oregon State
University. Mary Flahive is a professor of Mathematics at Oregon
State University. Robby Robson is president of Eduworks, an e-learning
consulting firm. None has a rabbit.
Table of contents
Preface * Fibonacci Numbers * Homogeneous Linear Recurrence
Relations * Finite Difference Equations * Generating Functions *
Nonnegative Difference Equations * Leslie's Population Matrix
Model * Matrix Difference Equations * Modular Recurrences *
Computational Complexity * Some Nonlinear Recurrences * Appendix
A: Worked Examples * Appendix B: Complex Numbers * Appendix C:
Highlights of Linear Algebra * Appendix D: Roots in the Unit
Circle * References * Index
Series: Interdisciplinary Applied Mathematics, Preliminary
entry 203
2005, Approx. 390 p. 75 illus., Hardcover
ISBN: 0-387-22964-7
About this book
Remarkable progress has recently been made in the development and
application of quantum trajectories as the computational tool for
solving the time dependent Schrodinger equation. Analogous
methods for stationary bound states are also being developed. The
purpose of this book is to present recent developments and
applications of quantum trajectory methods in the broader context
of the hydrodynamical formulation of quantum dynamics. While many
chapters of the book deal with Lagrangian quantum trajectories in
which the velocity matches that of the probability fluid, other
chapters deal with what will be termed post-Lagrangian
trajectories. There are also many state-of-the-art topics covered
that are unique to this book. On the pedagogical side, a number
of sections will be accessible to students who have had at least
one course in quantum dynamics. There is also considerable
material for advanced researchers, and chapters in the book cover
both methodology and applications.
Table of contents
Trajectory approaches to quantum mechanics - The Bohm
hydrodynamic equations - The phase space route to the
hydrodynamic equations - Quantum trajectories - Fitting methods
for computation of spatial derivatives - Applications to
wavepacket tunneling and decoherence - Application to electronic
transitions - The initial value representation and correlation
functions- Mixed quantum-classical dynamics - Moving adaptive
grids - Trajectory approach to the density matrix - Derivative
propagation along quantum trajectories - Quantum dynamics in
phase space - Non-Bohmain trajectory approaches to quantum
mechanics