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The third edition of this widely popular textbook is authored by a
master teacher. This book provides a mathematically rigorous
introduction to analysis of real valued functions of one variable.
This intuitive, student-friendly text is written in a manner that
will help to ease the transition from primarily computational to
primarily theoretical mathematics. The material is presented
clearly and as intuitive as possible while maintaining mathematical
integrity. The author supplies the ideas of the proof and leaves
the write-up as an exercise. The text also states why a step in a
proof is the reasonable thing to do and which techniques are
recurrent. Examples, while no substitute for a proof, are a
valuable tool in helping to develop intuition and are an important
feature of this text. Examples can also provide a vivid reminder
that what one hopes might be true is not always true. Features of
the Third Edition: Begins with a discussion of the axioms of the
real number system. The limit is introduced via sequences. Examples
motivate what is to come, highlight the need for hypothesis in a
theorem, and make abstract ideas more concrete. A new section on
the Cantor set and the Cantor function. Additional material on
connectedness. Exercises range in difficulty from the routine
"getting your feet wet" types of problems to the moderately
challenging problems. Topology of the real number system is
developed to obtain the familiar properties of continuous
functions. Some exercises are devoted to the construction of
counterexamples. The author presents the material to make the
subject understandable and perhaps exciting to those who are
beginning their study of abstract mathematics. Table of Contents
Preface Introduction The Real Number System Sequences of Real
Numbers Topology of the Real Numbers Continuous Functions
Differentiation Integration Series of Real Numbers Sequences and
Series of Functions Fourier Series Bibliography Hints and Answers
to Selected Exercises Index Biography James R. Kirkwood holds a
Ph.D. from University of Virginia. He has authored fifteen,
published mathematics textbooks on various topics including
calculus, real analysis, mathematical biology and mathematical
physics. His original research was in mathematical physics, and he
co-authored the seminal paper in a topic now called Kirkwood-Thomas
Theory in mathematical physics. During the summer, he teaches real
analysis to entering graduate students at the University of
Virginia. He has been awarded several National Science Foundation
grants. His texts, Elementary Linear Algebra, Linear Algebra, and
Markov Processes, are also published by CRC Press.
Elementary Linear Algebra is written for the first undergraduate
course. The book focuses on the importance of linear algebra in
many disciplines such as engineering, economics, statistics, and
computer science. The text reinforces critical ideas and lessons of
traditional topics. More importantly, the book is written in a
manner that deeply ingrains computational methods.
Linear Algebra, James R. Kirkwood and Bessie H. Kirkwood,
978-1-4987-7685-1, K29751 Shelving Guide: Mathematics This text has
a major focus on demonstrating facts and techniques of linear
systems that will be invaluable in higher mathematics and related
fields. A linear algebra course has two major audiences that it
must satisfy. It provides an important theoretical and
computational tool for nearly every discipline that uses
mathematics. It also provides an introduction to abstract
mathematics. This book has two parts. Chapters 1-7 are written as
an introduction. Two primary goals of these chapters are to enable
students to become adept at computations and to develop an
understanding of the theory of basic topics including linear
transformations. Important applications are presented. Part two,
which consists of Chapters 8-14, is at a higher level. It includes
topics not usually taught in a first course, such as a detailed
justification of the Jordan canonical form, properties of the
determinant derived from axioms, the Perron-Frobenius theorem and
bilinear and quadratic forms. Though users will want to make use of
technology for many of the computations, topics are explained in
the text in a way that will enable students to do these
computations by hand if that is desired. Key features include:
Chapters 1-7 may be used for a first course relying on applications
Chapters 8-14 offer a more advanced, theoretical course Definitions
are highlighted throughout MATLAB (R) and R Project tutorials in
the appendices Exercises span a range from simple computations to
fairly direct abstract exercises Historical notes motivate the
presentation
Elementary Linear Algebra is written for the first undergraduate
course. The book focuses on the importance of linear algebra in
many disciplines such as engineering, economics, statistics, and
computer science. The text reinforces critical ideas and lessons of
traditional topics. More importantly, the book is written in a
manner that deeply ingrains computational methods.
Today, virtually any advance in the life sciences requires a
sophisticated mathematical approach. The methods of mathematics and
computer science have emerged as critical tools to modeling
biological phenomena, understanding patterns, and making sense of
large data sets, such as those generated by the human genome
project. An Invitation to Biomathematics provides a comprehensive,
yet easily digested entry into the diverse world of mathematical
biology--the union of biology, mathematics, and computer science.
This textbook, expertly written by a team of experienced educators,
is divided into two parts. The first section presents core
principles as elucidated by classical problems such as population
growth, predator-prey interactions, epidemic models, and population
genetics, while the second applies these principles to modern
biomedical research. In addition, the supplementary work Laboratory
Manual of Biomathematics (available separately) is designed to
enable hands-on exploration of model development, model validation,
and model refinement.
* Provides a complete guide for development of quantification
skills crucial for applying mathematical methods to biological
problems.
* Includes well-known examples from across disciplines in the life
sciences including modern biomedical research.
* Explains how to use data sets or dynamical processes to build
mathematical models.
* Offers extensive illustrative materials.
* Written in clear and easy-to-follow language without assuming a
background in math or biology.
* A laboratory manual is available for hands-on, computer-assisted
projects based on material covered in the text.
Clear, rigorous, and intuitive, Markov Processes provides a bridge
from an undergraduate probability course to a course in stochastic
processes and also as a reference for those that want to see
detailed proofs of the theorems of Markov processes. It contains
copious computational examples that motivate and illustrate the
theorems. The text is designed to be understandable to students who
have taken an undergraduate probability course without needing an
instructor to fill in any gaps. The book begins with a review of
basic probability, then covers the case of finite state, discrete
time Markov processes. Building on this, the text deals with the
discrete time, infinite state case and provides background for
continuous Markov processes with exponential random variables and
Poisson processes. It presents continuous Markov processes which
include the basic material of Kolmogorov's equations, infinitesimal
generators, and explosions. The book concludes with coverage of
both discrete and continuous reversible Markov chains. While Markov
processes are touched on in probability courses, this book offers
the opportunity to concentrate on the topic when additional study
is required. It discusses how Markov processes are applied in a
number of fields, including economics, physics, and mathematical
biology. The book fills the gap between a calculus based
probability course, normally taken as an upper level undergraduate
course, and a course in stochastic processes, which is typically a
graduate course.
Designed as supplemental material to the textbook An Invitation to
Biomathematics, this laboratory manual expertly aids students who
wish to gain a deeper understanding of solving biological issues
with computer programs. This manual provides hands-on exploration
of model development, model validation, and model refinement,
enabling students to truly experience advancements made in biology
by mathematical models. Each of the projects offered can be used as
individual module in traditional biology or mathematics courses
such as calculus, ordinary differential equations, elementary
probability, statistics, and genetics.
This manual is a companion to the textbook, An Invitation of
Biomathematics (sold separately ISBN: 0120887711; or as a set ISBN:
0123740290).
* Can be used as a computer lab component of a course in
biomathematics or as homework projects for independent student work
* Biological topics include: Ecology, Toxicology, Microbiology,
Epidemiology, Genetics, Biostatistics, Physiology, Cell Biology,
and Molecular Biology
* Mathematical topics include: Discrete and continuous dynamical
systems, difference equations, differential equations, probability
distributions, statistics, data transformation, risk function,
statistics, approximate entropy, periodic components, and
pulse-detection algorithms
* Includes more than 120 exercises derived from ongoing research
studies
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