ISBN: 0-471-64956-2
Hardcover
352 pages
June 2004
An accessible, practical introduction to the principles of
differential equations
The field of differential equations is a keystone of scientific
knowledge today, with broad applications in mathematics,
engineering, physics, and other scientific fields. Encompassing
both basic concepts and advanced results, Principles of
Differential Equations is the definitive, hands-on introduction
professionals and students need in order to gain a strong
knowledge base applicable to the many different subfields of
differential equations and dynamical systems.
Nelson Markley includes essential background from analysis and
linear algebra, in a unified approach to ordinary differential
equations that underscores how key theoretical ingredients
interconnect. Opening with basic existence and uniqueness
results, Principles of Differential Equations systematically
illuminates the theory, progressing through linear systems to
stable manifolds and bifurcation theory. Other vital topics
covered include:
Basic dynamical systems concepts
Constant coefficients
Stability
The Poincare return map
Smooth vector fields
As a comprehensive resource with complete proofs and more than
200 exercises, Principles of Differential Equations is the ideal
self-study reference for professionals, and an effective
introduction and tutorial for students.
Table of Contents
1. Fundamental Theorems.
2. Classical Themes.
3. Linear Differential Equations.
4. Constant Coefficients.
5. Stability.
6. The Poincare Return Map.
7. Smooth Vector Fields.
8. Hyperbolic Phenomenon.
9. Bifurcations.
ISBN: 0-471-43419-1
Hardcover
584 pages
July 2004
Galois Theory is the algebraic study of groups that can be
associated with polynomial equations. This book covers the basic
material of Galois theory and discusses many related topics, such
as Abelian equations, solvable equations of prime degree, and the
casus irreducibilis, that are not mentioned in most standard
treatments. It also describes the rich history of Galois theory,
including the work of Lagrange, Gauss, Abel, Galois, Jordan, and
Kronecker.
Table of Contents
Preface.
Notation.
PART I: POLYNOMIALS.
Chapter 1. Cubic Equations.
Chapter 2. Symmetric Polynomials.
Chapter 3. Roots of Polynomials.
PART II: FIELDS.
Chapter 4. Extension Fields.
Chapter 5. Normal and Separable Extensions.
Chapter 6. The Galois Group.
Chapter 7. The Galois Correspondence.
PART III: APPLICATIONS.
Chapter 8. Solvability by Radicals.
Chapter 9. Cyclotomic Extensions.
Chapter 10. Geometric Constructions.
Chapter 11. Finite Fields.
PART IV: FURTHER TOPICS.
Chapter 12. Lagrange, Galois, and Kronecker.
Chapter 13. Computing Galois Groups.
Chapter 14. Solvable Permutation Groups.
Chapter 15. The Lemniscate.
Appendix A: Abstract Algebra.
Appendix B: Hints to Selected Exercises.
References.
Index.
ISBN: 0-470-86888-0
Hardcover
312 pages
July 2004
There have been many advances in the theory and applications of
discrete distributions in recent years. They can be applied to a
wide range of problems, particularly in the health sciences.
Discrete Distributions: Applications in the Health Sciences
describes a number of new discrete distributions that arise in
the statistical examination of real examples. For each example,
an understanding of the issues surrounding the data provides the
motivation for the subsequent development of the statistical
models.
Provides an overview of discrete distributions and their
applications in the health sciences.
Focuses on real examples, giving readers an insight into the
utility of the models.
Describes the properties of each distribution, and the methods
that led to their development.
Presents a range of examples from the health sciences, including
cancer, epidemiology, and demography.
Features discussion of software implementation - in SAS, Fortran
and R - enabling readers to apply the methods to their own
problems.
Written in an accessible style, suitable for applied
statisticians and numerate health scientists.
Software and data sets are made available on the Web.
Discrete Distributions: Applications in the Health Sciences
provides a practical introduction to these powerful statistical
tools and their applications, suitable for researchers and
graduate students from statistics and biostatistics. The focus on
applications, and the accessible style of the book, make it an
excellent practical reference source for practitioners from the
health sciences.
Table of Contents
Preface.
Introduction.
Maximum Negative Binomial Distribution.
Maximum Negative Hypergeometric Distribution.
Univariate Distributions for Twins.
Multivariate Distributions for Twins.
Family Disease Clusters.
Sums of Dependent Bernouilli's.
Weighted Binomial Distributions.
Applications to Teratology Experiments.
Complements.
References.
Index.
ISBN: 0-471-60161-6
Hardcover
736 pages
August 2004
This book provides in-depth mathematical and complete coverage of
mixed modelsf statistical properties and numerical algorithms.
State-of-the-art methodologies are discussed, among them the
linear mixed-effects model, the growth curve model, the
generalized growth curve model, robust models, models with linear
covariance structures, models for binary and count clustered
data, the generalized estimating equations approach, nonlinear
mixed models, and diagnostics. Special attention is given to
algorithms and their implementations. Several appendices make the
text self-contained. Innovative applications include tumor
regrowth and statistical analysis of shapes and images.
Table of Contents
Introduction: Why mixed models?
MLE for LME model.
Statistical properties of the LME model.
Growth curve model and generalizations.
Meta-analysis model.
Nonlinear marginal model.
Generalized linear mixed model.
Nonlinear mixed effects model.
Diagnostics and influence analysis.
Tumor regrowth curves.
Statistical analysis of shape.
Statistical image analysis.
Appendix.
References.
Index.
ISBN: 0-471-47017-1
Hardcover
352 pages
August 2004
This book presents some of the most recent developments and
classical methods in Multivariate Analysis of Variance (MANOVA),
Repeated Measures, and Growth Curves. It attempts to deal with
the problem of poor approximations by offering more exact methods
for data analysis. Through examples such as following the change
in consumer demand of a product over time and analyzing data from
clinical trials, Exact Methods in MANOVA, Mixed Models, and
Repeated Measures shows readers how these methods are more useful
and more accurate in predicting results
Table of Contents
Preface.
1. Exact Parametric Inference.
1.1 Introduction.
1.2 Test Statistics and p-Values.
1.3 Test Variables and Generalized p-Values.
1.4 Substitution Method.
1.5 Fixed Level Testing.
1.6 Generalized Confidence Intervals.
1.7 Substitution Method in Interval Estimation.
1.8 Generalized p-Values Based Intervals.
2. Methods in Analysis of Variance.
2.1 Introduction.
2.2 Comparing Two Population Means.
2.3 Case of Unequal Variances.
2.4 One-Way ANOVA.
2.5 Multiple Comparisons: Case of Equal Variances.
2.6 Multiple Comparisons: Case of Unequal Variances.
2.7 Two-Way ANOVA Under Equal Variances.
2.8 Two-Way ANOVA Under Heteroscedasticity.
2.9 Two-Factor Nested Design.
3. Introduction to Mixed Models.
3.1 Introduction.
3.2 Random Effects One-Way ANOVA.
3.3 Inference About Variance Components.
3.4 Fixed Level Testing.
3.5 Inference About the Mean.
3.6 Two-Way Mixed Model without Replicates.
4. Higher-Way Mixed Models.
4.1 Introduction.
4.2 Canonical Form of the Problem.
4.3 Testing Fixed Effects.
4.4 Estimating Variance Components.
4.5 Testing Variance Components.
4.6 Confidence Intrvals.
4.7 Functions of Variance Components.