Elaydi, Saber

An Introduction to Difference Equations, 3rd ed.

Series: Undergraduate Texts in Mathematics
2005, XXII, 546 p. 119 illus., Hardcover
ISBN: 0-387-23059-9

About this textbook

This book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material, yet the presentation is simple enough for the book to be used by advanced undergraduate and beginning graduate students. This third edition includes more proofs, more graphs, and more applications. The author has also updated the contents by adding a new chapter on Higher Order Scalar Difference Equations, and also recent results on local and global stability of one-dimensional maps, a new section on the various notions of asymptoticity of solutions, a detailed proof of Levin-May Theorem, and the latest results on the LPA flour-beetle model.

Table of contents

* Preface * List of Symbols * Dynamics of First-Order Difference Equations * Linear Difference Equations of Higher Order * Systems of Linear Difference Equations * Stability Theory * Higher Order Scalar Difference Equations * The Z-Transform Method and Volterra Difference Equations * Oscillation Theory * Asymptotic Behavior of Difference Equations * Applications to Continued Fractions and Orthogonal Polynomials * Control Theory * Answers and Hints to Selected Problems * Appendix A: Stability of Nonhyperbolic Fixed Points of Maps on the Real Line * Vandermonde Matrix * Stability of Nondifferentiable Maps * Stable Manifold and Hartman-Grobman-Cushing Theorems * Levin-May Theorem * Classical Orthogonal Polynomials * Identities and Formulas * References * Index

Lehmann, E.L., Romano, Joseph P.

Testing Statistical Hypotheses, 3rd ed.

Series: Springer Texts in Statistics
2005, XII, 786 p. 20 illus., Hardcover
ISBN: 0-387-98864-5

About this textbook

This classic textbook, now available from Springer, summarizes developments in the field of hypotheses testing. Optimality considerations continue to provide the organizing principle. However, they are now tempered by a much stronger emphasis on the robustness properties of the resulting procedures. This book is an essential reference for any graduate student in statistics.

Table of contents

The General Decision Problem.- The Probability Background.- Uniformly Most Powerful Tests.- Unbiasedness: Theory and First Applications.- Unbiasedness: Applications to Normal Distributions.- Invariance.- Linear Hypotheses.- The Minimax Principle.- Multiple Testing and Simultaneous Inference.- Conditional Inference.- Basic Large Sample Theory.- Quadratic Mean Differentiable Families.- Large Sample Optimality.- Testing Goodness of Fit.- General Large Sample Methods.

Rjasanow, Sergej, Wagner, Wolfgang

Stochastic Numerics for the Boltzmann Equation

Series: Springer Series in Computational Mathematics, Vol. 37
2005, XIII, 256 p., Hardcover
ISBN: 3-540-25268-1

About this book

Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.

Written for:

Graduate students and researchers

Keywords:

Boltzmann equation
Monte Carlo methods
interacting particle systems
rarified gas dynamics
stochastic numerics

Mache, Detlef H.; Szabados, Jozsef; Bruin, Marcel G. de (Eds.)

Trends and Applications in Constructive Approximation

Series: International Series of Numerical Mathematics, Vol. 151
2005, XV, 281 p., Hardcover
ISBN: 3-7643-7124-2

About this book

This volume contains contributions from international experts in the fields of constructive approximation. This area has reached out to encompass the computational and approximation-theoretical aspects of various interesting fields in applied mathematics such as (multivariate) approximation methods, quasi-interpolation,and approximation by (orthogonal) polynomials, as well as the modern mathematical developments in neuro fuzzy approximation, RBF-networks, industrial and engineering applications.

Table of contents

Preface.- Articles by: Adell, Lekuona, Altomare, Rasa, Braess, de Bruin, Mache, Catinas, Davydov, Sestini, Morandi, Igel, Wiegand, Friedrichs, Meyer, Mazure, Mhaskar, Michels, Obermaier, Szwarc, Platte, Kuzmin, Fredebeul, Turek, Rasa, Sablonniere, Szabados, Toussaint, Weishui, Della Vecchia, Mastroianni and Vertesi

Petkov, Vesselin

Relativity and the Nature of Spacetime

2005, XII, 294 p. 60 illus., Hardcover
ISBN: 3-540-23889-1

About this book

The most important question addressed in this book is "what is the nature (the ontological status) of spacetime?" or, equivalently, "what is the dimensionality of the world at the macroscopic level?" The answer to this question is developed via a thorough analysis of relativistic effects and explicitly asking whether the objects involved in those effects are three-dimensional or four-dimensional. This analysis clearly shows that if the world and the physical objects were three-dimensional, none of the kinematic relativistic effects and the experimental evidence supporting them would be possible. The implications of this result for physics, philosophy, and our entire world view are discussed.

Table of contents

Introduction.- On the Impossibility of Detecting Uniform Motion.- Exploring the Internal Logic of Galileo's Principle of Relativity.- Relativity in Euclidean Space and in Spacetime.- Relativity and the Dimensionality of the World: Spacetime Is Real.- Quantum Mechanics and the Nature of Spacetime.- The Nature of Spacetime and the Validity of Scientific Theories.- Propagation of Light in Non-inertial Reference Frames.- Calculating the Electric Field of a Charge in a Non-inertial Reference Frame.- Inertia as a Manifestation of the Reality of Spacetime.- Appendices.- References.- Index.

Kurdila, Andrew J., Zabarankin, Michael

Convex Functional Analysis

Series: Systems & Control: Foundations & Applications
2005, XIV, 234 p., Hardcover
ISBN: 3-7643-2198-9

About this book

This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.

Table of contents


by Barry Cipra (Editor), Erik Demaine (Editor), Martin Demaine (Editor), Tom Rodgers (Editor)

Tribute to a Mathemagician

Summary
The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain.

The contributors to this volume?virtually a list of Whofs Who in the World of Puzzles?trace their inspiration to Martin Gardnerfs puzzle column in Scientific American and to his contributions to the world of recreational mathematics.

Tribute to a Mathemagician contains an author index for the two previous books in the collection of books based on the Gatherings for Gardner.

Sample puzzles and games include:

Tripos
Black Jack
Chinese ceramic puzzle vessels
Paper folding
Mongolian interlocking puzzles
Rolling block puzzles
Sliding puzzles
Cryptic crosswords
The Panex puzzle
Polyonimo puzzles
and more

Details
ISBN: 1-56881-204-3
Year: 2004
Format: Hardcover
Pages: 350