2010, XVI, 296 p., Hardcover
ISBN: 978-0-8176-4986-9
Due: August 29, 2010
Lays the foundation for solving problems in reliability, insurance, finance, and credit risk
Exercises and solutions to selected problems accompany each chapter
Many of the chapters that examine central topics in applied probability can be read independently, allowing both instructors and readers extra flexibility in the use of the book
With an emphasis on models and techniques, this textbook introduces many of the fundamental concepts of stochastic modeling that are now a vital component of almost every scientific investigation. These models form the basis of well-known parametric lifetime distributions such as exponential, Weibull, and gamma distributions, as well as change-point and mixture models. The authors also consider more general notions of non-parametric lifetime distribution classes. In particular, emphasis is placed on laying the foundation for solving problems in reliability, insurance, finance, and credit risk. Exercises and solutions to selected problems accompany each chapter in order to allow students to explore these foundations.
The key subjects covered include:
* Exponential distributions and the Poisson process
* Parametric lifetime distributions
* Non-parametric lifetime distribution classes
* Multivariate exponential extensions
* Association and dependence
* Renewal theory
* Problems in reliability, insurance, finance, and credit risk
This work differs from traditional probability textbooks in a number of ways. Since no measure theory knowledge is necessary to understand the material and coverage of the central limit theorem and normal theory related topics has been omitted, the work may be used as a single-semester senior undergraduate or first-year graduate textbook as well as in a second course on probability modeling. Many of the chapters that examine central topics in applied probability can be read independently, allowing both instructors and readers extra flexibility in their use of the book.
Probability and Statistical Models is for a wide audience including advanced undergraduate and beginning-level graduate students, researchers, and practitioners in mathematics, statistics, engineering, and economics.
Preface.- Preliminaries.- Exponential Distribution.- Poisson Process.- Parametric Families.- Lifetime Distribution Classes.- Multivariate Lifetime Distributions.- Association and Dependence.- Renewal Theory.- Risk Theory.- Asset Pricing Theory.- Credit Risk Modeling.- Bibliographical Notes.- Bibliography.- Answers and Solutions to Selected Problems.- Index.
2010, XIV, 216 p. 62 illus., 31 in color., Hardcover
ISBN: 978-1-4419-7019-0
Due: August 29, 2010
Second Order Differential Equations presents a classical piece of theory concerning hypergeometric special functions as solutions of second-order linear differential equations. The theory is presented in an entirely self-contained way, starting with an introduction of the solution of the second-order differential equations and then focusingon the systematic treatment and classification of these solutions.
Each chapter contains a set of problems which help reinforce the theory. Some of the preliminaries are covered in appendices at the end of the book, one of which provides an introduction to Poincare-Perron theory, and the appendix also contains a new way of analyzing the asymptomatic behavior of solutions of differential equations.
This textbook is appropriate for advanced undergraduate and graduate students in Mathematics, Physics, and Engineering interested in Ordinary and Partial Differntial Equations. A solutions manual is available online.
Preface.- Introduction.- Basic Properties of the Solutions.- Equations of the Fuchsian Type.- Equations with One to Four Regular Singular Points.- The Hypergeometric Differential Equation.- Legendre Functions and Related Functions.- Confluent Hypergeometric Functions.- Heun's Differential Equation.- The Gamma Function and Related Functions.- Difference Equations.- Partial Fractions.- Circles and Ellipses in the Complex Plane.- Elementary and Special Functions.- Notation.- Bibliography.- Index
Series: Applied and Numerical Harmonic Analysis
2010, XX, 430 p. 45 illus., Hardcover
ISBN: 978-0-8176-4887-9
Due: September 3, 2010
This book?an outgrowth of an international conference held in honor of Jacques Peyriere?provides readers with an overview of recent developments in the mathematical fields related to fractals. Included are original research contributions as well as surveys written by experts in their respective fields.
The chapters are thematically organized into five major sections:
* Geometric Measure Theory and Multifractals;
* Harmonic and Functional Analysis and Signal Processing;
* Dynamical Systems and Analysis on Fractals;
* Stochastic Processes and Random Fractals;
* Combinatorics on Words.
Recent Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.
Preface.- Geometric Measure Theory and Multifractals.- Harmonic and Functional
Analysis and Signal Processing.- Dynamical Systems and Analysis on Fractals.-
Stochastic Processes and Random Fractals.- Combinatorics on Words.
Series: Texts in Applied Mathematics, Vol. 32
2010, 530 p. 220 illus., 110 in color., Hardcover
ISBN: 978-1-4419-6411-3
Due: May 29, 2010
This book is a major revision of Numerical Methods for Wave Equations in Geophysical Fluid Dynamics; the new title of the second edition conveys its broader scope. The second edition is designed to serve graduate students and researchers studying geophysical fluids, while also providing a non-discipline-specific introduction to numerical methods for the solution of time-dependent differential equations. The methods considered are those at the foundation of real-world atmospheric or ocean models, with the focus being on the essential mathematical properties of each method. The fundamental character of each scheme is examined in prototypical fluid-dynamical problems like tracer transport, chemically reacting flow, shallow-water waves, and waves in an internally stratified fluid. The book includes exercises and is well illustrated with figures linking theoretical analyses to results from actual computations. Changes from the first edition include new chapters, discussions and updates throughout. Dale Durran is Professor and Chair of Atmospheric Sciences and Adjunct Professor of Applied Mathematics at the University of Washington. Reviews from the First Edition: gThis book will no doubt become a standard within the atmospheric science community, but its comfortable applied mathematical style will also appeal to many interested in computing advective flows and waves. It is a contemporary and worthy addition to the still-sparse list of quality graduate-level references on the numerical solution of PDEs." SIAM Review, 2000, 42, 755-756 (by David Muraki) gThis book presents an extensive overview of past and current numerical methods used in the context of solving wave systems c It is directed primarily at flows that do not develop shocks and focuses on standard fluid problems including tracer transport, the shallow-water equations and the Euler equations c the book is well organized and written and fills a long-standing void for collected material on numerical methods useful for studying geophysical flows." Bulletin of the American Meteorological Society, 2000, 81, 1080-1081 (by Robert Wilhelmson)
Introduction*Ordinary Differential Equations*Finite-Difference Approximation of the Wave Equation*Diffusion, Sources and Sinks*Series Expansion Methods*Finite-Volume Methods*Semi-Lagrangian Methods*Physically Insignificant Fast Waves*Nonreflecting Boundary Conditions*Appendix
Series: Algebra and Applications, Vol. 12
2010, 200 p., Hardcover
ISBN: 978-1-84996-503-3
Due: September 29, 2010
Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed.
Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined.
This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest.
Group Identities on Units of Group Rings.- Group Identities on Symmetric Units.- Lie Identities on Symmetric Elements.- Nilpotence of U(FG) and U+(FG) .- The Bounded Engel Property.- Solvability of U(FG) and U+(FG) .- Further Reading.- Some Results on Prime and Semiprime Rings