Clocksin, W.F., Oxford Brookes University, UK; Mellish, C.S., University of Edinburgh, UK

Programming in Prolog, 5th ed.
Using the ISO Standard

5th ed. 2003 XIII, 299 p. Softcover
3-540-00678-8

Originally published in 1981, this was the first textbook on programming in the Prolog language and is still the definitive introductory text on Prolog. Though many Prolog textbooks have been published since, this one has withstood the test of time because of its comprehensiveness, tutorial approach, and emphasis on general programming applications.

Prolog has continued to attract a great deal of interest in the computer science community, and has turned out to be the basis for an important new generation of programming languages and systems for Artificial Intelligence. Since the previous edition of Programming in Prolog, the language has been standardised by the International Organization for Standardization (ISO) and this book has been updated accordingly. The authors have also introduced some new material, clarified some explanations, corrected a number of minor errors, and removed appendices about Prolog systems that are now obsolete.

Keywords:
Artificial Intelligence, Kunstliche Intelligenz, Logic Programming, Logical Programming, Logisches Programmieren, PROLOG (EDV), Programmiersprache, Programmierung (EDV), Programming, Programming Language, Prolog, Prolog Implementations, Prolog-Implementierungen

Liseikin, V. D., Russian Academy of Sciences, Novosibirsk, Russia

A Computational Differential Geometry Approach to Grid Generation

2004 XIV, 264 p. 37 illus. Hardcover
3-540-14008-5

The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems. This monograph describes in detail the eminent role played by differential geometry in grid technology based on mapping. It demonstrates how the Beltrami operator helps to develop robust multidimensional grid generation codes, while supplying related numerical code. In particular, procedures for the construction of monitor metric tensors are given and their qualitative effect on the resulting mesh is analyzed. Reviewing concepts from Riemannian geometry, the book applies them to general grids with prescribed properties, and discusses the role of mean and of Gaussian curvature and other geometric characteristics for the Beltrami equations for grid generation. It addresses scientists and practitioners as well as graduate students from applied mathematics, physics, and engineering.

Keywords: Grid Generation, Riemannian Geometry, Beltramian Equations, Quasiconformal Grids, Scientific Computing

Contents:

From the contents: Background for Grid Generation.- Monitor Function Approaches.- Control of Grid Quality.- Grid Code.- Numerical Experiments.- Appendix. Calculus of Singularities.

Series: Scientific Computation.

Brunt, B. van, Massey University, Institute of Fundamental Sciences

The Calculus of Variations

2004 Approx. 300 p. 24 illus. Hardcover
0-387-40247-0

The calculus of variations has a long history of interaction with other branches of mathematics, such as geometry and differential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations.This book is an introductory account of the calculus of variations suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering. The mathematical background assumed of the reader is a course in multivariable calculus, and some familiarity with the elements of real analysis and ordinary differential equations. The book focuses on variational problems that involve one independent variable. The fixed endpoint problem and problems with constraints are discussed in detail. In addition, more advanced topics such as the inverse problem, eigenvalue problems, separability conditions for the Hamilton-Jacobi equation, and Noether's theorem are discussed. The text contains numerous examples to illustrate key concepts along with problems to help the student consolidate the material. The book can be used as a textbook for a one semester course on the calculus of variations, or as a book to supplement a course on applied mathematics or classical mechanics. Bruce van Brunt is Senior Lecturer at Massey University, New Zealand. He is the author of The Lebesgue-Stieltjes Integral, with Michael Carter, and has been teaching the calculus of variations to undergraduate and graduate students for several years.

Contents:

Preface.- Introduction.- The First Variation.- Some Generalizations.- Isoperimetric Problems.- Applications to Eigenvalue Problems.- Holonomic and Nonholonomic Constraints.- Problems with Variable Endpoints.- The Hamiltonian Formulation.- Noether's Theorem.- The Second Variation.- Appendix A: Some Results from Analysis and Differential Equations.- Appendix B: Function Spaces.- References.- Index.

Series: Universitext.

Puu, T., University of Umea, Sweden

Attractors, Bifurcations, & Chaos
Nonlinear Phenomena in Economics

2nd ed. 2003 XII, 549 p. 209 illus. Hardcover
3-540-40226-8

The first part of this book is an introduction to the mathematical methods of modern nonlinear dynamics. It deals with differential equations, ordinary and partial, iterated maps, and bifurcation theory. The second part focuses applications to economics and regional science. Topics such as business cycles, oligopoly, interregional trade, and economic development theory are included. Bifurcation analysis, and studies of the various attractors, with their basins, provide the core, both of the background material and the applications. Coexistence of attractors and multiplicity of development paths are emphasized throughout. The chapters devoted to spatial applications focus the emergence of geographical patterns.

Keywords: Bifurcation, Chaos, Dynamics, Economic Dynamics, Nonlinearity

Tweddle, I., University of Strathclyde, Glasgow, UK

James Stirling's Methodus Differentialis
An Annotated Translation of Stirling's Text

2003 VIII, 295 p. 12 illus. Hardcover
1-85233-723-0

James Stirling's "Methodus Differentialis" is one of the early classics of numerical analysis. It contains not only the results and ideas for which Stirling is chiefly remembered, for example, Stirling numbers and Stirling's asymptotic formula for factorials, but also a wealth of material on transformations of series and limiting processes. An impressive collection of examples illustrates the efficacy of Stirling's methods by means of numerical calculations, and some germs of later ideas, notably the Gamma function and asymptotic series, are also to be found.

This volume presents a new translation of Stirling's text that features an extensive series of notes in which Stirling's results and calculations are analysed and historical background is provided. Ian Tweddle places the text in its contemporary context, but also relates the material to the interests of practising mathematicians today. Clear and accessible, this book will be of interest to mathematical historians, researchers and numerical analysts.

Keywords: History of Mathematics, Analysis, Numerical analysis, Stirling numbers, Stirling's formula, Interpolation, Acceleration of convergence

Contents:

Introduction.- Background.- Some Mathematical Points.- Summary of the Contents of Stirling's Text.- Stirling's Principal Calculations.- Stirling's Text in Translation: Preface; Introduction; Part I: On the Summation of Series; Part II: On the Interpolation of Series.- Notes.- Appendix: Stirling's Letter to De Moivre Dated 17th June 1729.- References.- Index.

Series: Sources and Studies in the History of Mathematics and Physical Sciences.


Winkelmann, R., University of Zurich, Switzerland

Econometric Analysis of Count Data

4th ed. 2003 XV, 304 p. 19 illus. Hardcover
3-540-40404-X

Graduate students and researchers are provided with an up-to-date survey of statistical and econometric techniques for the analysis of count data, with a focus on conditional distribution models. Proper count data probability models allow for rich inferences, both with respect to the stochastic count process that generated the data, and with respect to predicting the distribution of outcomes. The book starts with a presentation of the benchmark Poisson regression model. Alternative models address unobserved heterogeneity, state dependence, selectivity, endogeneity, underreporting, and clustered sampling. Testing and estimation is discussed from frequentist and Bayesian perspectives. Finally, applications are reviewed in fields such as economics, marketing, sociology, demography, and health sciences. The fourth edition contains several new sections, for example on nonnested hurdle models, quantile regression and on software. Many other sections have been entirely rewritten and extended.

Keywords: Arbeitsmarktmobilitat, Count process, Selektivitat, Zahldaten, Zeitreihenanalyse, count process, maximum likelihood, over dispersion, poisson regression, sample selection, Okonometrie

From the reviews:

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

"Winkleman has published numerous articles on using content models in economics and other social science journals. Because these are both applied and theoretical, he is well suited to write a monograph in this area. This book provides a very useful survey for anyone doing serious research using count datacfor those who are doing substantive research using count data, [this book] will prove quite useful."

Contents:

Introduction.- Probability Models for Count Data.- Econometric Modeling - Basic Issues.- Econometric Modeling - Extensions.- Correlated Count Data.- Bayesian Analysis of Count Variables.- Applications.

Hiai, F., Tohoku University, Sendai, Japan; Kosaki, H., Kyushu University, Fukuoka, Japan

Means of Hilbert Space Operators

2003 VIII, 148 p. Softcover
3-540-40680-8

The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such as comparison results, norm estimates and convergence criteria are established. After some general theory, special investigations are focused on three one-parameter families of A-L-G (arithmetic-logarithmic-geometric) interpolation means, Heinz-type means and binomial means. In particular, norm continuity in the parameter is examined for such means. Some necessary technical results are collected as appendices.

Contents:

Introduction.- Double integral transformations.- Means of operators and their comparison.- Convergence of means.- A-L-G interpolation means Ma.- Heinz-type means Aa.- Binomial means Ba.- Certain alternating sums of operators.- Appendices.- References.- Index.

Series: Lecture Notes in Mathematics. Vol.. 1820

Greiner, W., University of Frankfurt, Germany

Classical Mechanics
Point Particles and Relativity

2003 Approx. 505 p. 317 illus. Softcover
0-387-95586-0

The series of texts on Classical Theoretical Physics is based on the highly successful series of courses given by Walter Greiner at the Johann Wolfgang Goethe University in Frankfurt am Main, Germany. Intended for advanced undergraduates and beginning graduate students, the volumes in the series provide not only a complete survey of classical theoretical physics but also an enormous number of worked examples and problems to show students clearly how to apply the abstract principles to realistic problems.

Contents:

Part I: Vector Calculus Introduction and Basic Definitions / The Scalar Product / Component Representation of a Vector / The Vector Product (Axial Vector) / The Triple Scalar Product / Application of Vector Calculus / Differentiation and Integration of Vectors / The Moving Trihedral--the Frenet Formulae / Areas in Space / Coordinate Frames / Vector Differential Operations / Determination of Line Integrals / The Integral Theorems of Gauss and Stokes / Calculation of Surface Integrals / Volume (Space) Integrals. Part II: Newtonian Mechanics Newton's Axioms / Basic Concepts of Mechanics / The General Linear Motion / The Free Fall / Friction / The Harmonic Oscillator / Mathematical Interlude--Series Expansion, Euler's Formulas / The Damped Harmonic Oscillator / The Pendulum / Mathematical Deepening: Differential Equations / Planetary Motions / Special Problems in Central Fields / The Earth and Our Solar System. Part III: Theory of Relativity Relativity Principle and Michelson-Morley Experiment / The Lorentz Transformation / Properties of the Lorentz Transformation / Addition Theorem of the Velocities / The Basic Quantities of Mechanics in the Minkowski Space / Applications of the Special Theory of Relativity.

Series: Classical Theoretical Physics.