Edited by:
C. Brezinski / L. Wuytack
Numerical Analysis:
Historical Developments in the 20th Century
Description
Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on 'Numerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.
Contents
Approximation in normed linear spaces (G.A. Watson).
A tutorial history of least squares with applications to astronomy and geodesy (Y. Nievergelt). Convergence acceleration during the 20th century (C. Brezinski). On the history of multivariate polynomial interpolation (M. Gasca, T. Sauer). Numerical linear algebra algorithms and software (J.J. Dongarra, V. Eijkhout). Iterative solution of linear systems in the 20th century (Y. Saad, H.A. van der Vorst). Eigenvalue computation in the 20th century (G. H. Golub, H.A. van der Vorst). Historical developments in convergence analysis for Newton's and Newton-like methods (T. Yamamoto). A survey of truncated-Newton methods (S.G. Nash). Cubature formulae and orthogonal polynomials (R. Cools, I.P. Mysovskikh, H.J. Schmid). Computation of Gauss-type quadrature formulas (D.P. Laurie). A review of algebraic multigrid (K. Stuben). From finite differences to finite elements: A short history of numerical analysis of partial differential equations (V. Thomee). A perspective on the numerical treatment of Volterra equations (C.T.H. Baker). Numerical methods for ordinary differential equations in the 20th century (J.C. Butcher). Retarded differential equations (C.T.H. Baker).
Year 2001
Hardbound
ISBN: 0-444-50617-9
512 pages
Edited by
R.J. Daverman, University of Tennessee, Knoxville, TN, USA
R.B. Sher, Union Hall, VA, USA
Handbook of Geometric Topology
Description
Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Contents
Topics in transformation groups (A. Adem and J.F .Davis).
Piecewise linear topology (J.L. Bryant).
Infinite dimensional topology and shape theory (A. Chigogidze).
Nonpositive curvature and reflection groups (M.W. Davis).
Nielsen fixed point theory (R. Geoghegan).
Mapping class groups (N.V. Ivanov).
Seifert manifolds (Kyung Bai Lee and F. Raymond).
Quantum invariants of 3-manifolds and CW-complexes (W. Lueck).
Hyperbolic manifolds (J.G .Ratcliffe).
Flows with knotted closed orbits (J. Franks and M.C. Sullivan).
Heegaard splittings of compact 3-manifolds (M. Scharlemann).
Representations of 3-manifold groups (P.B. Schalen).
Homology manifolds (S. Weinberger).
R-trees in topology, geometry, and group theory (F. Bonathon).
Dehn surgery on knots (S. Boyer).
Geometric group theory (J. Cannon).
Cohomological dimension theory (J. Dydak).
Metric spaces of curvature greater than or equal to k (C. Plaut).
Topological rigidity theorems (C.W. Stark).
Year 2001
Hardbound
ISBN: 0-444-82432-4
1136 pages
Darrell Duffie
Dynamic Asset Pricing Theory, Third Edition
Cloth | 2001
ISBN: 0-691-09022-X
472 pp. | 6 x 9 | 2 tables, 12 line illus.
This is a thoroughly updated edition of Dynamic Asset Pricing Theory, the standard text for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis, so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models.
Readers will be particularly intrigued by this latest edition's most significant new feature: a chapter on corporate securities that offers alternative approaches to the valuation of corporate debt. Also, while much of the continuous-time portion of the theory is based on Brownian motion, this third edition introduces jumps--for example, those associated with Poisson arrivals--in order to accommodate surprise events such as bond defaults. Applications include term-structure models, derivative valuation, and hedging methods. Numerical methods covered include Monte Carlo simulation and finite-difference solutions for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. A system of appendixes reviews the necessary mathematical concepts. And references have been updated throughout. With this new edition, Dynamic Asset Pricing Theory remains at the head of the field.
Darrell Duffie is the James Irvin Miller Professor of Finance at the Graduate School of Business, Stanford University. He teaches and does research in the area of asset valuation, risk management, credit risk modeling, and fixed-income and equity markets. His other books include Security
Markets: Stochastic Models and Futures Markets.
Review:
"This is an important addition to the set of text/reference books on asset pricing theory. It will, if it has not already, become the standard text for the second Ph.D. course in security markets. Its treatment of contingent claim valuation, in particular, is unrivaled in its breadth and coherence."--Journal of Economic Literature
K.P.S Bhaskara Rao
Theory of Generalized Inverses Over Commutative Rings
ISBN: 0-415-27248-3
Pub Date: 01 MAR 2002
Type: Hardback Book
Extent: 192 pages (Dimensions 234X156 mm)
The theory of generalized inverses of real or complex matrices is a well developed and well documented subject. But the wider subject of generalized inverses of matrices over rings has reached a suitable state for a comprehensive treatment only recently. This book provides just that!
The author, who contributed to this development, provides here a book for students of the subject. Mathematicians working in g-inverses of matrices, algebraists and control theorists will be interested in the results presented here. The book would also be suitable for graduate courses on G-inverves in algebra.
Contents:
1. Elementary Results on Rings 2. Matrix Algebra Over Rings 3. Regular Elements in a Ring 4. Regularity - Principal Ideal Rings 5. Regularity - Basics 6. Regularity - Integral Domains 7. Regularity - Communtative Rings 8. Special Topics
Series Information: Algebra, Logic and Applications
Alexander A. Samarskii, Alexander P. Mikhailov
Principles of Mathematical Modelling
Ideas, Methods, Examples
ISBN: 0-415-27280-7
Type: Hardback Book
ISBN: 0-415-27281-5
Type: Paperback Book
Pub Date: 14 DEC 2001
Extent: 360 pages (Dimensions 246X174 mm)
This book demonstrates the versatility of the increasingly multi-disciplinary field of mathematical modelling. The authors consider the principles of model construction and use common approaches to build models from a range of subject areas. Although the contents of the book reflect the interests and experiences of the authors, it includes examples of mathematical modelling in subjects from mechanics to social science. A general approach is adopted where ideas and examples are favoured over rigorous mathematical procedures. This insightful book will be of interest to specialists, teachers and students of this fascinating discipline.
Contents:
Introduction Part I 1. Elementary Mathematical Models 2. Examples of Models Following from the Fundamental Laws of Nature 3. Variational Principles and Mathematical Models 4. Example of the Hierarchy of Models 5. The Universality of Mathematical Models 6. Several Models of Elementary Nonlinear Objects Part II Derivation of Models from the Fundamental Laws of Nature 1. Conservation of the Mass of Substance 2. Conservation of Energy 3. Conservation of the Number of Particles 4. Joint Application of Several Fundamental Laws Part III Models Deduced from Variational Principles, Hierarchies of Models 1. Equations of Motion, Variational Principles and Conservation Laws in Mechanics 2. Models of Some Mechanical Systems 3. The Boltzmann Equation and its Derivative Equations Part IV Models of Some Hardly Formalizable Objects 1. Universality of Mathematical Models 2. Some Models of Financial and Economic Processes 3. Some Rivalry Models 4. Dynamics of Distribution of Power in Hierarchy Part V 1. Application of Similarity Methods 2. The Maximum Principle and Comparison Theorems 3. An Averaging Method 4. On Transition to Discrete Models Part VI Mathematical Modeling of Complex Objects 1. Problems of Technology and Ecology 3. Fundamental Problems of Natural Science 3. Computing Experiement With Models of Hardly Formalizable Objects References Index
Author Biography:
Professor Alexander A. Samarskii is Director of the Institute of Mathematical Modelling at the Russian Academy of Science and has been the leader of the Russian National Program for Mathematical Modelling in Science and Technology since 1985. He is a world-renowned researcher who has obtained outstanding results and contributed grately to the development of these subjects.
Professor Alexander P Mikhailov is a Head of Department at the Institute of Mathematical Modelling at the Russian Academy of Science and is a Professor of M V Lomonosov Moscow State University. His research interests include mathematical physics, the theory of nonlinear phenomena, mathematical modelling of dissipative structures and mathematical modelling of socio-political processes.