Christopher G. Small, Department of Statistics and Actuarial Science University of Waterloo Waterloo, Ontario N2L 3G1 Canada, and Jinfang Wang, School of Agriculture Obihiro University of Agriculture and Veterinary Medicine Inada-cho, Obihiro, Hokkaido 080-8555, Japan

Numerical methods for nonlinear estimating equations

(Hardback)
0-19-850688-0
Publication date: July 2003
294 pages, 15, 234mm x 156mm
Series: Oxford Statistical Science Series

Excellent balance of theory and applications
Extensively illustrated
Diverse applications are described

Description
This book provides a comprehensive study of nonlinear estimating equations and artificial likelihoods for statistical inference. It includes a variety of examples from practical applications and is ideal for research statisticians and advanced graduate students.

Readership:
Researchers and advanced students in statistics and applied sciences seeking a comprehensive study of nonlinear estimating equations and artificial likelihoods for statistical inference.

Contents/contributors
Introduction
Estimating functions
Numerical algorithms
Working with roots
Methodologies for root selection
Artificial likelihoods and estimating functions
Root selection and dynamical systems
Bayesian estimating functions
Bibliography
Index

Harold Cohen

Fundamentals and Applications of Complex Analysis

April 2003, ISBN 0-306-47748-3, Hardbound

This book is intended to serve as a text for both beginning and second courses in complex analysis of functions of one complex variable. The material that is appropriate for more advanced study is developed from elementary material. The concepts are illustrated with large numbers of examples, many of which involve problems students encounter in other courses. For example, students who have taken an introductory physics course will have encountered analysis of simple AC circuits. This text revisits such analysis using complex numbers. Cauchy's residue theorem is used to evaluate many types of definite integrals that students are introduced to in the beginning calculus sequence. Methods of conformal mapping are used to solve problems in electrostatics. The book contains material that is not considered in other popular complex analysis texts. For example, one chapter is devoted to an analysis of multivalued functions, with applications to the evaluation of certain types of integrals. Another chapter deals with the singularity structure of functions that are defined by integrals which cannot be evaluated in terms of elementary functions. A third chapter develops dispersion relations, which are mathematical tools for determining a complete function from a knowledge of just the real part, or just the imaginary part of the function.

Contents
1. Introduction. 2. Complex Numbers. 3. Complex Variables. 4. Series, Limits and Residues. 5. Evaluation of Integrals. 6. Multivalued Functions, Branch Points and Cuts. 7. Singularities of Functions Defined by Integrals. 8. Conformal Mapping. 9. Dispersion Relations. Appendix 1: Derivation of Green's Theorem. Appendix 2: Derivation of the Geometric Series. Appendix 3: Evaluation of an Integral. Appendix 4: Transformation of Laplace's Equation. Appendix 5: Transformation of Boundary Conditions. Index.


David ATKINSON, Mahouton Norbert HOUNKONNOU
and Porter W JOHNSON

Exercises in Quantum Mechanics
- a Self-Contained book of questions and answers

200 pages, 9x6 inches
April 2003 softcover
ISBN 1-58949-026-6

Contents:

1. Relativity and Quantization
2. Charged Particle in Electromagnetic Field
3. Dirac Hydrogen Atom
4. Quantum Field Theory
5. Group Theory and the Noether Theorem
6. Scattering Theory and Feynman Graphs
7. Quantum Electrodynamics
8. Dimensional Regularization
9. Dyson-Schwinger Equations
APPENDIX
Bibliography
Index

Bourbaki, N., Paris, France

Elements of Mathematics
Algebra II Chapters 4-7

1st ed. 1990. 2nd printing 2003 VII, 461 p. Softcover
3-540-00706-7

This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's textbook, Algebre, Chapters 4 to 7 (1981).

The English translation of the new and expanded version of Bourbaki's Algebre, Chapters 4 to 7 completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 has been entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and based on it is Chapter 7: modules over a p.i.d. studies of torsion modules, free modules, finite type modules, with applications to abelian groups and endomorphisms of vector spaces. Sections on semi-simple endomorphisms and Jordan decomposition have been added.

Chapter IV: Polynomials and Rational Fractions

Chapter V: Commutative Fields

Chapter VI: Ordered Groups and Fields

Chapter VII: Modules Over Principal Ideal Domains

Contents:

Capter IV: Polinomials and Rational Fractions.- Chapter V: Commutative Fields.- Chapter VI: Ordered Groups and Fields.- Chapter VII: Modules Over Principal Ideal Domains.


Bonnard, B., Universite de Bourgogne, Dijon, France; Chyba, M., University of Hawaii, Honolulu, HI, USA

Singular Trajectories and Their Role in Control Theory

2003 XVI, 357 p. Softcover
3-540-00838-1

The role of singular trajectories in control theory is analysed in this volume that contains about 60 exercises and problems. A section is devoted to the applications of singular trajectories to the optimisation of batch reactors. The theoretical part based on the Martinet case concerns the singularity analysis of singular trajectories in sub-Riemannian geometry. An algorithm is given to evaluate conjugate points and a final chapter discusses open problems. The volume will interest mathematicians and engineers.


Series: Mathematiques et Applications. Vol.. 40

Howie, J. M., University of St. Andrews, UK

Complex Analysis

2003 XI, 260 p. 83 illus. Softcover
1-85233-733-8

Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers differentiation integration Cauchy's theorem and its consequences Laurent series and the residue theorem applications of contour integration conformal mappings and harmonic functions A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.

Series: Springer Undergraduate Mathematics Series.

Parker, D. F., University of Edinburgh, UK

Fields, Flows and Waves
An Introduction to Continuum Models

2003 XII, 270 p. 90 illus. Softcover
1-85233-708-7

This book, derived from an innovative course of lectures, is a first introduction to the mathematical description of fields, flows and waves. It shows students, early in their studies, how many of the topics they have encountered are useful in constructing, analysing and interpreting phenomena in the real world. Designed for second-year undergraduate students in mathematics, mathematical physics, and engineering, it presumes only a limited familiarity with several variable calculus and vector fields. It develops the concepts of flux, conservation law and boundary value problem through simple examples of heat flow, electric potentials and gravitational fields. The ideas are developed through worked examples, and a range of exercises (with solutions) is provided to test understanding. Chapters 1-7 contain ample material for an introductory lecture course, while later chapters on waves in fluids, solids and electromagnetism, and on bio-mathematics, show how the extension of earlier ideas leads to the description and explanation of important topics in modern technology and science.

Contents: Preface.- The Continuum Description.- Unsteady Heat Flow.- Fields and Potentials.- Laplace's Equation and Poisson's Equation.- Motion of an Elastic String.- Fluid Flow.- Elastic Deformations.- Vibrations and Waves.- Electromagnetic Waves and Light.- Chemical and Biological Models.- Solutions.- Bibliography.- Index

Series: Springer Undergraduate Mathematics Series.