Godement, Roger

Analysis I
Convergence, Elementary functions

Series: Universitext

2004, XXII, 430 p., Softcover
ISBN: 3-540-05923-7
Due: November 12, 2003

About this textbook

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

Written for: Undergraduate students, and lecturers in analysis

Keywords: convergence, derivations, analytic functions, Fourier integrals

Table of contents




Walker, Peter

Examples and Theorems in Analysis

2003, Approx. 250 p. 19 illus., Softcover
ISBN: 1-85233-493-2
Due: November 1, 2003

About this textbook

Examples and Theorems in Analysis takes a unique and very practical approach to mathematical analysis. It makes the subject more accessible by giving the examples equal status with the theorems. The results are introduced and motivated by reference to examples which illustrate their use, and further examples then show how far the assumptions may be relaxed before the result fails. A number of applications show what the subject is about and what can be done with it; the applications in Fourier theory, distributions and asymptotics show how the results may be put to use. Exercises at the end of each chapter, of varying levels of difficulty, develop new ideas and present open problems. Written primarily for first- and second-year undergraduates in mathematics, this book features a host of diverse and interesting examples, making it an entertaining and stimulating companion that will also be accessible to students of statistics, computer science and engineering, as well as to professionals in these fields.

Written for: Undergraduate students of mathematics; students and researchers in mathematics, statistics, computer science and engineering

Table of contents

Preface.- Sequences.- Functions and Continuity.- Differentiation.- Constructive Integration.- Improper Integrals.- Series.- Applications.- Appendix A: Fubini's Theorem.- Appendix B: Hints and Solutions for Exercises.- References.- Index.

Weingartner, Paul (Ed.)

Alternative Logics. Do Sciences Need Them?

2004, XVII, 367 p. 29 Illus., Hardcover
ISBN: 3-540-40744-8
Due: November 13, 2003

About this book

Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected in this volume address and explore the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In part II the authors offer several logics that deviate in different ways from classical logics. The twelve papers in part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. Most of the contributions are revised and partially extended versions of papers presented at a conference of the same title of the Academie Internationale de Philosophie des Sciences held at the Internationales Forschungszentrum Salzburg in May 1999. Others have been added to complete the picture of recent research in alternative logics as they have been developed for applications in the sciences.

Written for: Researchers, graduate students

Table of contents


Lando, Sergei K. , Zvonkin, Alexander K.
Gamkrelidze, R.V.; Vassiliev, V.A. (Eds.)

Graphs on Surfaces and Their Applications

Series: Encyclopaedia of Mathematical Sciences , Vol. 141

2004, 470 p., 150 figs., Hardcover
ISBN: 3-540-00203-0
Due: November 25, 2003

About this book

Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

Written for: Graduate students and researchers

Table of contents

Ockendon, Hilary, Ockendon, John R.

Waves and Compressible Flow

Series: Texts in Applied Mathematics , Vol. 47

2004, Approx. 230 pp., Softcover
ISBN: 0-387-40399-X
Due: December 1, 2003

About this textbook


This books aims to provide students and researchers with a basis for understanding the wide range of wave phenomena with which any mathematician may be confronted in applications. Compressible flow is the main focus of the book however the authors show how wave phenomena in electromagentism and solid mechanics can be treated using similar mathematical methods. This book originated from a course at Oxford University and previous book by H Ockendon and R Taylor entitled Inviscid Fluid Flows. This monograph has been retitled and revised throughly to reflect scientific interest. The book has exercises at end of each chapter and should appeal to senior undergraduate and graduate students interested in fluid mechanics.

Written for: researchers graduate studentsnone

Table of contents

Introduction * The equations of Inviscid Compressible Flow * Models for Linear Wave Propagation * Theories for Linear Waves * Nonlinear Waves and Shocks in Fluids