AMS Chelsea Publishing, Volume: 319;
1983; 284 pp; Hardcover
Print ISBN: 978-1-4704-2969-0
This second edition includes exercises at the end of each chapter, revised bibliographies, references and an index.
This text starts on an intermediate level of generality: sufficiently general to convey to the student the flavor of abstract methods in analysis and to cover many important applications, and still down-to-earth to make easy reading for beginners. The tradition founded by Banach, and favorable experiences from many courses, point to metric spaces as a suitable initial subject, and the present book keeps in this tradition … The authors have selected and presented in a clear and readable way the basic material which is most likely to be used frequently. A wealth of examples, counterexamples, applications and exercises accompany the abstract theory throughout.
-- Mathematical Reviews
An attractive feature of the book is that each major theorem is followed by … illustrations of its use. There are many well-chosen problems. Some problems ask the reader to apply an abstract idea to a concrete situation and others ask the reader to develop more theory.
-- American Mathematical Monthly
Contemporary Mathematics, Volume: 693
2017; 411 pp; Softcover
Print ISBN: 978-1-4704-2836-5
This volume is dedicated to the memory of Bjorn Jawerth. It contains original research contributions and surveys in several of the areas of mathematics to which Bjorn made important contributions. Those areas include harmonic analysis, image processing, and functional analysis, which are of course interrelated in many significant and productive ways.
Among the contributors are some of the world's leading experts in these areas. With its combination of research papers and surveys, this book may become an important reference and research tool.
This book should be of interest to advanced graduate students and professional researchers in the areas of functional analysis, harmonic analysis, image processing, and approximation theory. It combines articles presenting new research with insightful surveys written by foremost experts.
Graduate students and research mathematicians interested in harmonic analysis and applications to image processing.
Contemporary Mathematics Volume: 694
2017; 229 pp; Softcover
Print ISBN: 978-1-4704-3678-0
This volume contains the proceedings of the international conference Finite Simple Groups: Thirty Years of the Atlas and Beyond Celebrating the Atlases and Honoring John Conway, which was held from November 2?5, 2015, at Princeton University, Princeton, New Jersey.
Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics.
The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.
Graduate students and research mathematicians interested in algebra, group theory, representation theory, combinatorics, coding theory, number theory, and algebraic geometry.
Part of Cambridge IISc Series
Publication planned for: October 2017
format: Hardback
isbn: 978110841641
Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.
Contains separate chapters on First and Second Order Linear Equations and Qualitative theory
Includes advanced topics such as qualitative analysis of linear and nonlinear systems
Covers many important results from variable real analysis and linear algebra
Includes plenty of real-world applications, solved examples and numerical problems
List of tables
List of figures
Preface
1. Introduction and examples: physical models
2. Preliminaries
3. First and second order linear equations
4. General theory of initial value problems
5. Linear systems and qualitative analysis
6. Series solutions: Frobenius theory
7. Regular Sturm?Liouville theory
8. Qualitative theory
9. Two point boundary value problems
10. First order partial differential equations: method of characteristics
Appendix A. Poinca`e?Bendixon and Leinard's theorems
Bibliography
Index.
Part of Carus Mathematical Monographs
Date Published: June 2017
format: Hardback
isbn: 9780883851425
Several optical phenomena can occur when the sun is near the horizon, some of which can actually be seen, for instance as a dark strip in the middle of the solar disk, or as a green flash. These are a result of the way the atmosphere affects the geometry of light rays. In this book, Broer uses the Fermat principle to deduce laws for refraction and reflection. By expressing these as conservation laws, he can handle both the case of inhomogeneous layers of air and the case of continuous variation in the refraction index. Building from this elementary theory, more advanced mathematical theories are discussed, including how the Fermat Principle leads to a Riemannian metric whose geodesics are the paths of light rays, thus demonstrating the physical applicability of Riemannian geometry. Intended for teachers and professors to enlighten their courses, or for students and researchers in mathematics, science and engineering.
Written in a personal and engaging style, this book will provide an interesting read to many
Accessible to all levels, from teachers and professors, to pupils, students and researchers in mathematics, science and engineering
Includes a surprising application of optical phenomena near the horizon to the brachistochrone problem, an ingenious mix of optics and mechanics
1. Introduction and overview
Part I. Geometry of Light Rays in the Atmosphere:
2. Geometric optics
3. Atmospheric optics
4. Light and the cycloid
Part II. Light Rays as Geodesics:
5. The principles of Fermat and Hamilton
6. The brachistochrone revisited
7. Light rays as geodesics on a surface of revolution
8. Scholium generale.