2008, Approx. 330 p. 111 illus., Hardcover
ISBN: 978-0-8176-4509-0
Due: April 2008
About this textbook
Introductory text for analysis of functions of several variables
Covers wide range of topics and applications
Motivates the topics with examples, observations, exercises, and illustrations
Exciting historical background motivates the subject
This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.
The wide range of topics covered include: differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differential forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.
Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.
Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis.
Table of contents
Preface.-Differential Calculus.-The differential calculus for scalar functions.-The differential calculus for vector-valued functions.-The theorems of the differential calculus.-Invertibility of map Rn to Rn.-Differential calculus in Banach spaces.-Exercises.-The Integral Calculus.-Lebesquefs integral.-Convergence theorems.-Mollifiers and approximation.-Integral calculus.-Measure and area.-The Gauss-Green formula.-Exercises.-Curves and Differential Forms.-Differential forms, fields, and work.-Conservative fields, exact forms, and potentials.-closed forms and irrotational fields.-Stokes formula in the plane.-Exercises.-Holomorphic functions.-Functions from C to C.-The fundamental theorem of calculus in C.-The fundamental theorems about holomorphic functions.-Examples of holomorphic functions.-Pointwise singularities of holomorphic functions.-Residues.-Further consequences of Cauchy formulas.-Maximum principle.-Schwarz lemma-Local properties.-Biholomorphisms.-Riemannfs theorem on conformal representations.-Harmonic functions and Riemannfs theorem.-Exercises.-Surfaces and level sets.-Surfaces and immersions.-Implicit functions.-Some applications.-The curvature of curves and surfaces.-Exercises.-Systems of Ordinary Differential Equations.-Linear equations.-Stability.-The theorem of Poincare-Bendixson.-Exercises.-Appendix A: Mathematicians and other scientists.-References.-Index
Series: Progress in Mathematics , Vol. 266
2008, Approx. 300 p., Hardcover
ISBN: 978-3-7643-8641-2
Due: April 2008
About this book
Comprehensive account of very recent results in geometric analysis
Essentially self-contained, supplying the necessary background material which is not easily available in book form and presenting much of it in a new, original form
The aim of the book is to describe very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. An extension of the Bochner technique to the non compact setting is analyzed in detail, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). To make up for the lack of compactness, a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory, are developed. All needed tools are described in detail, often with an original approach. Some of the applications presented concern the topology at infinity of submanifolds, Lp cohomology, metric rigidity of manifolds with positive spectrum, and structure theorems for Kaelher manifolds.
Table of contents
Introduction.- 1. Harmonic Maps, (1,1)-Geodesic Maps and Basic Hermitian and Kahlerian Geometry.- 2. Comparison Results.- 3. Review of Spectral Theory.- 4. Vanishing Results.- 5. A Finite Dimensionality Result.- 6. Applications to Harmonic Maps.- 7. Topological Applications.- 8. Constancy of (1,1)-Geodesic Maps and the Structure of Complete Kahler Manifolds.- 9. Splitting and Gap Theorems in the Presence of a Poincare-Sobolev Inequality.- Appendices.- Bibliography.- Index.
Originally published by Center of Excellence, 1991
1st ed. 1991. 2008, Approx. 250 p. 300 illus., Softcover
ISBN: 978-0-387-75469-7
Due: July 2008
About this textbook
Appeals to talented students from various levels
Provides insights into combinatorial theory, geometry and graph theory
Explores practical applications of combinatorial geometry
Engages a general audience
This second edition of Alexander Sofierfs Geometric Etudes in Combinatorial Mathematics provides supplementary reading materials to students of all levels interested in pursuing mathematics, especially in algebra, geometry, or combinatorial geometry.
Within the text, Sofier outlines an introduction to graph theory and combinatorics while exploring topics such as the pigeonhole principle, Borsuk problem, and theorems of Helly and Szokefalvi?Nagy. The book introduces these ideas along with practical applications that will prepare young readers for the mathematical world.
Geometric Etudes in Combinatorial Mathematics is not only educational, it is inspirational. This distinguished mathematician captivates the young readers, propelling them to search for solutions of lifefs problems- problems that previously seemed hopeless.
Table of contents
Introductions.- Preface.- Tiling a Checker Rectangle.- Proofs of Existence.- A Word About Graphs.- Ideas of Combinatorial Geometry.- Continued.- Bibliography.- Index.- Notations.
Version: eReference (online access)
2008, eReference.
ISBN: 978-0-387-30162-4
Due: July 2008
About this book
No similar reference work on Algorithms is currently available
Comprehensive A-Z coverage of this complex subject area makes this volume easily accessible to professionals and researchers in all fields who are interested in a particular aspect of Algorithms
Targeted literature references provide additional value for researchers looking to study a topic in more detail
Entries are cross-linked with journal articles
The Encyclopedia of Algorithms will provide a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. The first edition of the reference will focus on high-impact solutions from the most recent decade; later editions will widen the scope of the work.
Nearly 500 entries will be organized alphabetically by problem, with subentries allowing for distinct solutions and special cases to be listed by the year. An entry will include:
a description of the basic algorithmic problem
the input and output specifications
the key results
examples of applications
citations to the key literature.
Open problems, links to downloadable code, experimental results, data sets, and illustrations may be provided. All entries will be written by experts with links to Internet sites that outline their research work will be provided. The entries will be peer-reviewed.
This defining reference will be published in print and on line. The print publication will include an index of subjects and authors as well as a chronology for locating recent solutions. The online edition will supplement this index with hyperlinks as well as include hyperlinks in the text of the entries to related entries, xRefer citations, and other useful URLs mentioned above.
Series: Progress in Mathematics , Preliminary entry 401
2009, Approx. 350 p., Hardcover
ISBN: 978-0-8176-4734-6
Due: March 2009
About this book
This volume arises from a meeting organized at IHP in January 2007 in honor of the 80th birthday of Murray Gerstenhaber and the 70th birthday of Jim Stasheff. The meeting was centered on algebraic deformations and higher homotopies, seminal concepts pioneered by Gerstenhaber and Stasheff in the early 1960s that now are ubiquitous in fundamental areas of mathematics (algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics) and of theoretical physics (quantum field theory, string theory).
The existence of these unifying themes together with the exceptional expository clarity of all speakers had the effect of exposing people in the audience, irrespective of their specific area, to a rich and variety of research fields. It is the aim of this volume to bring most of these exceptional speakers together again to share their ideas in written form for the benefit of researchers and students from all backgrounds in mathematics.
Contributors: Baum, Breen, Felder, Fukaya, Giaquinto, Gutt, Huebschmann, Kajiura, Keller, Kosmann-Schwarzbach, Latschev, Loday, Merkulov, Sternheimer, Sullivan, and Torossian.
Table of contents
Preface.-Paper by Baum.-Paper by Breen.-Paper by Felder.-Paper by Fukaya.-Paper by Giaquinto.-Paper by Gutt.-Paper by Huebschmann.-Paper by Kajiura.-Paper by Keller.-Paper by Kosmann-Schwarzbach.-Paper by Latschev.-Paper by Loday.-Paper by Merkulov.-Paper by Sternheimer.-Paper by Sullivan.-Paper by Torossian.-Index.