Introduction To Global Analysis
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Author | : Donald W. Kahn |
Publisher | : Courier Corporation |
Total Pages | : 20 |
Release | : 2013-11-07 |
Genre | : Mathematics |
ISBN | : 0486152294 |
This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.
Author | : Calvin C. Moore |
Publisher | : Springer Science & Business Media |
Total Pages | : 337 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461395925 |
Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classicallv in the Gauss-Bonnet theorem and its generalizations. which culminate in the Ativah-Singer Index Theorem [ASI] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topologie al properties of the manifold. The Ativah-Singer Index Theorem has been generalized in several directions. notably by Atiyah-Singer to an index theorem for families [AS4]. The typical setting here is given by a family of elliptic operators (Pb) on the total space of a fibre bundle P = F_M_B. where is defined the Hilbert space on Pb 2 L 1p -llbl.dvollFll. In this case there is an abstract index class indlPI E ROIBI. Once the problem is properly formulated it turns out that no further deep analvtic information is needed in order to identify the class. These theorems and their equivariant counterparts have been enormously useful in topology. geometry. physics. and in representation theory.
Author | : William R. Parzynski |
Publisher | : McGraw-Hill Companies |
Total Pages | : 376 |
Release | : 1982 |
Genre | : Mathematics |
ISBN | : |
Author | : Maxwell Rosenlicht |
Publisher | : Courier Corporation |
Total Pages | : 270 |
Release | : 2012-05-04 |
Genre | : Mathematics |
ISBN | : 0486134687 |
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
Author | : S. Ramanan |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821837028 |
The power that analysis, topology and algebra bring to geometry has revolutionised the way geometers and physicists look at conceptual problems. Some of the key ingredients in this interplay are sheaves, cohomology, Lie groups, connections and differential operators. In Global Calculus, the appropriate formalism for these topics is laid out with numerous examples and applications by one of the experts in differential and algebraic geometry. Ramanan has chosen an uncommon but natural path through the subject. In this almost completely self-contained account, these topics are developed from scratch. The basics of Fourier transforms, Sobolev theory and interior regularity are proved at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex. Many new perspectives on traditional and modern questions of differential analysis and geometry are the hallmarks of the book. The book is suitable for a first year graduate course on Global Analysis.
Author | : Gerald Bilodeau |
Publisher | : Jones & Bartlett Learning |
Total Pages | : 350 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0763774928 |
This book presents a concise and sharpley focused introduction to the basic concepts of analysis - from the development of real numbers through uniform convergences of a sequence of functions - and includes coverage both of the analysis of functions of more than one variable and of differential equations. Examples and figures are used extensively to assist the reader in understanding the concepts and then applying them.
Author | : Leonhard Euler |
Publisher | : Springer Science & Business Media |
Total Pages | : 341 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461210216 |
From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."
Author | : Immanuel Maurice Wallerstein |
Publisher | : Duke University Press |
Total Pages | : 132 |
Release | : 2004 |
Genre | : History |
ISBN | : 9780822334422 |
A John Hope Franklin Center Book.
Author | : Irena Swanson |
Publisher | : World Scientific |
Total Pages | : 455 |
Release | : 2021-02-18 |
Genre | : Mathematics |
ISBN | : 9811225877 |
This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series.The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head.The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.
Author | : Andreas Kriegl |
Publisher | : American Mathematical Soc. |
Total Pages | : 631 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 0821807803 |
For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR