Book Description
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 : Donald W. Kahn
Publisher : Courier Corporation
Page : 20 pages
File Size : 35,53 MB
Release : 2013-11-07
Category : 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 : Donald W. Kahn
Publisher :
Page : 336 pages
File Size : 41,96 MB
Release : 1980-01-01
Category : Mathematics
ISBN : 9780123940506
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 : Immanuel Maurice Wallerstein
Publisher : Duke University Press
Page : 132 pages
File Size : 28,50 MB
Release : 2004
Category : History
ISBN : 9780822334422
A John Hope Franklin Center Book.
Author : Calvin C. Moore
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 44,41 MB
Release : 2012-12-06
Category : 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 : S. Ramanan
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 13,30 MB
Release : 2005
Category : 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
Page : 350 pages
File Size : 42,21 MB
Release : 2010
Category : 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 : Maxwell Rosenlicht
Publisher : Courier Corporation
Page : 270 pages
File Size : 30,59 MB
Release : 2012-05-04
Category : 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 : Irena Swanson
Publisher : World Scientific
Page : 455 pages
File Size : 34,62 MB
Release : 2021-02-18
Category : 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 : Leonhard Euler
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 48,69 MB
Release : 2012-12-06
Category : 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 : Floris Takens
Publisher :
Page : 111 pages
File Size : 35,14 MB
Release : 1973
Category : Differential equations
ISBN :