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Author: Barry Simon Publisher: American Mathematical Soc. ISBN: 1470410990 Category : Mathematics Languages : en Pages : 811
Book Description
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.
Author: Barry Simon Publisher: American Mathematical Soc. ISBN: 1470410990 Category : Mathematics Languages : en Pages : 811
Book Description
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.
Author: C. E. Springer Publisher: Courier Corporation ISBN: 048632091X Category : Mathematics Languages : en Pages : 258
Book Description
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.
Author: John Snygg Publisher: Springer Science & Business Media ISBN: 081768283X Category : Mathematics Languages : en Pages : 472
Book Description
Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.
Author: Peter W. Michor Publisher: American Mathematical Soc. ISBN: 0821820036 Category : Mathematics Languages : en Pages : 510
Book Description
"This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.
Author: P.M. Gadea Publisher: Springer Science & Business Media ISBN: 9048135648 Category : Mathematics Languages : en Pages : 446
Book Description
A famous Swiss professor gave a student’s course in Basel on Riemann surfaces. After a couple of lectures, a student asked him, “Professor, you have as yet not given an exact de nition of a Riemann surface.” The professor answered, “With Riemann surfaces, the main thing is to UNDERSTAND them, not to de ne them.” The student’s objection was reasonable. From a formal viewpoint, it is of course necessary to start as soon as possible with strict de nitions, but the professor’s - swer also has a substantial background. The pure de nition of a Riemann surface— as a complex 1-dimensional complex analytic manifold—contributes little to a true understanding. It takes a long time to really be familiar with what a Riemann s- face is. This example is typical for the objects of global analysis—manifolds with str- tures. There are complex concrete de nitions but these do not automatically explain what they really are, what we can do with them, which operations they really admit, how rigid they are. Hence, there arises the natural question—how to attain a deeper understanding? One well-known way to gain an understanding is through underpinning the d- nitions, theorems and constructions with hierarchies of examples, counterexamples and exercises. Their choice, construction and logical order is for any teacher in global analysis an interesting, important and fun creating task.
Author: Jeffrey Marc Lee Publisher: American Mathematical Soc. ISBN: 0821848151 Category : Mathematics Languages : en Pages : 690
Book Description
Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and structures of modern differential geometry. It includes the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, and de Rham cohomology.
Author: Nicolas K. Laos Publisher: World Scientific ISBN: 9789810231804 Category : Mathematics Languages : en Pages : 580
Book Description
This book studies the interplay between mathematical analysis and differential geometry as well as the foundations of these two fields. The development of a unified approach to topological vector spaces, differential geometry and algebraic and differential topology of function manifolds led to the broad expansion of global analysis. This book serves as a self-contained reference on both the prerequisites for further study and the recent research results which have played a decisive role in the advancement of global analysis.
Author: Mohammad Hasan Shahid Publisher: Springer Nature ISBN: 9811554552 Category : Mathematics Languages : en Pages : 284
Book Description
This book is a collection of selected research papers, some of which were presented at the International Conference on Differential Geometry, Algebra and Analysis (ICDGAA 2016), held at the Department of Mathematics, Jamia Millia Islamia, New Delhi, from 15–17 November 2016. It covers a wide range of topics—geometry of submanifolds, geometry of statistical submanifolds, ring theory, module theory, optimization theory, and approximation theory—which exhibit new ideas and methodologies for current research in differential geometry, algebra and analysis. Providing new results with rigorous proofs, this book is, therefore, of much interest to readers who wish to learn new techniques in these areas of mathematics.
Author: Raymond O. Wells Publisher: Springer Science & Business Media ISBN: 0387738916 Category : Mathematics Languages : en Pages : 315
Book Description
A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.
Author: Barry Simon
Author: Barry Simon
Author: C. E. Springer
Author: John Snygg
Author: Peter W. Michor
Author: P.M. Gadea
Author: Jeffrey Marc Lee
Author: Nicolas K. Laos
Author: Mohammad Hasan Shahid
Author: Raymond O. Wells
Author: Richard L. Bishop