Analysis And Algebra On Differentiable Manifolds A Workbook For Students And Teachers PDF Download
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Author | : Pedro M. Gadea |
Publisher | : Springer Science & Business Media |
Total Pages | : 635 |
Release | : 2012-12-30 |
Genre | : Mathematics |
ISBN | : 9400759525 |
Download Analysis and Algebra on Differentiable Manifolds Book in PDF, ePub and Kindle
This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear. A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics. In this 2nd edition: • 76 new problems • a section devoted to a generalization of Gauss’ Lemma • a short novel section dealing with some properties of the energy of Hopf vector fields • an expanded collection of formulae and tables • an extended bibliography Audience This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.
Author | : P.M. Gadea |
Publisher | : Springer Science & Business Media |
Total Pages | : 446 |
Release | : 2009-12-12 |
Genre | : Mathematics |
ISBN | : 9048135648 |
Download Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers Book in PDF, ePub and Kindle
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 | : P.M. Gadea |
Publisher | : Springer |
Total Pages | : 438 |
Release | : 2009-12-09 |
Genre | : Mathematics |
ISBN | : 9789048135639 |
Download Analysis and Algebra on Differentiable Manifolds Book in PDF, ePub and Kindle
This book is a collection of 375 completely solved exercises on differentiable manifolds, Lie groups, fibre bundles, and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. It is the first book consisting of completely solved problems on differentiable manifolds, and therefore will be a complement to the books on theory. A 42-page formulary is included which will be useful as an aide-mémoire, especially for teachers and researchers on these topics. The book includes 50 figures. Audience: The book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics, and some branches of engineering.
Author | : T.Y. Lam |
Publisher | : Springer Science & Business Media |
Total Pages | : 427 |
Release | : 2009-12-08 |
Genre | : Mathematics |
ISBN | : 0387488995 |
Download Exercises in Modules and Rings Book in PDF, ePub and Kindle
This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.
Author | : Irene Fonseca |
Publisher | : Springer Science & Business Media |
Total Pages | : 602 |
Release | : 2007-08-22 |
Genre | : Science |
ISBN | : 0387690069 |
Download Modern Methods in the Calculus of Variations Book in PDF, ePub and Kindle
This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.
Author | : Charles Herbert Clemens |
Publisher | : |
Total Pages | : 356 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : |
Download Geometry for the Classroom Book in PDF, ePub and Kindle
Author | : Loring W. Tu |
Publisher | : Springer Science & Business Media |
Total Pages | : 426 |
Release | : 2010-10-05 |
Genre | : Mathematics |
ISBN | : 1441974008 |
Download An Introduction to Manifolds Book in PDF, ePub and Kindle
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Author | : Jonathan S. Golan |
Publisher | : Springer Science & Business Media |
Total Pages | : 444 |
Release | : 2004-01-31 |
Genre | : Computers |
ISBN | : 9781402018244 |
Download The Linear Algebra a Beginning Graduate Student Ought to Know Book in PDF, ePub and Kindle
Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. The book is intended to be used in one of several possible ways: (1) as a self-study guide; (2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or (3) as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication. The book also contains over 1000 exercises, many of which are very challenging.
Author | : Lynn Arthur Steen |
Publisher | : Courier Corporation |
Total Pages | : 274 |
Release | : 2013-04-22 |
Genre | : Mathematics |
ISBN | : 0486319296 |
Download Counterexamples in Topology Book in PDF, ePub and Kindle
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Author | : Constantin Costara |
Publisher | : Springer Science & Business Media |
Total Pages | : 472 |
Release | : 2003-09-30 |
Genre | : Mathematics |
ISBN | : 9781402015601 |
Download Exercises in Functional Analysis Book in PDF, ePub and Kindle
This book of exercises in Functional Analysis contains almost 450 exercises (all with complete solutions), providing supplementary examples, counter-examples and applications for the basic notions usually presented in an introductory course in Functional Analysis. It contains three parts. The first one contains exercises on the general properties for sets in normed spaces, linear bounded operators on normed spaces, reflexivity, compactness in normed spaces, and on the basic principles in Functional Analysis: the Hahn-Banach theorem, the Uniform Boundedness Principle, the Open Mapping and the Closed Graph theorems. The second one contains exercises on the general theory of Hilbert spaces, the Riesz representation theorem, orthogonality in Hilbert spaces, the projection theorem and linear bounded operators on Hilbert spaces. The third one deals with linear topological spaces, and includes a large number of exercises on the weak topologies.