Analysis And Algebra On Differentiable Manifolds A Workbook For Students And Teachers
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Analysis And Algebra On Differentiable Manifolds
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Author : Pedro M. Gadea
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-30
Analysis And Algebra On Differentiable Manifolds written by Pedro M. Gadea and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-30 with Mathematics categories.
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.
Analysis And Algebra On Differentiable Manifolds A Workbook For Students And Teachers
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Author : P.M. Gadea
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-10-31
Analysis And Algebra On Differentiable Manifolds A Workbook For Students And Teachers written by P.M. Gadea and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-31 with Mathematics categories.
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.
Analysis And Algebra On Differentiable Manifolds
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Author : P.M. Gadea
language : en
Publisher: Springer
Release Date : 2009-12-09
Analysis And Algebra On Differentiable Manifolds written by P.M. Gadea and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-09 with Mathematics categories.
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.
Analysis And Algebra On Differentiable Manifolds A Workbook For Students And Teachers
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Author : P.M. Gadea
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-12
Analysis And Algebra On Differentiable Manifolds A Workbook For Students And Teachers written by P.M. Gadea and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-12 with Mathematics categories.
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.
The Linear Algebra A Beginning Graduate Student Ought To Know
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Author : Jonathan S. Golan
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-01-31
The Linear Algebra A Beginning Graduate Student Ought To Know written by Jonathan S. Golan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-31 with Computers categories.
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.
The Astrophysics Of Galactic Cosmic Rays
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Author : Roland Diehl
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-02-28
The Astrophysics Of Galactic Cosmic Rays written by Roland Diehl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-02-28 with Medical categories.
Proceedings from two ISSI workshops, 18-22 October 1999 and 15-19 May 2000, Bern, Switzerland
Exercises In Functional Analysis
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Author : Constantin Costara
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-09-30
Exercises In Functional Analysis written by Constantin Costara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-30 with Mathematics categories.
This book contains almost 450 exercises, all with complete solutions; it provides supplementary examples, counter-examples, and applications for the basic notions usually presented in an introductory course in Functional Analysis. Three comprehensive sections cover the broad topic of functional analysis. A large number of exercises on the weak topologies is included.
Exercises In Abelian Group Theory
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Author : Grigore Calugareanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-04-30
Exercises In Abelian Group Theory written by Grigore Calugareanu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-30 with Mathematics categories.
This is the first book on Abelian Group Theory (or Group Theory) to cover elementary results in Abelian Groups. It contains comprehensive coverage of almost all the topics related to the theory and is designed to be used as a course book for students at both undergraduate and graduate level. The text caters to students of differing capabilities by categorising the exercises in each chapter according to their level of difficulty starting with simple exercises (marked S1, S2 etc), of medium difficulty (M1, M2 etc) and ending with difficult exercises (D1, D2 etc). Solutions for all of the exercises are included. This book should also appeal to experts in the field as an excellent reference to a large number of examples in Group Theory.
Mathematical Modelling
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Author : J. Caldwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-03-31
Mathematical Modelling written by J. Caldwell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-31 with Mathematics categories.
Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science, engineering, business and management. Recent developments in computer technology and related software have provided the necessary tools of increasing power and sophistication which have significant implications for the use and role of mathematical modelling in the above disciplines. In the past, traditional methods have relied heavily on expensive experimentation and the building of scaled models, but now a more flexible and cost effective approach is available through greater use of mathematical modelling and computer simulation. In particular, developments in computer algebra, symbolic manipulation packages and user friendly software packages for large scale problems, all have important implications in both the teaching of mathematical modelling and, more importantly, its use in the solution of real world problems. Many textbooks have been published which cover the art and techniques of modelling as well as specific mathematical modelling techniques in specialist areas within science and business. In most of these books the mathematical material tends to be rather tailor made to fit in with a one or two semester course for teaching students at the undergraduate or postgraduate level, usually the former. This textbook is quite different in that it is intended to build on and enhance students’ modelling skills using a combination of case studies and projects.
Algorithmic Principles Of Mathematical Programming
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Author : Ulrich Faigle
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Algorithmic Principles Of Mathematical Programming written by Ulrich Faigle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.