Calculus On Manifolds A Modern Approach To Classical Theorems Of Advanced Calculus Book PDF, EPUB Download & Read Online Free

Calculus On Manifolds
Author: Michael Spivak
Publisher: CRC Press
ISBN: 0429970455
Pages: 162
Year: 2018-05-04
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This little book is especially concerned with those portions of ?advanced calculus? in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.
Calculus On Manifolds
Author: Michael Spivak
Publisher: CRC Press
ISBN: 0429981538
Pages: 162
Year: 2018-05-04
View: 376
Read: 1024
This little book is especially concerned with those portions of ?advanced calculus? in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.
Calculus On Manifolds
Author: Michael Spivak
Publisher: Hachette UK
ISBN: 0813346126
Pages: 160
Year: 1971-01-22
View: 151
Read: 1276
This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.
Advanced Calculus
Author: Harold M. Edwards
Publisher: Springer Science & Business Media
ISBN: 146120271X
Pages: 508
Year: 2013-12-01
View: 674
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This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies.
Analysis On Manifolds
Author: James R. Munkres
Publisher: CRC Press
ISBN: 0429973772
Pages: 384
Year: 2018-02-19
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A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.
Calculus
Author: Michael Spivak
Publisher:
ISBN: 0914098896
Pages: 670
Year: 1994-01-01
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Advanced Calculus
Author: Lynn Harold Loomis, Shlomo Sternberg
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Pages: 596
Year: 2014-02-26
View: 854
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An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Analysis and Algebra on Differentiable Manifolds
Author: Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk
Publisher: Springer Science & Business Media
ISBN: 9400759525
Pages: 618
Year: 2012-12-30
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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.
Differential Forms and Connections
Author: R. W. R. Darling
Publisher: Cambridge University Press
ISBN: 0521468000
Pages: 256
Year: 1994-09-22
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This book introduces the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--and covers both classical surface theory, the modern theory of connections, and curvature. Also included is a chapter on applications to theoretical physics. The author uses the powerful and concise calculus of differential forms throughout. Through the use of numerous concrete examples, the author develops computational skills in the familiar Euclidean context before exposing the reader to the more abstract setting of manifolds. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. Nearly 200 exercises make the book ideal for both classroom use and self-study for advanced undergraduate and beginning graduate students in mathematics, physics, and engineering.
Multivariable mathematics
Author: Theodore Shifrin
Publisher: John Wiley & Sons Inc
ISBN: 047152638X
Pages: 491
Year: 2005
View: 1101
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Multivariable Mathematics combines linear algebra and multivariable mathematics in a rigorous approach. The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author includes all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible, and also includes complete proofs. * Contains plenty of examples, clear proofs, and significant motivation for the crucial concepts. * Numerous exercises of varying levels of difficulty, both computational and more proof-oriented. * Exercises are arranged in order of increasing difficulty.
Advanced Calculus
Author: Gerald B. Folland
Publisher:
ISBN: 9861548726
Pages: 461
Year: 2002
View: 574
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Differential Calculus and Its Applications
Author: Michael J. Field
Publisher: Courier Corporation
ISBN: 0486298841
Pages: 336
Year: 2013-04-10
View: 234
Read: 491
Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.
Vector Calculus, Linear Algebra, and Differential Forms
Author: John H. Hubbard, Barbara Burke Hubbard
Publisher:
ISBN: 0130414085
Pages: 800
Year: 2002
View: 959
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This text covers most of the standard topics in multivariate calculus and a substantial part of a standard first course in linear algebra. Appendix material on harder proofs and programs allows the book to be used as a text for a course in analysis. The organization and selection of material present
Differential Geometry of Manifolds
Author: Stephen T. Lovett
Publisher: CRC Press
ISBN: 1439865469
Pages: 440
Year: 2010-06-11
View: 744
Read: 855
From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices provide background information on point set topology, calculus of variations, and multilinear algebra—topics that may not have been covered in the prerequisite courses of multivariable calculus and linear algebra. Differential Geometry of Manifolds takes a practical approach, containing extensive exercises and focusing on applications of differential geometry in physics, including the Hamiltonian formulation of dynamics (with a view toward symplectic manifolds), the tensorial formulation of electromagnetism, some string theory, and some fundamental concepts in general relativity.
Introduction to Smooth Manifolds
Author: John M. Lee
Publisher: Springer Science & Business Media
ISBN: 0387217525
Pages: 631
Year: 2013-03-09
View: 1171
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Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why

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