Lectures on Classical Differential Geometry

Author: Dirk Jan Struik

Publisher: Courier Corporation

ISBN: 9780486656090

Category: Mathematics

Page: 232

View: 4686

Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
Posted in Mathematics

Lectures on Classical Differential Geometry

Second Edition

Author: Dirk J. Struik

Publisher: Courier Corporation

ISBN: 0486138186

Category: Mathematics

Page: 240

View: 8260

Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, envelopes, more. Many problems and solutions. Bibliography.
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Differential Geometry

Author: Heinrich W. Guggenheimer

Publisher: Courier Corporation

ISBN: 0486157202

Category: Mathematics

Page: 400

View: 3067

This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.
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Elementary Differential Geometry

Author: A.N. Pressley

Publisher: Springer Science & Business Media

ISBN: 1848828918

Category: Mathematics

Page: 474

View: 6313

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com ul>
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Curves and Surfaces

Author: Sebastián Montiel,Antonio Ros,Donald G. Babbitt

Publisher: American Mathematical Soc.

ISBN: 0821847635

Category: Mathematics

Page: 376

View: 8933

This introductory textbook puts forth a clear and focused point of view on the differential geometry of curves and surfaces. Following the modern point of view on differential geometry, the book emphasizes the global aspects of the subject. The excellent collection of examples and exercises (with hints) will help students in learning the material. Advanced undergraduates and graduate students will find this a nice entry point to differential geometry. In order to study the global properties of curves and surfaces, it is necessary to have more sophisticated tools than are usually found in textbooks on the topic. In particular, students must have a firm grasp on certain topological theories. Indeed, this monograph treats the Gauss-Bonnet theorem and discusses the Euler characteristic. The authors also cover Alexandrov's theorem on embedded compact surfaces in $\mathbb{R}^3$ with constant mean curvature. The last chapter addresses the global geometry of curves, including periodic space curves and the four-vertices theorem for plane curves that are not necessarily convex. Besides being an introduction to the lively subject of curves and surfaces, this book can also be used as an entry to a wider study of differential geometry. It is suitable as the text for a first-year graduate course or an advanced undergraduate course.
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Curvature in Mathematics and Physics

Author: Shlomo Sternberg

Publisher: Courier Corporation

ISBN: 0486292711

Category: Mathematics

Page: 416

View: 7937

Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.
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Differential Geometry of Curves and Surfaces

Revised and Updated Second Edition

Author: Manfredo P. do Carmo

Publisher: Courier Dover Publications

ISBN: 0486806995

Category: Mathematics

Page: 512

View: 5474

One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.
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Geometry from a Differentiable Viewpoint

Author: John McCleary

Publisher: Cambridge University Press

ISBN: 0521116074

Category: Mathematics

Page: 357

View: 9578

A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.
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Lectures on Analytic and Projective Geometry

Author: Dirk J. Struik

Publisher: Courier Corporation

ISBN: 0486173526

Category: Mathematics

Page: 304

View: 7479

This undergraduate text develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. 1953 edition.
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Analysis and Algebra on Differentiable Manifolds

A Workbook for Students and Teachers

Author: Pedro M. Gadea,Jaime Muñoz Masqué,Ihor V. Mykytyuk

Publisher: Springer Science & Business Media

ISBN: 9400759525

Category: Mathematics

Page: 618

View: 4103

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.
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Riemannian Geometry

A Modern Introduction

Author: Isaac Chavel

Publisher: Cambridge University Press

ISBN: 1139452576

Category: Mathematics

Page: N.A

View: 6019

This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.
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Introduction to Modern Algebra and Matrix Theory

Second Edition

Author: O. Schreier,E. Sperner

Publisher: Courier Corporation

ISBN: 0486278654

Category: Mathematics

Page: 400

View: 2990

This unique text provides students with a basic course in both calculus and analytic geometry — no competitive editions cover both topics in a single volume. Its prerequisites are minimal, and the order of its presentation promotes an intuitive approach to calculus. Algebraic concepts receive an unusually strong emphasis. Numerous exercises appear throughout the text. 1951 edition.
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Differential Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 0486318621

Category: Mathematics

Page: 384

View: 5324

An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.
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Geometry, Topology and Physics, Second Edition

Author: Mikio Nakahara

Publisher: CRC Press

ISBN: 9780750306065

Category: Mathematics

Page: 596

View: 5164

Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
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Differential Geometry of Manifolds

Author: Stephen T. Lovett

Publisher: CRC Press

ISBN: 1439865469

Category: Mathematics

Page: 440

View: 8665

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.
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Lectures on Differential Geometry

Author: S S Chern,W H Chen,K S Lam

Publisher: World Scientific Publishing Company

ISBN: 9813102985

Category: Mathematics

Page: 368

View: 2479

This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.
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An Introduction to Differential Geometry

Author: T. J. Willmore

Publisher: Courier Corporation

ISBN: 0486282104

Category: Mathematics

Page: 336

View: 5133

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
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Calculus On Manifolds

A Modern Approach To Classical Theorems Of Advanced Calculus

Author: Michael Spivak

Publisher: CRC Press

ISBN: 0429970455

Category: Mathematics

Page: 162

View: 7005

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.
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Topology and Geometry for Physicists

Author: Charles Nash,Siddhartha Sen

Publisher: Courier Corporation

ISBN: 0486318362

Category: Mathematics

Page: 320

View: 3238

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. "Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.
Posted in Mathematics