An Introduction to Differential Geometry


Author: T. J. Willmore
Publisher: Courier Corporation
ISBN: 0486282104
Category: Mathematics
Page: 336
View: 7394
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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.

Differential Geometry


Author: Heinrich W. Guggenheimer
Publisher: Courier Corporation
ISBN: 0486157202
Category: Mathematics
Page: 400
View: 3241
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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.

Differentialgeometrie von Kurven und Flächen


Author: Manfredo P. do Carmo
Publisher: Springer-Verlag
ISBN: 3322850722
Category: Technology & Engineering
Page: 263
View: 3059
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Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang

Lectures on Classical Differential Geometry


Author: Dirk Jan Struik
Publisher: Courier Corporation
ISBN: 9780486656090
Category: Mathematics
Page: 232
View: 8586
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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.

Differential Geometry


Author: Erwin Kreyszig
Publisher: Courier Corporation
ISBN: 0486318621
Category: Mathematics
Page: 384
View: 4196
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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.

Differentialgeometrie

Kurven - Flächen - Mannigfaltigkeiten
Author: Wolfgang Kühnel
Publisher: Springer-Verlag
ISBN: 3658006153
Category: Mathematics
Page: 284
View: 6571
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Dieses Buch ist eine Einführung in die Differentialgeometrie und ein passender Begleiter zum Differentialgeometrie-Modul (ein- und zweisemestrig). Zunächst geht es um die klassischen Aspekte wie die Geometrie von Kurven und Flächen, bevor dann höherdimensionale Flächen sowie abstrakte Mannigfaltigkeiten betrachtet werden. Die Nahtstelle ist dabei das zentrale Kapitel "Die innere Geometrie von Flächen". Dieses führt den Leser bis hin zu dem berühmten Satz von Gauß-Bonnet, der ein entscheidendes Bindeglied zwischen lokaler und globaler Geometrie darstellt. Die zweite Hälfte des Buches ist der Riemannschen Geometrie gewidmet. Den Abschluss bildet ein Kapitel über "Einstein-Räume", die eine große Bedeutung sowohl in der "Reinen Mathematik" als auch in der Allgemeinen Relativitätstheorie von A. Einstein haben. Es wird großer Wert auf Anschaulichkeit gelegt, was durch zahlreiche Abbildungen unterstützt wird. Bei der Neuauflage wurden einige zusätzliche Lösungen zu den Übungsaufgaben ergänzt.

Introduction to Differential Geometry for Engineers


Author: Brian F. Doolin,Clyde F. Martin
Publisher: Courier Corporation
ISBN: 0486281949
Category: Mathematics
Page: 176
View: 2538
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This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers.The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.

Differential Geometric Structures


Author: Walter A. Poor
Publisher: Courier Corporation
ISBN: 0486151913
Category: Mathematics
Page: 352
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This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.

Der absolute Differentialkalkül und seine Anwendungen in Geometrie und Physik


Author: Tullio Levi-Civita
Publisher: N.A
ISBN: N.A
Category: Calculus of tensors
Page: 310
View: 5904
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Differential Geometry


Author: William C. Graustein
Publisher: Courier Corporation
ISBN: 0486153231
Category: Mathematics
Page: 240
View: 5443
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This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of 3 dimensions, using vector notation and technique. Nearly 200 problems.1935 edition.

An Introduction to Differential Equations and Their Applications


Author: Stanley J. Farlow
Publisher: Courier Corporation
ISBN: 0486135136
Category: Mathematics
Page: 640
View: 9497
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This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

Differential Forms with Applications to the Physical Sciences


Author: Harley Flanders
Publisher: Courier Corporation
ISBN: 0486139611
Category: Mathematics
Page: 240
View: 5750
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A graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. Includes 45 illustrations. Index.

Tensor and Vector Analysis

With Applications to Differential Geometry
Author: C. E. Springer
Publisher: Courier Corporation
ISBN: 0486498018
Category: Mathematics
Page: 242
View: 8134
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Assuming only a knowledge of basic calculus, this textpresents an elementary and gradual development of tensortheory. From this treatment, the traditional material ofcourses on vector analysis is deduced as a particular case. Inaddition, the book forms an introduction to metric differentialgeometry.Reprint of The Ronald Press Company, New York, 1962 edition.

Lectures on Classical Differential Geometry

Second Edition
Author: Dirk J. Struik
Publisher: Courier Corporation
ISBN: 0486138186
Category: Mathematics
Page: 240
View: 5298
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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.

Gravitational Curvature

An Introduction to Einstein's Theory
Author: Theodore Frankel
Publisher: Courier Corporation
ISBN: 048628915X
Category: Science
Page: 192
View: 9048
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This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence and stresses the global aspects of cosmology. Suitable for independent study as well as for courses in differential geometry, relativity, and cosmology. 1979 edition.

Vector Methods Applied to Differential Geometry, Mechanics, and Potential Theory


Author: D. E. Rutherford
Publisher: Courier Corporation
ISBN: 9780486439037
Category: Mathematics
Page: 135
View: 5910
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Designed to familiarize undergraduates with the methods of vector algebra and vector calculus, this text offers both a clear view of the abstract theory as well as a concise survey of the theory's applications to various branches of pure and applied mathematics. A chapter on differential geometry introduces readers to the study of this subject by the methods of vector algebra. The next section explores the many aspects of the theory of mechanics adaptable to the use of vectors, and a full discussion of the vector operator "nabla" proceeds to a treatment of potential theory and Laplace's equation. This includes applications to the theories of gravitation, hydrodynamics, and electricity. A brief chapter on four-dimensional vectors concludes the text.

Differentialgeometrie, Topologie und Physik


Author: Mikio Nakahara
Publisher: Springer-Verlag
ISBN: 3662453002
Category: Science
Page: 597
View: 2443
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Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.

Introduction to Differentiable Manifolds


Author: Louis Auslander,Robert E. MacKenzie
Publisher: Courier Corporation
ISBN: 048615808X
Category: Mathematics
Page: 224
View: 4797
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This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.

An Introduction to Linear Algebra and Tensors


Author: M. A. Akivis,V. V. Goldberg
Publisher: Courier Corporation
ISBN: 0486148785
Category: Mathematics
Page: 192
View: 9170
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Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.

A Combinatorial Introduction to Topology


Author: Michael Henle
Publisher: Courier Corporation
ISBN: 9780486679662
Category: Mathematics
Page: 310
View: 533
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Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.