An Introduction to Differential Geometry


Author: T. J. Willmore
Publisher: Courier Corporation
ISBN: 0486282104
Category: Mathematics
Page: 336
View: 4802
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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.

Introduction to Differential Geometry for Engineers


Author: Brian F. Doolin,Clyde F. Martin
Publisher: Courier Corporation
ISBN: 0486281949
Category: Mathematics
Page: 176
View: 7745
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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 Geometry


Author: Erwin Kreyszig
Publisher: Courier Corporation
ISBN: 0486318621
Category: Mathematics
Page: 384
View: 2937
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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.

Lectures on Classical Differential Geometry


Author: Dirk Jan Struik
Publisher: Courier Corporation
ISBN: 9780486656090
Category: Mathematics
Page: 232
View: 4582
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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.

Differentialgeometrie von Kurven und Flächen


Author: Manfredo P. do Carmo
Publisher: Springer-Verlag
ISBN: 3322850722
Category: Technology & Engineering
Page: 263
View: 2787
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Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang

Differential Geometry


Author: Heinrich W. Guggenheimer
Publisher: Courier Corporation
ISBN: 0486157202
Category: Mathematics
Page: 400
View: 5432
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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.

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


Author: D. E. Rutherford
Publisher: Courier Corporation
ISBN: 048615453X
Category: Mathematics
Page: 144
View: 6344
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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. 1957 edition.

Differential Forms with Applications to the Physical Sciences


Author: Harley Flanders
Publisher: Courier Corporation
ISBN: 0486139611
Category: Mathematics
Page: 240
View: 5999
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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: 5466
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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: 8689
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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.

Differential Geometric Structures


Author: Walter A. Poor
Publisher: Courier Corporation
ISBN: 0486151913
Category: Mathematics
Page: 352
View: 4811
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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.

Differential Geometry


Author: William C. Graustein
Publisher: Courier Corporation
ISBN: 0486153231
Category: Mathematics
Page: 240
View: 9728
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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.

Gravitational Curvature

An Introduction to Einstein's Theory
Author: Theodore Frankel
Publisher: Courier Corporation
ISBN: 048628915X
Category: Science
Page: 192
View: 4036
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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.

Differential Geometry


Author: Heinrich Walter Guggenheimer
Publisher: Dover Books on Mathematics
ISBN: 9780486634333
Category: Mathematics
Page: 378
View: 751
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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.

A Combinatorial Introduction to Topology


Author: Michael Henle
Publisher: Courier Corporation
ISBN: 9780486679662
Category: Mathematics
Page: 310
View: 4075
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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.

An Introduction to Differential Equations and Their Applications


Author: Stanley J. Farlow
Publisher: Courier Corporation
ISBN: 0486135136
Category: Mathematics
Page: 640
View: 2244
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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.

A Treatise on the Differential Geometry of Curves and Surfaces


Author: Luther Pfahler Eisenhart
Publisher: Courier Corporation
ISBN: 9780486438207
Category: Mathematics
Page: 474
View: 7417
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Created especially for graduate students by a leading writer on mathematics, this introduction to the geometry of curves and surfaces concentrates on problems that students will find most helpful.

Foundations of Modern Analysis


Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486640624
Category: Mathematics
Page: 250
View: 5889
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Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

Differentialgeometrie

Kurven - Flächen - Mannigfaltigkeiten
Author: Wolfgang Kühnel
Publisher: Springer-Verlag
ISBN: 3834896551
Category: Mathematics
Page: 280
View: 1491
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Dieses Buch ist eine Einführung in die Differentialgeometrie. 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. Im Laufe der Neuauflagen wurde der Text erweitert, neue Aufgaben wurden hinzugefügt und am Ende des Buches wurden zusätzliche Hinweise zur Lösung der Übungsaufgaben ergänzt. Der Text wurde für die fünfte Auflage gründlich durchgesehen und an einigen Stellen verbessert.

First-order Logic


Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 9780486683706
Category: Mathematics
Page: 158
View: 9198
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Considered the best book in the field, this completely self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus in on the tableau point of view. Topics include trees, tableau method for propositional logic, Gentzen systems, more. Includes 144 illustrations.