Lectures on Classical Differential Geometry

Author: Dirk Jan Struik

Publisher: Courier Corporation

ISBN: 9780486656090

Category: Mathematics

Page: 232

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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.

Lectures on Classical Differential Geometry

Second Edition

Author: Dirk J. Struik

Publisher: Courier Corporation

ISBN: 0486138186

Category: Mathematics

Page: 240

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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.



Lectures on Linear Algebra

Author: I. M. Gelfand

Publisher: Courier Corporation

ISBN: 9780486660820

Category: Mathematics

Page: 185

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Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.

Wave Mechanics

Volume 5 of Pauli Lectures on Physics

Author: Wolfgang (Physiker) Pauli

Publisher: Courier Corporation

ISBN: 9780486414621

Category: Science

Page: 205

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Focuses on wave functions of force-free particles, description of a particle in a box and in free space, particle in a field of force, multiple particles, eigenvalue problems, more.

Differential Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 9780486667218

Category: Mathematics

Page: 352

View: 8510

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Text from preface: "This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space"

Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition

Author: mary Gray

Publisher: CRC Press

ISBN: 9780849371646

Category: Mathematics

Page: 1088

View: 4694

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The Second Edition combines a traditional approach with the symbolic manipulation abilities of Mathematica to explain and develop the classical theory of curves and surfaces. You will learn to reproduce and study interesting curves and surfaces - many more than are included in typical texts - using computer methods. By plotting geometric objects and studying the printed result, teachers and students can understand concepts geometrically and see the effect of changes in parameters. Modern Differential Geometry of Curves and Surfaces with Mathematica explains how to define and compute standard geometric functions, for example the curvature of curves, and presents a dialect of Mathematica for constructing new curves and surfaces from old. The book also explores how to apply techniques from analysis. Although the book makes extensive use of Mathematica, readers without access to that program can perform the calculations in the text by hand. While single- and multi-variable calculus, some linear algebra, and a few concepts of point set topology are needed to understand the theory, no computer or Mathematica skills are required to understand the concepts presented in the text. In fact, it serves as an excellent introduction to Mathematica, and includes fully documented programs written for use with Mathematica. Ideal for both classroom use and self-study, Modern Differential Geometry of Curves and Surfaces with Mathematica has been tested extensively in the classroom and used in professional short courses throughout the world.

Differential Geometry

Author: Heinrich W. Guggenheimer

Publisher: Courier Corporation

ISBN: 0486157202

Category: Mathematics

Page: 400

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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.

Journey into Mathematics

An Introduction to Proofs

Author: Joseph J. Rotman

Publisher: Courier Corporation

ISBN: 0486151689

Category: Mathematics

Page: 256

View: 7761

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This treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition.

A Concise History of Mathematics

Author: Dirk Jan Struik

Publisher: Courier Corporation

ISBN: 9780486602554

Category: Mathematics

Page: 228

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This compact, well-written history covers major mathematical ideas and techniques from the ancient Near East to 20th-century computer theory, surveying the works of Archimedes, Pascal, Gauss, Hilbert, and many others. "The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature.

Advanced Calculus of Several Variables

Author: Charles Henry Edwards

Publisher: Courier Corporation

ISBN: 9780486683362

Category: Mathematics

Page: 457

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Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.

First-order Logic

Author: Raymond M. Smullyan

Publisher: Courier Corporation

ISBN: 9780486683706

Category: Mathematics

Page: 158

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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.

Elementare Differentialgeometrie

Author: Christian Bär

Publisher: Walter de Gruyter

ISBN: 3110224593

Category: Mathematics

Page: 356

View: 5139

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This textbook presents an introduction to the differential geometry of curves and surfaces. This second, revised edition has been expanded to include solutions and applications in cartography. Topics include Euclidean geometry, curve theory, surface theory, curvature concepts, minimal surfaces, Riemann geometry and the Gauss-Bonnet theorem.

Introduction to Linear Algebra

Author: Marvin Marcus,Henryk Minc

Publisher: Courier Corporation

ISBN: 9780486656953

Category: Mathematics

Page: 261

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Rigorous, self-contained introduction at undergraduate level covers vector spaces and linear transformations, linear equations and determinants, characteristic roots. Includes 16 sets of true-false quizzes and exercises — with worked-out solutions — a complete theory of permutations and much more.



Differentialgeometrie

Kurven - Flächen - Mannigfaltigkeiten

Author: Wolfgang Kühnel

Publisher: Springer-Verlag

ISBN: 3658006153

Category: Mathematics

Page: 284

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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.

Partielle Differentialgleichungen

Eine Einführung

Author: Walter A. Strauss

Publisher: Springer-Verlag

ISBN: 366312486X

Category: Mathematics

Page: 458

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Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.