Differential Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 0486318621

Category: Mathematics

Page: 384

View: 3514

DOWNLOAD NOW »

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 von Kurven und Flächen

Author: Manfredo P. do Carmo

Publisher: Springer-Verlag

ISBN: 3322850722

Category: Technology & Engineering

Page: 263

View: 3250

DOWNLOAD NOW »

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: 8853

DOWNLOAD NOW »

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 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: 8932

DOWNLOAD NOW »

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.

Differential Geometry

Author: William C. Graustein

Publisher: Courier Corporation

ISBN: 0486153231

Category: Mathematics

Page: 240

View: 2672

DOWNLOAD NOW »

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.

Differential Geometry

Author: K. L. Wardle

Publisher: Courier Corporation

ISBN: 0486462722

Category: Mathematics

Page: 96

View: 7136

DOWNLOAD NOW »

Elementary account covers curvature and torsion, involutes and evolutes, curves on a surface, curvature of surfaces, and developable and ruled surfaces. Numerous problems include complete solutions. 1965 edition.

An Introduction to Differential Geometry

Author: T. J. Willmore

Publisher: Courier Corporation

ISBN: 0486282104

Category: Mathematics

Page: 336

View: 9858

DOWNLOAD NOW »

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.

A Treatise on the Differential Geometry of Curves and Surfaces

Author: Luther Pfahler Eisenhart

Publisher: Courier Corporation

ISBN: 0486159469

Category: Mathematics

Page: 496

View: 3743

DOWNLOAD NOW »

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.

Differential Geometry

Author: Heinrich W. Guggenheimer

Publisher: Courier Corporation

ISBN: 0486157202

Category: Mathematics

Page: 400

View: 1462

DOWNLOAD NOW »

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.

Lectures on Classical Differential Geometry

Second Edition

Author: Dirk J. Struik

Publisher: Courier Corporation

ISBN: 0486138186

Category: Mathematics

Page: 240

View: 7289

DOWNLOAD NOW »

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.

Differentialgeometrie

Kurven - Flächen - Mannigfaltigkeiten

Author: Wolfgang Kühnel

Publisher: Springer-Verlag

ISBN: 3834896551

Category: Mathematics

Page: 280

View: 9341

DOWNLOAD NOW »

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.

Differential Geometric Structures

Author: Walter A. Poor

Publisher: Courier Corporation

ISBN: 0486151913

Category: Mathematics

Page: 352

View: 8157

DOWNLOAD NOW »

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.

Thinking in Problems

How Mathematicians Find Creative Solutions

Author: Alexander A. Roytvarf

Publisher: Springer Science & Business Media

ISBN: 0817684069

Category: Mathematics

Page: 405

View: 2386

DOWNLOAD NOW »

This concise, self-contained textbook gives an in-depth look at problem-solving from a mathematician’s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to solving mathematical problems, and this book outlines the tools necessary to improve the reader’s technique. The text is divided into twelve chapters, each providing corresponding hints, explanations, and finalization of solutions for the problems in the given chapter. For the reader’s convenience, each exercise is marked with the required background level. This book implements a variety of strategies that can be used to solve mathematical problems in fields such as analysis, calculus, linear and multilinear algebra and combinatorics. It includes applications to mathematical physics, geometry, and other branches of mathematics. Also provided within the text are real-life problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a self-study guide. Prerequisites include linear algebra and analysis.

Differential Geometry

Author: Heinrich Walter Guggenheimer

Publisher: Dover Books on Mathematics

ISBN: 9780486634333

Category: Mathematics

Page: 378

View: 4443

DOWNLOAD NOW »

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.

Tensor and Vector Analysis

With Applications to Differential Geometry

Author: C. E. Springer

Publisher: Courier Corporation

ISBN: 048632091X

Category: Mathematics

Page: 256

View: 543

DOWNLOAD NOW »

Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.

Differential Forms with Applications to the Physical Sciences

Author: Harley Flanders

Publisher: Courier Corporation

ISBN: 0486139611

Category: Mathematics

Page: 240

View: 6888

DOWNLOAD NOW »

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.

Introduction to Differential Geometry for Engineers

Author: Brian F. Doolin,Clyde F. Martin

Publisher: Courier Corporation

ISBN: 0486281949

Category: Mathematics

Page: 176

View: 3208

DOWNLOAD NOW »

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.

Curvature in Mathematics and Physics

Author: Shlomo Sternberg

Publisher: Courier Corporation

ISBN: 0486292711

Category: Mathematics

Page: 416

View: 306

DOWNLOAD NOW »

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.