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Lectures on Classical Differential G 2ND Edition

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Lectures on Classical Differential G 2ND Edition Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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.

Synopsis:

Excellent brief introduction covers curves, theory of surfaces, fundamental equations, geometry on a surface, conformal mapping, other topics. Problems.

Synopsis:

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, geometry on a surface, envelopes, conformal mapping, minimal surfaces, more. Well-illustrated, with abundant pro

Table of Contents

PREFACE

BIBLIOGRAPHY

CHAPTER 1. CURVES

  1-1 Analytic representation

  1-2 "Arc length, tangent "

  1-3 Osculating plane

  1-4 Curvature

  1-5 Torsion

  1-6 Formulas of Frenet

  1-7 Contact

  1-8 Natural equations

  1-9 Helices

  1-10 General solution of the natural equations

  1-11 Evolutes and involutes

  1-12 Imaginary curves

  1-13 Ovals

  1-14 Monge

CHAPTER 2. ELEMENTARY THEORY OF SURFACES

  2-1 Analytical representation

  2-2 First fundamental form

  2-3 "Normal, tangent plane"

  2-4 Developable surfaces

  2-5 Second fundamental form

  2-6 Euler's theorem

  2-7 Dupin's indicatrix

  2-8 Some surfaces

  2-9 A geometrical interpretation of asymptotic and curvature lines

  2-10 Conjugate directions

  2-11 Triply orthogonal systems of surfaces

CHAPTER 3. THE FUNDAMENTAL EQUATIONS

  3-1 Gauss

  3-2 The equations of Gauss-Weingarten

  3-3 The theorem of Gauss and the equations of Codazzi

  3-4 Curvilinear coordinates in space

  3-5 Some applications of the Gauss and the Codazzi equations

  3-6 The fundamental theorem of surface theory

CHAPTER 4. GEOMETRY ON A SURFACE.

  4-1 Geodesic (tangential) curvature

  4-2 Geodesics

  4-3 Geodesic coordinates

  4-4 Geodesics as extremals of a variational problem

  4-5 Surfaces of constant curvature

  4-6 Rotation surfaces of constant curvature

  4-7 Non-Euclidean geometry

  4-8 The Gauss-Bonnet theorem

CHAPTER 5. SOME SPECIAL SUBJECTS

  5-1 Envelopes

  5-2 Conformal mapping

  5-3 Isometric and geodesic mapping

  5-4 Minimal surfaces

  5-5 Ruled surfaces

  5-6 lmaginaries in surface theory

SOME PROBLEMS AND PROPOSITIONS

APPENDIX: The method of Pfaffians in the theory of curves and surfaces

ANSWERS TO PROBLEMS

INDEX

Product Details

ISBN:
9780486656090
Author:
Struik, Dirk Jan
Publisher:
Dover Publications
Author:
Struik, Dirk Jan
Author:
Struik, Dirk J.
Author:
Mathematics
Location:
New York :
Subject:
Mathematics
Subject:
Geometry - General
Subject:
Geometry
Subject:
Geometry - Differential
Subject:
General Mathematics
Subject:
Mathematics-Differential Geometry
Copyright:
Edition Number:
2
Edition Description:
Second Edition
Series:
Dover Books on Mathematics
Publication Date:
19880431
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
240
Dimensions:
8.5 x 5.38 in 0.59 lb

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Related Subjects

Science and Mathematics » Mathematics » Differential Geometry
Young Adult » General

Lectures on Classical Differential G 2ND Edition New Trade Paper
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Product details 240 pages Dover Publications - English 9780486656090 Reviews:
"Synopsis" by ,
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.
"Synopsis" by , Excellent brief introduction covers curves, theory of surfaces, fundamental equations, geometry on a surface, conformal mapping, other topics. Problems.

"Synopsis" by , 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, geometry on a surface, envelopes, conformal mapping, minimal surfaces, more. Well-illustrated, with abundant pro
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