|
Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
|
Buy Now
A Treatise On The Differential Geometry Of Curves And Surfaces (1909) (Hardcover)
Loot Price: R1,434
Discovery Miles 14 340
|
|
|
A Treatise On The Differential Geometry Of Curves And Surfaces (1909) (Hardcover)
Expected to ship within 10 - 15 working days
|
A TREATISE ON THE DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES BY
IJTTHEU PFAIILKR EISENHAIIT PKOPKHHOIt OK MATUKMATKH IN 1 ltINCMTON
UNIVJCIWITY GOT AND COMPANY BOSTON NEW YOKE CHICAGO LONDON PREFACE
This book is a development from courses which I have given in
Princeton for a number of years. During this time I have come to
feel that more would be accomplished by my students if they had an
introductory treatise written in English and otherwise adapted to
the use of men beginning their graduate work. Chapter I is devoted
to the theory of twisted curves, the method in general being that
which is usually followed in discussions of this subject. But in
addition I have introduced the idea of moving axes, and have
derived the formulas pertaining thereto from the previously
obtained Freiiet-Serret fornmlas. In this way the student is made
familiar with a method which is similar to that used by Darboux in
the tirst volume of his Lepons, and to that of Cesaro in his
Gcomctria Ittiriiiseca. This method is not only of great advantage
in the treat ment of certain topics and in the solution of
problems, but it is valu able iu developing geometrical thinking.
The remainder of the book may be divided into threo parts. The
iirst, consisting of Chapters II-VI, deals with the geometry of a
sur face in the neighborhood of a point and the developments
therefrom, such as curves and systems of curves defined by
differential equa tions. To a large extent the method is that of
Gauss, by which the properties of a surface are derived from the
discussion of two qxiad ratie differential forms. However, little
or no space is given to the algebraic treatment of differential
forms and their invariants. In addition, the method of moving axes,
as defined in the first chapter, has been extended so as to be
applicable to an investigation of the properties of surf ac. es and
groups of surfaces. The extent of the theory concerning ordinary
points is so great that no attempt has been made to consider the
exceptional problems. Por a discussion of uch questions as the
existence of integrals of differential equa tions and boundary
conditions the reader must consult the treatises which deal
particularly with these subjects. lu Chapters VII and VIII the
theory previously developed is applied to several groups of
surfaces, such as the quadrics, ruled surfaces, minimal surfaces,
surfaces of constant total curvature, and surfaces with plane and
spherical lines of curvature iii iv PREFACE The idea of
applicability of surfaces is introduced in Chapter IIT as a
particular case of conformal representation, and throughout the
book attention is called to examples of applicable surfaces.
However, the general problems concerned with the applicability of
surfaces are discussed in Chapters IX and X, the latter of which
deals entirely with the recent method of Weingarten and its
developments. The remaining four chapters are devoted to a
discussion of infinitesimal deformation of surfaces, congruences of
straight Hues and of circles, and triply orthogonal systems of
surfaces. It will be noticed that the book contains many examples,
and the student will find that whereas certain of them are merely
direct applications of the formulas, others constitute extensions
of the theory which might properly be included as portions of a
more ex tensive treatise. At first I felt constrained to give such
references as would enable thereader to consult the journals and
treatises from which some of these problems were taken, but finally
it seemed best to furnish, no such key, only to remark that the
flncyklopadie der mathematisc7ien Wissensckaften may be of
assistance. And the same may be said about references to the
sources of the subject-matter of the book. Many important citations
have been made, but there has not been an attempt to give every
reference. However, I desire to acknowledge niy indebtedness to the
treatises of Uarboux, Biancln, and Scheffers...
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
You might also like..
|
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
