, Michael Spivak
Brandeis University
Calculus on Manifo
A MODERN APPROACH TO CLASSICAL THE
OF ADVANCED CALCULUS
, Calculus on Manifolds
A Modem Approach to Classical Theorems of Advanc
Copyright© 1965 by Addison-Wesley Publishing
All rights reserved
Library of Congress Card Catalog Number 66-1
Manufactured in the United States of Ameri
The manuscript was put into production on April 2
this volume was published on October 26, 19
ISBN 0-8053-9021-9
24 25 26 27 28-CRW-9998979695
Twenty-fourth printing, January 1995
, Editors' Foreword
Mathematics has been expanding i n all directions a
rate during the past half century. New fields hav
the diffusion into other disciplines has proceeded
our knowledge of the classical areas has grown eve
found . At the same time, one of the most strikin
modern mathematics is the constantly increasing in
ship between its various branches. Thus the p
students of mathematics are faced with an immens
of material. In addition to the traditional areas
matics as presented in the traditional manner-
Brandeis University
Calculus on Manifo
A MODERN APPROACH TO CLASSICAL THE
OF ADVANCED CALCULUS
, Calculus on Manifolds
A Modem Approach to Classical Theorems of Advanc
Copyright© 1965 by Addison-Wesley Publishing
All rights reserved
Library of Congress Card Catalog Number 66-1
Manufactured in the United States of Ameri
The manuscript was put into production on April 2
this volume was published on October 26, 19
ISBN 0-8053-9021-9
24 25 26 27 28-CRW-9998979695
Twenty-fourth printing, January 1995
, Editors' Foreword
Mathematics has been expanding i n all directions a
rate during the past half century. New fields hav
the diffusion into other disciplines has proceeded
our knowledge of the classical areas has grown eve
found . At the same time, one of the most strikin
modern mathematics is the constantly increasing in
ship between its various branches. Thus the p
students of mathematics are faced with an immens
of material. In addition to the traditional areas
matics as presented in the traditional manner-
