Analysis On Manifolds (Google eBook)

Front Cover
Westview Press, Jul 7, 1997 - Science - 380 pages
4 Reviews

A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.

  

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LibraryThing Review

User Review  - raydulany - LibraryThing

This book does an excellent job covering its subject matter in great detail. Munkres does not fudge on a single proof; there are no carelessly thrown about phrases that rely on the reader possessing a ... Read full review

LibraryThing Review

User Review  - rwturner - LibraryThing

I wasn't very happy with this book. It turned out to not be very useful for the class I bought it for because it focuses on Euclidean space, and we were interested in normed vector spaces in general. It's drier than necessary and I thought the proofs were very tedious. Read full review

Contents

I
1
II
11
III
25
IV
32
V
41
VI
49
VII
56
VIII
63
XXV
196
XXVI
203
XXVII
209
XXVIII
219
XXIX
220
XXX
226
XXXI
236
XXXII
244

IX
71
X
81
XII
91
XIII
98
XIV
104
XV
121
XVI
135
XVII
136
XVIII
144
XIX
152
XX
161
XXI
169
XXII
179
XXIII
180
XXIV
188
XXXIII
252
XXXIV
262
XXXV
267
XXXVI
275
XXXVIII
281
XXXIX
293
XL
297
XLI
301
XLII
310
XLIII
323
XLV
324
XLVI
334
XLVII
345
Copyright

Common terms and phrases

Popular passages

Page 32 - A subset of Rn is compact if and only if it is closed and bounded. This is known as the lemma of Heine-Borel, or, in terms of limit points, as the Bolzano- Weierstrass theorem.
Page 39 - R", then the line segment joining a and b is defined to be the set of all points x of the form x = a + f(b - a), where 0 < t < 1.
Page 91 - In this paper, we derive a necessary and sufficient condition for the existence of the diffusion approximation for a four-class two-station multiclass queueing network (known as Kumar-Seidman network) under a priority service discipline.
Page 90 - R be defined by setting f(x) => 1/f if * as p/q, where p and q are positive integers with no common factor, and f(x) = 0 otherwise.
Page 86 - R : (a) f(x) = 0 if x is rational and f(x) = 1 if x is irrational.
Page 13 - A necessary and sufficient condition for A to be invertible is that A be square and of maximal rank.
Page 38 - X is said to be connected if X cannot be written as the union of two disjoint non-empty sets A and B, each of which is open in X.
Page 91 - Show that a metric space (X,d) is separable if and only if for every e > 0 there is a countable set CE so that every point in the space is closer than e to some point in CE.
Page 32 - The space X is said to be compact if every open covering of X contains a finite subcollection that also forms an open covering of X.
Page 26 - A subset U of X is said to be open in X if for each x0 0" there is a corresponding c > 0 such that U (X0", e) is contained in U.

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