Analysis On Manifolds (Google eBook)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  LibraryThingThis 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  LibraryThingI 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
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 
Common terms and phrases
alternating tensors arbitrary basis belonging calculus called chain rule change of variables choose class Cr closed column compact rectifiable compute consider contained continuous function coordinate patch corresponding cover cube define the integral definition denote diffeomorphism entries equals equation euclidean EXAMPLE EXERCISES extended integral fact fcform fcmanifold fctensor fctuple Figure finite follows formula Fubini theorem function g given holds implies induced orientation inner product interval inverse function Jlnt lemma let f Let g Let Q linear transformation manifold matrix measure zero metric space neighborhood nonnegative nonsingular notation onetoone open set operator ordinary integral orthogonal orthonormal partial derivatives partition of unity permutation preceding theorem Proof properties prove the theorem rank rectangle Q rectifiable sets satisfies scalar fields sequence Step subset subspace Suppose tangent vector TP(M unit normal vanishes variables theorem vector field vector space
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 HeineBorel, 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 fourclass twostation multiclass queueing network (known as KumarSeidman 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 nonempty 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.