## Analysis On ManifoldsA 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 |

### Other editions - View all

### Common terms and phrases

alternating tensors arbitrary basis belonging calculus called change of variables column compact rectifiable compute contained continuous function coordinate patch corresponding cover cube define the integral definition denote Df(a Df(x diffeomorphism equals equation example EXERCISES extended integral f and g f exists f is continuous f is integrable Figure finite follows formula Fubini theorem function f given Hint implies induced orientation interval inverse function k-form k-tensor k-tuple lemma Let f Let g Let Q linear transformation manifold matrix measure zero metric space neighborhood non-singular notation one-to-one open set operator ordinary integral orthogonal orthonormal partial derivatives partition of unity permutation Proof properties prove the theorem rank rectangle Q rectifiable sets scalar fields sequence ſº ſo f Step subset subspace Suppose tangent vector vanishes variables theorem vector field vector space

### Popular passages

Page 13 - A necessary and sufficient condition for A to be invertible is that A be square and of maximal rank.

### References to this book

A Course in Metric Geometry Dmitri Burago,I͡Uriĭ Dmitrievich Burago,Sergeĭ Ivanov No preview available - 2001 |