
| foreword acknowledgments chapter ⅰ differential calculus 1. categories 2. finite dimensional vector spaces 3. derivatives and composition of maps 4. integration and taylor's formula 5. the inverse mapping theorem chapter ⅱ manifolds 1. atlases, charts, morphisms 2. submanifolds, immersions, submersions 3. partitions of unity 4. manifolds with boundary chapter ⅲ vector bundles 1. definition, pull backs |
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