## Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus (Google eBook)This little book is especially concerned with those portions of OCOadvanced calculusOCO in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approa" |

### What people are saying - Write a review

#### Review: Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus

User Review - Brandon Meredith - GoodreadsWhat yo mamma never told you you could do with calculus! Read full review

#### Review: Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus

User Review - Brian - GoodreadsI just read this again because another book was obfuscating exterior calculus for me, where it had formerly been clear. It's Spivak's usual clear (and very brief style) which I love. Stokes' Theorem in half a page! Read full review

### Contents

1 | |

Differentiation | 15 |

Integration | 46 |

Integration on Chains | 75 |

Integration on Manifolds | 109 |

Bibliography | 139 |

### Common terms and phrases

A C R Ak(V basis boundary bounded function calculus called chain rule Chapter classical theorems closed rectangle closed set compact set consider continuously differentiable coordinate system define F defined by f(x,y definition denoted Df(a Dif(a Dif(x,y differentiable function div F Divergence Theorem dz A dx equation fc-cube fc-dimensional manifold fc-form fc-tensor Figure finite number Fubini's theorem function g G Rn Hence Hint induced orientation inner product integrable interior intersects Jordan-measurable l)-form least upper bound Lemma linear transformation manifold-with-boundary mathematics matrix measure Michael Spivak ms(f n-chain non-zero open cover open interval open rectangle open set containing orientation-preserving partial derivatives partition of unity Problem prove reader Rm is differentiable satisfies singular n-cubes sional manifold Stokes subrectangle subset suffices Suppose Theorem 2-2 theorem is true unique usual orientation vector field vector space volume element

### References to this book

A Course in Metric Geometry Dmitri Burago,I︠U︡riĭ Dmitrievich Burago,Sergeĭ Ivanov Limited preview - 2001 |

Opérateurs pseudo-différentiels et théorème de Nash-Moser Serge Alinhac,Patrick Gérard No preview available - 1991 |