Table of Contents
1.0 Euclidean spaces, tangent spaces, and tangent vector fields
1.1 The algebra of differential forms
1.3 The fundamental correspondence
1.4 The Converse of Poincaré’s Lemma, I
2.3 Orientation and signed volume
2.4 The converse of Poincaré’s Lemma, II
3: Push-forwards and Pull-backs in
3.2 Points, tangent vectors, and push-forwards
3.3 Differential forms and pull-backs
3.4 Pull-backs, products, and exterior derivatives
3.5 Smooth homotopies and the Converse of Poincaré’s Lemma, III
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