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# Differential Forms: A Complement to Vector Calculus by Weintraub

Differential Forms: A Complement to Vector Calculus by Steven H. Weintraub.

The book was used for Introduction to differential forms: course.

The proofs of some theorems are too long if weighted against their importance.

The discussion of orientation of manifolds is too informal. The last, "advanced" chapter makes up for that somewhat.

No non-trivial exercises (proofs etc). Straightforward computations only.

No discrete differential forms, unfortunately.

## Contents

Preface

II Oriented manifolds

The notion of a manifold (with boundary)

III Differential forms revisited

k-forms

IV Integration of differential forms over oriented manifolds

The integral of a 0-form over a point (evaluation)

The integral of a 1-form over a curve (line integrals)

The integral of a 2-form over a surface (flux integrals)

The integral of a 3-form over a solid body (volume integrals)

Integration via pull-backs

V The generalized Stokes's Theorem

Statement of the theorem

The fundamental theorem of calculus and its analog for line integrals

Green's and Stokes's theorems

Proof of the GST

Differential forms in $R^n$ and Poincare's lemma