Differential forms - Reference request

[Joppy]

Hi.

Can anyone recommend a text introducing differential forms along with all the necessary pre-requisites for understanding them? For example, I'm not really familiar with tensor calculus but would like to shortcut studying it completely separately to learning differential forms. If that's too much of a stretch, two books is ok too :).

Thanks.

 

[S.G. Janssens]

Would Spivak's Calculus On Manifolds be something along those lines?

 

[Joppy]

Would Spivak's Calculus On Manifolds be something along those lines?

So many nice pictures! Thanks a lot for the recommendation :).

 

[steenis]

Books on differential forms, these six book are easy introductions:
Bachman - A Geometric Approach to Differential Forms (2nd edition, 2012)
Bressoud - Second Year Calculus; From Celestial Mechanics to Special Relativity (1991)
Do Carmo - Differential Forms and Applications (1994)
Edwards - Advanced Calculus; A Differential Forms Approach (1994)
Hubbard - Vector Calculus, Linear Algebra and Differential Forms (1998)
Weintraub - Differential Forms; Theory and Practice (2nd edition, 2014)

These books are more difficult:
Bott - Differential Forms in Algebraic Topology (1982)
Cartan - Differential Forms (1970)
Dray - Differential Forms and the Geometry of General Relativity (2015)
Flanders - Differential Forms with Applications to the Physical Sciences (Dover edition, 1989)
Lovelock - Tensors, Differential Forms, and Variational Principles (1975,1989)
Suhubi - Exterior analysis; using applications of differential forms (2013)

 

[steenis]

Guillemin - Theory of Differential Forms (2014)

This is a free book, you can download it here:

18.952

 

[Joppy]

Books on differential forms, these six book are easy introductions:
Bachman - A Geometric Approach to Differential Forms (2nd edition, 2012)
Bressoud - Second Year Calculus; From Celestial Mechanics to Special Relativity (1991)
Do Carmo - Differential Forms and Applications (1994)
Edwards - Advanced Calculus; A Differential Forms Approach (1994)
Hubbard - Vector Calculus, Linear Algebra and Differential Forms (1998)
Weintraub - Differential Forms; Theory and Practice (2nd edition, 2014)

These books are more difficult:
Bott - Differential Forms in Algebraic Topology (1982)
Cartan - Differential Forms (1970)
Dray - Differential Forms and the Geometry of General Relativity (2015)
Flanders - Differential Forms with Applications to the Physical Sciences (Dover edition, 1989)
Lovelock - Tensors, Differential Forms, and Variational Principles (1975,1989)
Suhubi - Exterior analysis; using applications of differential forms (2013)

An extensive list! This will keep me busy for a while.