Recent content by Bachman

The book has been published! Just a quick note to officially announce the release of my book, "A Geometric Approach to Differential Forms." It has been published by Birkhauser, and is available via their webisite, Amazon.com, Barnes & Noble, etc. I have done what I can to keep the purchase...

Dear all, I have been going through my book agaiin with my current students and we have found a few errors. I'll post them: Exercise 1.6 (4) The coefficient should be \frac{2}{5} instead of \frac{5}{2} Exercise 3.21 ... then V_{\omega}=\langle F_x, F_y, F_z \rangle . Exercise 4.8...

Melinda, You can also see that in dimensions bigger than three you will not always be able to factor 2-forms by just writing one down. If there are at least four coordinates then consider the following 2-form: \omega=dx_1 \wedge dx_2 + dx_3 \wedge dx_4 Now, if this 2-form could be...

Hi all, Sorry I have been silent for a few days. Busy, busy busy... And even now I do not have time to give proper responses, but here are a quick few... Mathwonck, please read a bit more carefully if you are going to take on a role as "proofreader": To your comment about integrating...

Because the \omega-\nu plane is two-dimensional, and cross products are only defined for three-dimensional vectors. Dave.

Yes, yes. Technically, an n-form on a vector space M is a multi-linear, alternating operator on the cartesian product of n copies of M. Dave.

The equation on page 45 is supposed to motivate the study of n-forms. The integrand there is not an n-form. But it IS a function that takes two vectors and returns a real number. The point illustrated there is that you need such a function if your answer is going to be independent of the choice...

I make a distinction in my book between "1-form" and "differential 1-form." A 1-form is, indeed, a linear functional. It acts on a single tangent space. So, choosing a specific point p, a 1-form is a linear functional on T _p \mathbb R^n . A "differential 1-form", on the other hand, is a...

Tom, I'm still not sure where the confusion lies. The tangent space to C is a line, denoted as T_pC . At the bottom of page 18 I say "We are no longer thinking of this tangent line (i.e. the space T_pC ) as lying in the same plane that the graph does. Rather, it lies in \mathbb T...

Oh yes, of course. Thank you. What I meant to say was "The tangent space to \mathbb R^2 at the point p is a plane, with AXES dx and dy ."

A few quick replies... First, I do recommend switching to the most current edition, if only because there are more (and better) exercises. If you are really considering the text for Calc IV then the first chapter of the most current edition should definitely be covered, if only as a review...

Hello all, My name is Dave Bachman. Tom, thanks so much for inviting me to join your thread, and for looking at my book! The version that is up on the arXiv is a little old. A more current one is available on my web page at: http://pzacad.pitzer.edu/~dbachman The idea of the text is...