Differential forms Definition and 137 Threads

On page 7 it gives two conditions for a linear function on the space of p-vectors built from a linear function on the underlying L space. I do not understand! Does anybody ? Then it continues by saying that the two properties are an axiomatic characterization on the space of p-vectors. So, if...

Homework Statement Let x_1,...,x_n: M \rightarrow R be functions on a manifold which form a local coordinate system on some region. Show that every differential form on this region can be written uniquely in the form w^k = \sum_{i_1<...<i_k} a_{i_1,...i_k}(\bf{x})dx_{1_i} \wedge .. \wedge...

Introduction to smooth manifolds, by John Lee, page 304. The right-hand side of (c) near the top of the page has a factor \omega_I\circ F. I've been doing the calculation over and over for hours now and I keep getting just \omega_I. Is that F supposed to be there? Edit: I should add that...

Homework Statement Hi all I can find a differential form defined on R2\{0,0}, which is closed but not exact, but is it possible to find a differential form defined on all R2, which is closed but not exact?

Which book/books are a good intro into manifolds? Maybe a book that is both oriented towards a physicist but also includes rigor. How is this book An Introduction to Manifolds by Loring W. Tu In the preface it says one year of real analysis and a semester of abstract algebra would suffice as a...

I'm just wondering: in what field of mathematics are differential forms frequently used by professional mathematicians?

What is the benefit of expressing Maxwell's equation in the language of differential forms? Differential forms seem to be inferior to the language of tensors. Sure you can do fancy things with the exterior derivative and hodge star, but with tensors you can derive those same identities with...

I need a book like Schaum's Outline of Differential Forms (which doesn't exist). One that sets out a few ideas, then beats them into your thick skull with a TONS of exercises and provides fully worked out solutions. Does anyone know of such a book?

Hello, I have a question related to the calculation of curvature using exterior differential forms (Misner, pp. 354-363). In all the examples given in the book (i.e. Friedmann, Schwarzschild, pulsating star metrics), the "guess and check" method used to find the connection forms (Eq. (14.31))...

Recently I discovered geometric algebra which looks very exciting. I was wondering if there is any connection between geometric algebra and differential forms? I see that different research groups recommend the use of differential forms (http://www.ee.byu.edu/forms/forms-home.html" ), and...

(i) if \alpha=\sum_i \alpha_i(x) dx_i \in \Omega^1, \beta=\sum_j \beta_j(x) dx_j then\alpha \wedge \beta = \sum_{i,j} \alpha_i(x) \beta_j(x) dx_i \wdge dx_j \in \Omega^2 NOW THE STEP I DON'T FOLLOW - he jumps to this in the lecture notes: \alpha \wedge \beta = \sum_{i<j} (\alpha_i...

Homework Statement Calculate the contravariant components of the differential 1-form \omega|_x = x^3 dx^1 - (x^2)^2 dx^3 that is raise it into \omega ^\#|_x \eta ^{\mu\nu}(x)=diag(1,-1,-1,-1) The Attempt at a Solution I'm at lost here. I don't really understand how these...

Hi, I'm trying to solve a problem in David Bachman's Geometric Approach to Differential Forms (teaching myself.) The problem is to integrate the scalar function f(x,y,z) = z^2 over the top half of the unit sphere centered at the origin, parameterized by \phi(r,\theta) = (rcos\theta, rsin\theta...

(Ok, post edited. It should be ready for reading.) I'm attending an electrodynamics course and the notation is in differential forms. The course material, however, is not yet finished so it's very coarse. We're supposed to have an introduction to differential forms as the course proceeds, but...

I've just begun investigating differential forms. I have no experience in this field and no formal, university level training in mathematics, so please bear with me. I understand that a differential form may be thought of as a family of linear functionals; more precisely, it is a function that...

My differential forms book (Flanders/Dover) defines an inner product on wedge products for vectors that have a defined inner product, and uses that to define the hodge dual. That wedge inner product definition was a determinant of inner products. I don't actually have that book on me right...

I have a quetion about the forms. When we say, "differential forms of degree one (or more)" rather than degree zero, the algebra is now mixed with topological properties. Am I correct? I am simply trying to find my way to understand this.

Would this be the right forum to pose questions on this topic?

Hello everyone, I'm new to this forum. I have a doubt about differential forms, related to the divergence. On a website I read this: "In general, it is true that in R^3 the operation of d on a differential 0-form gives the gradient of that differential 0-form, that on a differential 1-form...

I'm practicing some differential forms stuff and got a bit stuck on something. I'd type it out but the action is very long so it's easier if I just link to where I'm getting it from, this paper http://gesalerico.ft.uam.es/tesis/pablo_camara.pdf Equation (4.20) (pdf page 51) is the IIA action...

First off, I'm no geometer. I've jumped from looking into QFT from an operator algebra perspective to one looking at it from a differential geometry perspective. It's been a fairly nice ride...modulo the fact that I know very little differential geometry. Thus I have been going through a bit of...

Hi, I'm seeing that many authors like Griffiths and Halliday/Resnick (I've not seen Jackson and Landau/Lif****z) are deriving the differential form of Gauss's law from the integral form (which is easily proven) by using the divergence theorem to convert both sides to volume integrals and then...

Hi, I don't know if this is the right place to post, but can someone help me understand what differential forms are intuitively? And the wedge product intuitively? And finally, how can they help see the bigger picture of multiple integrals, curls, divergence, gradient, etc. I don't know that...

I am reading some books about differential forms. I don't quite understand what is the geometrical meaning of star (hodge) operator. Can anyone give me a hand please? Leon

Hello, I'm interested in starting differential forms, Is this book any good? What audience is it intended for? What prerequisites (E.G. Linear Algebra, Calculus(At what level), etc.) would one need to fully appreciate the scope and depth of information presented in this book? Thanks for...

Has anyone ever read or used this book http://www.chapters.indigo.ca/books/item/books-978048665840/0486658406/Tensors+Differential+Forms+And+Variational+Principles?ref=Search+Books%3a+'Tensor+Differential+Forms' Is it any good?

I decided earlier this week that I was going to compute by hand the genus of an elliptic curve. I've had a miserable (but enlightening!) time! I eventually stumbled upon the trick in Shafaravich: I should be looking at the rational differential forms, and counting zeroes & poles of things...

Recently, I've begun to study the Geometric Algebra approach to differential geometry (Hestenes[84]) and although I do not claim to be an expert in this area (not at all!) I'm really starting to like what I see. It seems a major problem with the differential forms approach is that it...

Who has any litterature about non-linear differential forms, especially for example if I would like to compute the following : (dx\wedge dy)(dx\wedge dy\wedge dz) is it equal to (dx)^2\wedge (dy)^2\wedge dz ?? Thanks in advance.

What are differential forms? Is this what I'm going to learn about in my upcoming differential geometry class?

The language of differential forms is creeping into the textbooks on nonlinear continuum mechanics, replacing traditional vector mechanics. I've been struggling to come to terms with this. There's a thread in the 'Tensor Analysis and D.G' forum, where the contributors are mainly physicists...

Hello folks, I found a lovely little book online called A Geometric Approach to Differential Forms by David Bachman on the LANL arXiv. I've always wanted to learn this subject, and so I did something that would force me to: I've agreed to advise 2 students as they study it in preparation...

I'm just learning about differential forms and I've noticed something in my homework assignment. We have to evaluate zdx + xdy + ydz, over directed line segments in R-three by the method of pullback. Let a, b, and c be vectors in R-three. I noticed that Integral from a to c does NOT equal...

Is there any book in exterior algebra and differential forms which has problems worked out..ie solutions manual which comes along with the book?

I was reading lethe's thread on differential forms and suddenly it dawned on me that I had no idea what differential forms were for, or why the process was developed. Do they replace vector calculus, or are they a more powerful form of linear algebra or what? For me it is much easier to study...

I like the Geometric Algebra approach to incorporating differential forms into physics that is taken by Dr. David Hestenes and contained in his numerous works over the last few decades but see no mention of Geometric Calculus here. Are you familiar with it...

don't want my words on PF