Forms Definition and 482 Threads

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

I have the solution to this particular problem, the problem is the person who solved it used a method that unfamiliar with. Does anyone know how to solve this problem using Binomial expansion. I know that the answer is e^k where K is some constant. this is the problem...

I'm having trouble recognizing when an expression produces an indeterminate form. for exampe what are the following: e^\infty \sqrt{\infty} more generally what is a^\infty 1^\infty

show that if a number n is represented by a quadratic form f of discriminant d then 4an is a square mod |d|. I have no clue how to even start this proof. I tried using the jacobi symbol.. but it's not gettin me anywhere. Could someone give me a hint.. :confused:

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...

what is the boiling point of water in a zero gravity environment? Is the freezing point of water different in a zero gravity environment than in a kitchen freezer on Earth?

I have a question that i have to do, the only problem is time. Since i have to finish my stats assignment, would anyone tell me the steps involved in solving this problem(in order), Rotate and translate the coordinate axes, as necessary to bring the conic section 3x^2 -8xy -12y^2 -30x-64y=0...

I am looking for a book/s (yes I know this is the wrong section, but it will probably get more replies here :-p ). I want a book/s that is a big overview of all the transit systems (US and Europe in particular) But I also want a huge emphasis on cars in the US. I do not want a book that was...

I need to compute the following thing trace ( (dg + g^g)^2) = d (tr (g ^ dg + 2/3 g ^ g ^ g)) im messing up completely b/c I don't know how to use trace with differential forms tr (dg + g^g) ^ (dg + g^g))

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...

Given two one forms f = (1,1,0,0,) and g=(-1,0,1,0): what are the components of f(x)g ... would appreciate any help.

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'm try to prove some trig identities and I need to know how to write the following functions in their exponential forms: sin^{-1}z cos^{-1}z sinh^{-1}z cosh^{-1}z I know how the sine and cosine functions are expressed with exponents, but I'm not sure how that would translate to the...

So I'm fiddling about with formulae...trying things out...consolidating...as you do...and something didn't work - why? The infinitesimal area element in polar coordinates dA = r*d(theta)*dr . Agreed? Now in the same coordinate system x = r \cos{\theta} ; y = r \sin{\theta} . Taking...

Hi. I have an assignment lying around, in which I have to find numerically stable forms of some expressions. A few still elude me, so I was wondering if someone might have a suggestion. e^{x}-e This has large rounding errors if x is close to 1 sinh (x) - tanh (x) Large...

The question speaks for itself, pretty much. The term artificial could be defined as: Constructed, as in a fine plate of spaghetti. Humans, well we all know what they are. Aliens, same deal. Life, that which...which, nevermind.

Questions related to the Topic Title of this Thread: STM Question: "Which factor should dominate Space-Time-Matter discussions?" Time Question: "Does time exist or is it a human construct?" Matter Question: "Should mass be used in place of matter?" My thoughts on the STM Question...

I will try my hardest not to fret off to any religious beliefs of God, mostly speak of ideas to how we approach God. In my eyes, there can be 3 types of Gods. a) Creator b) Manager c) Sustainer Most I presume at this forum believe in a (Creator), that a super natural being, (infinite...

If I cut a ball of mercury with a knife it forms into other balls why is this

http://tv.ksl.com/index.php?nid=5&sid=97513

Quantum (number) configurations, but not classical configurations, repeat within the limits of spacetime. Would you entertain such a definition? I believe it to be a fundamental concept hereto overlooked.

Can anyone suggest insight, or a course of study, that can improve understanding of twisted (or pseudo) forms. I have learned from reading Frankel and Burke, that half the forms used in physical theory are twisted, and though I've studied their chapters on the subject, my intuition is still...

We are about ¾ way through this “Hewitt” textbook in “Conceptual Physics”. Chapter 19 (Vibrations and Waves) explains that that there are two type waves shapes. These are transverse waves, and longitudinal waves. It seems to me that something either doesn’t add up, or is being left out. The...

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...

Can the universe be understood entirely through the mathematical formulations of physics or is it too much in a state of fluidity and flux for human words and math to give a comprehensive, clear, and holistic vision to humans? My apologies for such an awkward, clumsy sentence.

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...

Greetings ! Can anyone please explain to me, preferably with as little math and as much theory as possible , how matrices work in terms of forms and dimensions and what's the relevant mechanism ? I mean, I used to program Star Trek spaceships for a computer game I once made using...

don't want my words on PF

Do you think that they will ever contact us or vice versa? I can`t believe that with all the Trillions of planets there are there is not one planet with remotely the same conditions or atmosphere of earth?

When ever we find a new interaction that needs to be described we tend to model it on the most understood interaction, both theoretically and experimentally, namely Electrodynamics. But that has a hidden danger, and one element of that danger is differential forms. They are certainly very nifty...

What is your preferred way of remembering and writing down the Friedmann equations and in what form do you include dark energy in them? Heres the way that seems best to me. It is a balance between making them uncluttered but not so simplified as to lose intelligibility. For one bit of...