Forms Definition and 448 Threads

I just discovered this forum: very very nice! And here's my first question: An exterior p-form is a multilinear antisymmetric map from p copies of a vector space (in particular, a tangent space located at some point P of a manifold) to the reals. Now what could it mean to have an integral of a...

Find a solution to the equation if possible. Give the answer in exact form and in decimal form. 1 = 8cos(2x + 1) - 3 1 = 8tan(2x + 1) - 3 I don't know how to do this one.. but I know how to do the simpler ones like.. 2 = 5sin(3x) 2/5 = sin(3x) (sin-1(2/5)) / 3 = 0.137172 Those...

Rotating water forms a parabola - why?? I've done some experiments involving rotating a beaker of water, and then measuring the height of the parabola that forms. I am now trying to explain this in my write up, but there are some things that I am simply not understanding, and any help would be...

Why is 1^\infty an indeterminate form? If you keep multiplying 1 by itself doesn't the answer stay 1?

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?

What would be an experiment i could prefrom to show how different forms of energy are converted into electrical impulses?? Simple ones Thanks Nath

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...

Do concentrated forms of light, such as a laser, have mass?

A while back in maths we were introduced to the linear equation in two forms: a x + b y = c (1) y = m x + c (2) Now I can use both forms of these, but I was told that: y = m x + c \Leftrightarrow a x + b y = c where m = \frac{a}{b} Thiis can't be right can it? As: a x + b y = c b...

Whats isoamyl? Hi i have a quick question I'm supposed to show how isoamyl propanoate is fromed. I know that this is esterification and that one of the reactants is propanoic acid but i don't know what the alcohol isoamyl is? I tried searching on google and all i get is test questions:mad: Plz help

I'm new to quantum mechanics, i.e. the type of QM you don't learn through books by Brian Greene :biggrin: . I know there aren't any derivations for an operator associated with an observable and they are usually defined in a certain form. So why do they have those particular forms. Was it trial...

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...

They have been around for some time now, but where did the idea of little green men come from, or the big eyed hairless Ivan type, how many different alien forms are there ?

Calcium is essential in the prevention of bone loss. This is particularly important for women who are approaching menopause as they're susceptible to osteoporosis. I'm not sure what age women should begin incorporating more calcium into their diet but I do know that they need more after...

I need to come up with female replacements for the following male words. For instance, as she replaces he and Queen replaces King. man son prince lord my lord your lordship The replacements should have the same general meaning, but it doesn't need to be exact. The problem is that the...

I am working a problem: Find the polar form of the equation 6x^2 + 3xy + 6y^2 = -3 I have run this 4 separate times and have come up with 4 different answers. PLEASE HELP! r^2= 6 over -6 - 3sin(theta)cos(theta) r^2=-3 over 6 - 3sin(theta)cos(theta) r^2=9 over 6 +...

let f:U \rightarrow R^n be a differentiable function with a differentiable inverse f^{-1}: f(u) \rightarrow R^n . if every closed form on U is exact, show that the same is true for f(U). Hint: if dw=0 and f^{\star}w = d\eta, consider (f^{-1})^{\star}\eta...

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?

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 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...

[FONT=Arial]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...

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...