Forms Definition and 482 Threads

I've been trying to create a program that takes a user supplied indefinite integral and integrates it using the methods I have been learning in my calculus class; substitution, integration by parts, trig substitution, partial fractions, elementary anti-derivatives, etc. I've been trying to use...

Homework Statement Construct the analytic mapping \phi(x,y) for the H^{2+} \times S^1 representation of SL(2;R) Homework Equations g(x) \circ g(y) = g(\phi(x,y)) The Attempt at a Solution So, all points in SL(2;R) lie on the manifold H^{2+} \times S^1. I also know that SL(2;R) is...

As in the title , I recently somehow want to learn differential form , but ,actually , I do not really know where I should start , or what books I should read .. So,can anyone recommend some useful books ?

As 'unnati D' stated, in the now locked thread, "i believe the concept of a separate life force, existing without d support of an atomic body is worth exploring." This caught my interest, and even if his views may seem misguided and somewhat chaotic, there is an interesting concept worth...

Benzene forms the electron shell configuration of two rings of electrons, parallel to the molecule, shown here http://upload.wikimedia.org/wikipedia/commons/thumb/9/90/Benzene_Orbitals.svg/750px-Benzene_Orbitals.svg.png so my question is, if an electron beam is run through the center of the...

Homework Statement http://d.imagehost.org/view/0659/Capture Link to wolfram alfa:http://www.wolframalpha.com/input/?i=integrate%28cos%28e^x%29*e^x What i don't understand is why whey do it like this and why i can't integrate by parts in this case? Thanks for any replies!

Hi, I'm trying to understand the use of Maurer-Cartan one-forms in physics. As far as I understand it's a Lie-algebra valued one-form which sends vectors at an arbitrary point g on the Lie-group to the identity e (the Lie algebra). But my question is: what is the use of these things in...

Can general relativity be constructed with differential forms?

Hey, A quick question. In the definition of a differential form, we normally require that they be sections of the k-th exterior power of the cotangent bundle. However, on page 14 of Jurdjevic's book on...

Homework Statement How many equivalence classes under congruence (as in two quadratic forms - n dimensional vector space over field - being congruent if one can be obtained from the other by a change of coordinates) are there when (i) n=4 and field is complex numbers (ii) n=3 and field is real...

Hello, I am interested to know how many readers think that we will find life in our solar system, if so when?. I am confident that we will find basic life forms in a human lifetime. also if anyone thinks that there is more that one intelligent civilisation in our galaxy other than our own...

Homework Statement Give the two common forms of the mathematical equation for slope (involving X & Y)? Homework Equations ? The Attempt at a Solution Can you guys please give me the two common forms of the mathematical equation for slope? I don't know what it is but I am guessing...

Tensor densities are normally defined in terms of coordinate transformations. Could they also be defined as functions of p tangent vectors and q cotangent vectors, just as tensors are defined, except relaxing the condition of linearity? Can anyone suggest a good, basic introduction to...

Given an observable realization (A,b,c). Determine in terms of the matrices A,b, and c the similarity transfrom T, that brings the this system to the observability canonical form. Can this be done if (A,b,c) is not observable too? I don't know where to start. I am thinking pick...

limit proofs(indeterminate forms??) Homework Statement We work in the real numbers. Are the following true or false? Give a proof or counterexample. (a) If \sum a^4_n converges, then \sum a^5_n converges. (b) If \sum a^5_n converges, then \sum a^6_n converges. (c) If a_n \geq 0 for all...

IINW, temperature is a measure of the translational velocity of particles. Differences in temperature will cause energy flow, in the form we call 'heat'. I have a few questions: 1. Why don't we have a measure for rotational & vibrational energies? Why just translational? 2. Will heat...

Homework Statement Well, I've made a double limit using the polar forms. The thing is the limit is wrong, I've made a plot, and then I saw that the limit doesn't exist, and what I want to know is what I'm reasoning wrong, and some tips to get a deeper comprehension on this limits, and on what I...

In trying to understand connection one-forms, I have to learn what a Lie-algebra valued form is. I already understand what a vector-valued form is. I also understand why \nabla (e) = e \otimes \omega where \omega is a one-form, \nabla is an affine connection /covariant...

Hi I'm just wondering how other life forms on different planets might be able to evolve. Some of my thoughts: 1) other life forms don't necessarily need oxygen do they? On this planet we use oxygen to generate energy through combustion. Other life forms could generate energy by i)...

Let R be a commutative semiring. That is a triple (R,+,.) such that (R,+) is a commutative monoid and (R,.) is a commutative semigroup. Let {\mathbf \alpha}_i = \alpha_1,\alpha_2,\ldots,\alpha_n . The n-variate indeterminate is just free monoid on n letters. However, it is common to...

Most places I've read say it's because the car forms a Faraday cage, but a few say that is incorrect and that it's actually from the skin effect. The notable case of the latter explanation is from the Boston Museum of Science: http://www.mos.org/sln/toe/cage.html This guy, Dr. Davis from the...

Hi, I had a silly idea that probably doesn't work, but I thought I'd ask about it anyway. I understand that vectors can be thought of as derivative operators, e.g. \frac{d}{d\lambda} = \frac{dx^\mu}{d\lambda} \partial_\mu, where lambda parametrizes some curve. I also gather that one-forms...

So I am looking for a program that can compile language similar to Latex, metlab, etc. I have tried the latex website, but there are many things to install and download and I am hoping there is something that doesn't require installing 4 different programs to get a compiler... Any help is...

How can I found out in which p-adic fields a quadratic form represent 0? For example in which p-adic fields does the form 3x2+7y2-15z2 represent zero?

Hi I'm not a philosophy student, so please keep your reply simple. I was reading Wikipedia article on Renaissance where I wasn't able to understand some of the statements. Q1: Renaissance philosophy was the period of the history of philosophy in Europe that falls roughly between the...

Not so much a homework problem as a curiosity on my part. I chose to give a presentation recently on undefined numbers. With that, indeterminate's unsurprisingly found their way into my presentation. After reading up on the list of indeterminate forms, I stumbled upon the form 0^\infty and...

I am having a hard time understanding the theory that a collapsed hypergiant forms a gamma ray pulsating black hole. Can someone explain how the em radiation can travel so fast with such energy as to not only escape the event horizon but also do so with such intensity?

In math, differential forms are alternating: dx^dy=-dy^dx. But in physics, we seem to exchange the order freely: dxdy=dydx. What's going on? I am comfortable with an answer that involves tensors, differential geometry, physics, volume forms, etc. In fact, this is really something I should...

Homework Statement Make a change of variable that transforms the quadratic form with no cross-product term: 9x1^2 - 8x1x2 = 3x2^2 Homework Equations A = PDP^-1 Q = y^TDy The Attempt at a Solution I know the answer. This is a question regarding concept. The eigenvalues for...

Suppose the characteristic polynomial of a matrix A is \lambda^3(\lambda-1)(\lambda-2). If the nullity of A is two, what are the possible Jordan normal forms of A up to conjugation?I think that an example of a matrix with such characteristic polynomial is: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1...

Do You Experience "Number Forms"? A "number form" is an involuntary chart, of sorts, that pops into some people's minds when they consider things like calendars (months, days), times of day, the alphabet, or even just numbers from 1 to infinity. These "charts" have their elements grouped...

I am having trouble visualizing when a 2 form is exact and have a specific case that I am struggling with at the moment. Any help is welcome. Take an oriented 2 torus and divide it ,using parallel circles, into an even number of tube shaped regions. In each tube, assign a 2-form that fades...

I thought they were unique, but given a fraction a/b, couldn't you always write it as the (decimal representation of a/b without the decimal place)/ 10^(n) ? thanks

In English which if the following, if any, is incorrect and if so, why: having had; having had had; had had; had having had; has had had; having have had had. What tense to you call the last one? Can you say "He had had having had had" ?

P.S. I'm not sure where to post this question, in particular I can't find a number theory forum on the coursework section for textbook problems. Please move this thread to the appropriate forum if this is not where it should belong to. Thanks!

Homework Statement Find the matrix of f relative to Alpha' and Beta'. Alpha' = [(1,0,0), (1,1,0), (2,-1,1)] Beta' = [(-13,9), (10,-7)] The question originally reads that f is a bilinear form. I've found a (correct according to answer key) matrix A that is 3 -4 4 -5 -1 2...

Hi PF, I am currently trying to teach myself the rudiments of differential forms, in particular their application to physics, and there's something I'd like to ask. It seems like diff forms can be used to express all kinds of physics, but the area I haven't been able to figure out is stuff...

Homework Statement Given a real symmetric matrix A, prove that: a) A is positive definite if and only if A = (B^T)B for some real invertible matrix B b) A is positive semidefinite if and only if there exists a (possibly singular) real matrix Q such that A = (Q^T)Q Homework Equations...

Hi all, I posted this awhile back in the homework sections of the forums and received only one reply, which suggested that I post it here instead, though I understand that it belongs in the homework section. The fundamental problem is not this particular exercise but about integration of...

Let's say we want to write down the metric in a uniform field. I see two ways of going about this. Method 1: Straightforward arguments using the equivalence principle and photons in elevators show that if a photon with initial energy E rises or falls by dy, then its energy shift is given...

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...

Homework Statement find all Jordan forms of 8x8 matrices given the minimal polynomial x^2*(x-1)^3 Homework Equations The Attempt at a Solution The roots are clearly 0,1 and 0 has degree 2 while 1 has degree 3. The forms would be made up of the blocks [0,0;1,0] corresponding to 0...

So I am trying to compute all possible Jordan forms over the complex numbers given a minimal polynomial. My question is this: If the roots of the minimal polynomial are both real, should I proceed as if all of the possible forms are over real numbers?

Homework Statement A window has the shape of a square of side 2 surmounted by a semicir- cle. Find its area. Express the computation in terms of the integral of the area form w = dx ^ dy over a 2-chain in R2. Identify the chain. Homework Equations The Attempt at a Solution I...

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...

I read a problem a while ago which was to find a differential form on the circle which is not the differential of any function. Being a hapless physicist, this puzzled me for a while. I've found an answer in Spivak's Calculus on Manifolds, but I need a little help in following his reasoning...

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?

Homework Statement show that \left(\begin{array}{cc}2 & -1\\-1 & 1\end{array}\right) forms a basis for R^2Homework Equations The Attempt at a Solution ok...my instructor said he wants me to show that they are linearly independant and to show that they span to form a basis...not just by a...

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...