Forms Definition and 482 Threads

Homework Statement 48. Lim (cscx- cotx) x-0 52. lim (xe^1/x -x) x-∞ Homework Equations The Attempt at a Solution

Say I'm given a random 3-dimensional vector, pointing from the origin. How can I find the angle it forms with a plane defined by two other vectors?

Let Q: R3 \rightarrow R be the quadratic form given by Q(x) = 2x1x2 + 2x1x3 + 2x2x3 where x = (x1x2x3)t How do I write down the matrix A of the quadratic form Q in the standard matrix E. and how do I find the numeric values for \lambda

Homework Statement I was given the first definition but am not sure how to get the last 3 Homework Equations N/A The Attempt at a Solution I tried taking sup (with restriction being llxll=1) on both sides of the inequation, llF(x)ll=<llFll llxll, but would eventually end up...

Homework Statement Claim: The solution space of a linear homogeneous PDE Lu=0 (where L is a linear operator) forms a "vector space". Proof: Assume Lu=0 and Lv=0 (i.e. have two solutions) (i) By linearity, L(u+v)=Lu+Lv=0 (ii) By linearity, L(au)=a(Lu)=(a)(0)=0 => any linear...

I'm just curious, why, when solving limits, is 1^\infty considered an indeterminate form? Isn't 1 raised to any power equal to 1? Why isn't it so simple?

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...

Prove the following result: let G be a compact Lie group, H its closed subgroup and X = G/H. Let T(X) denote the space of G-invariant differential forms on X (e.g. \omega \in T(X) \Leftrightarrow \forall g \in G g^{*}\omega = \omega). Then T(X) is isomorphic to H^{*}(X), de Rham cohomology...

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?

I wasnt quite sure where to put this thread. This question occurred to me while I was looking at the group theory of standard model groups so I thought I'd put it here. Anyway, here is my question: One can define the Killing form for a group by taking the trace of two generators. One can...

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))...

Homework Statement Let the quadratic form F(x,y,z) be given as F(x,y,z) = 2x^2 + 3y^2 + 5z^2 - xy -xz - yz. Find the transitional matrix that would transform this form to a diagonal form. Homework Equations A quadratic form is a second degree polynomial equation in three...

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...

Homework Statement the set R^(2) with the usual vector addition forms an abelian group. For a belongs to R and x=(x1,x2) belongs to R^(2) we put a *x :=(ax1,0),this defines a scalar multiplication R*R^2 ---R^2 (a,x)---a*x. determine which of the axioms defining a vector space hold for the...

Homework Statement http://img16.imageshack.us/img16/6606/50381320.jpg Homework Equations Please see above picture The Attempt at a Solution I believe for question a) I just need to add up all the matrices and then row reduce to RREF, which gives me: [1,0,0] [0,1,0] or Do I...

(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...

Ok i don't really get how everyone forms isomers, in my class people just move carbons and other things to turn them into branches Is there a specific way to determine the isomer of a compound without guesswork and counting to c if the hydrogens and carbons stay the same? For example how...

I'm trying to study geometric algebra using Artin's book and am having some difficulty with what degenerate symmetric bilinear forms would be like. Does someone know of an example and brief explanation. Also, the opposite being "nondegenerate nonsymmetric bilinear form" would help me out. If I...

I know \lim_{n \rightarrow \infty} (1 + 1/n)^n = \lim_{n \rightarrow \infty} 1^{\infty} , which is an indeterminate form, converging to e in this case. But what if the original sequence is a_n = 1^n . Then as n tends to infinity, the function converges to 1 (because it's constant and the limit...

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...

Can a quadratic form always be diagonalised by a rotation?? Thx in advance

On an n-dimensional vector space an alternating n-form defines a measure. However a measure can be defined on its own right, without mentioning any alternating form. My question is that what condition must a measure satsfy that it can be originated from an alternating multilinear form. I mean an...

Can someone point me to a good comparison of the various forums of temperature measurement? (Thermocouples, Thermistors, IR, etc), I'm interested in finding out more about : relative cost, accuracy, size, output type, any other constraints on the technology.

A question about how find the canonical forms over R and C. An example, given a quadratic form,q(x,y,z)=x^2 + 2xy + 4yz + z^2 find the canonical forms over R and C. First step,i get the matrix 1 2^0.5 0 2^0.5 0 2...

Homework Statement Suppose that the matrix A has characteristic equation (lambda - 2)^3 * (lambda + 1)^2 (a) Write all 6 of the possible Jordan forms of A. (b) Compute det(A) and tr(A). Homework Equations The Attempt at a Solution To figure out Jordan forms I need to find the...

For an odd prime number p let Fp be the field with p elements, ie. the integers {0...,p-1} with addition and multiplication defined modulo p. How many quadratic forms are there on the vector space Fp^n I don even know how to start this question

Hello, I was tempted to put this in the math section but it is more of a visualization problem though it is most likley due to my lack of understanding the divergence and curl operators fully. I am comfortable with the closed loop integral of E dot dA and can visualize it as a solid closed...

Hi all, I am taking this math methods course in grad school, and in the lectures we stormed through differential geometry. My geometry is already horrible, I find it hard to understand all these forms, fields, tensors, wedge products etc... I would be glad if you could suggest some books...

I understand that the truth table involved, and how it works, but i don't get the timing of the diagrams. I've looked on numerous internet sites and through many books but i still don't understand how when J=K=0 and CLK= up, with Q having no change, that the out put (Q) is up, when the others...

The first brains came about in the precambrian or at the border with the cambrian around 560 million years ago when the first multi-celluar organisms emerged. It has always struck me how/why organisms developed brains. The brain must have emerged together with eyesight, since eyesight would be...

If a salt crystal forms after 3 days of evaporation, and the crystal mass is 30 mg, how many Na+ and Cl- ions was added to the crystal each second (average). How do I solve this?

I wonder if anyone has heard of this new (perhaps decades old?) idea I stumbled on. The matter that falls into an event horizon is quickly absorbed. Everyone knows that. But the key difference is what happens later. Underneath the energy barrier, the matter that is consummed is distributed...

(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 need to pass variables from one form to another for printing purposes. I'm using the PrintForm component to print the form. I'm familiar with this concept using VBScript and .asp... However, I am at a loss for how to do so using VB 2008.

Homework Statement V is a unitarian space of finite dimensions and T:V->V is a linear transformation. Every eigenvector of T is an eigenvector of T* (where (Tv,u) = (v,T*u) for all u and v in V). Prove that T(T*) = (T*)T.Homework Equations The Attempt at a Solution First of all, since the space...

Ok i am having a hard time with this one. Find the product z1z2 in standard form. Then write z1 and z2 in trig form and find their product again. Finally, convert the answer that is in trig form to standard form to show that the two products are equal. z1= 1+i, z2= 4i

I have a problem with determining eigenvalues. This is what I've got thus far: Homework Statement Identify and sketch the graph of the quadratic equation 4x² + 10xy + 4y² = 9The Attempt at a Solution We put it in the matrix form: \begin{pmatrix} 4 & 5 \\ 5 & 4 \\ \end{pmatrix} Now we find the...

it's a bit simple i know but i just forgot how to do it and i need to know its done for an exam next week...i just want to know how to add these two polar form vectors 8.54<69.44 + 4.123<14.036

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...

Homework Statement Let (M,g) be a spacetime. (a) Let A and A' be vector fields on M such that g(A,B)=g(A',B) for any future-pointing timelike vector field Y. Show that X=X'. (b) Let w and w' be two two-forms on M. Suppose that i¬A w = i¬A w' for any future -pointing timelike vector field A...

here is a question and how i tried to implement this method but it doesn't come out : http://img172.imageshack.us/my.php?image=img86771ok7.jpg every function can be expressed in a minterm form and a maxterm form i am confused about the laws for with we transform from one form to the...

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.

Suppose you have one limit lim_{x\rightarrow \ 0}(cos(x)/x) = \infty and a second limit lim_{x\rightarrow \ \infty}(x) = \infty What is the first limit subtracted by the second? Is it simply indeterminate because its inf - inf? One...

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

[SOLVED] Newton's third law Homework Statement My book gives two forms of Newton's Third Law: Weak Form: The forces exerted by two particles \alpha and \beta on each other are equal in magnitude and opposite in direction Strong Form: The forces exerted by two particles \alpha and \beta on each...

If a good sample of dinosaur DNA were found intact, could we make a clone? I know that the chances of finding intact complete DNA of a dinosaur is slim. A researcher recently claimed to have found likely dinosaur dna, although not complete enough for any hopes of cloning or anything. The...

[SOLVED] A formulation of continuity for bilinear forms Homework Statement My HW assignment read "Let H be a real Hilbert space and a: H x H-->R be a coninuous coersive bilinear form (i.e. (i) a is linear in both arguments (ii) There exists M>0 such that |a(x,y)|<M||x|| ||y|| (iii) there...