What is Forms: Definition and 482 Discussions

Secret Chiefs 3 (or SC3) is an avant-garde group led by guitarist/composer Trey Spruance (of Mr. Bungle and formerly, Faith No More). Their studio recordings and tours have featured different line-ups, as the group performs a wide range of musical styles, mostly instrumental, including surf rock, Persian, neo-pythagorean, Indian, death metal, film music, electronic music, and various others.
The band's name was inspired by the "Secret Chiefs" said to inspire and guide various esoteric and mystical groups of the previous two centuries. Spruance has expressed interest in, and drawn inspiration from, various mystical or occult systems such as Sufism, Kabbalah, Hermeticism and alchemy.

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  1. M

    Question about Differential Forms as Size of Projections

    Hello, I have a somewhat conceptual question about differential forms. I have been studying differential forms off and on for some time now and things are starting to come together for me. However, there is an irritating gap in my understanding. Regarding the geometric significance or...
  2. S

    Showing a given set of vectors forms a Parseval frame

    Homework Statement Show that the vectors ##\sqrt{\frac{2}{3}}(1,0), \sqrt{\frac{2}{3}}\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right), \sqrt{\frac{2}{3}}\left(-\frac{1}{2},-\frac{\sqrt{3}}{2}\right)## form a Parseval frame of ##\mathbb{R}^2##, but are neither linearly independent nor...
  3. E

    Indeterminant forms homework help

    Homework Statement lim{x\rightarrow∞} sqrt(x^(2)+5x+11)-x Homework Equations I know it is of type ∞-∞ The Attempt at a Solution I have worked this problem around to death, and I know I'm supposed to give them a common denominator to get ∞/∞ and use L'Hospital's Rule, but I end up...
  4. C

    A Maxwell's equation in differential forms formalism

    Homework Statement This is not actually a homework but a personal work. Here it is: Using the differential forms: F=\tfrac{1}{2!}{{F}_{\mu \nu }}d{{x}^{\mu }}\wedge d{{x}^{\nu }} and J=\tfrac{1}{3!}{{J}^{\mu }}{{\varepsilon }_{\mu \alpha \beta \gamma }}d{{x}^{\alpha }}\wedge d{{x}^{\beta...
  5. micromass

    Topology Differential Forms in Algebraic Topology by Bott and Tu

    Author: Raoul Bott, Loring Tu Title: Differential Forms in Algebraic Topology Amazon Link: https://www.amazon.com/dp/1441928154/?tag=pfamazon01-20 Prerequisities: Differential Geometry, Algebraic Topology Level: Grad Table of Contents: Introduction De Rham Theory The de Rham Complex...
  6. marellasunny

    Where would I use quadratic forms and how?

    Wiki defines :In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. Yes,all nice and dandy,I get to then express it in terms of matrices and then I find the eigen values and then find the canonical quadratic form,the usual boring linear algebra...
  7. D

    Indeterminate Forms and L'Hopital's Rule

    Homework Statement lim ln(x-1)/(x2-x-4) x->2 Homework Equations The Attempt at a Solution Well, I thought that every time I had answers as 0/0, 2/0 or 0/2, for instance, they would constitute as indeterminate forms. I have the answer sheet for this problem. It says "answer: 0/-2 =...
  8. T

    Aren't indeterminant forms misleading?

    So my calculus professor last semester said that 1∞ is just 1 if 1 is exactly 1. He said that 1∞ is an indeterminant form because the rate of change of x as x approaches 1 competes with the rate of change of ∞ as it gets larger in x∞. He also said that 0/0 is an indeterminant form because the...
  9. S

    Find Exterior Derivative of Differential Forms in Dim > 3

    So say I have a n-1 form \sum^{n}_{i=1}x^{2}_{i}dx_{1}...\widehat{dx_{i}}...dx_{n} and I want to find the exterior derivative, how do I know where to put which partial derivative for each term, would it simply be?? \sum^{n}_{i=1}...
  10. D

    Differential of a function vs differential forms

    Hi, I understand the concept of the differential of a (differentiable) function at a point as a linear transformation that "best" approximates the increment of the function there. So for example the differential of a function f : D \subseteq \mathbb{R}^2 \to \mathbb{R} could maybe be df = 8...
  11. M

    Confusion regarding differential forms and tangent space (Spivak,Calc. on Manifolds)

    I have been working through Spivak's fine book, but the part about differential forms and tangent spaces has left me confused. In particular, Spivak defines the Tangent Space \mathbb R^n_p of \mathbb R^n at the point p as the set of tuples (p,x),x\in\mathbb R^n. Afterwards, Vector fields are...
  12. R

    Trigonometric Methods - Calculating impedance in rectangular and polar forms

    Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression Z= (Z_1 Z_2)/(Z_1+ Z_2 ) If Z1 = 4 + j10 and Z2 = 12 – j3, calculate the impedance Z in both rectangular and polar forms. Homework Equations j2=-1 The Attempt at a Solution Z=...
  13. Islam Hassan

    HEP: Energy Only in Kinetic or Potential Forms?

    I read recently that all energy is either kinetic or potential. In high energy physics, it is easy to understand the kinetic bit, but potential energy eludes me. What are some examples of potential energy at the high energy physics/elementary particle level? Also, if strings exist, how is...
  14. W

    Using Forms to Define Orientation of Curves.

    Hi, All: There is a standard method to construct a nowhere-zero form to show embedded (in R^n ) manifolds are orientable ( well, actually, we know they're orientable and we then construct the form). Say M is embedded in R^n, with codimension -1. Then we can construct a nowhere-...
  15. W

    More on Diff. Forms and Distributions as Kernels

    Hi, Again: I'm trying to show that, given a 3-manifold M, and a plane field ρ (i.e., a distribution on TM) on M, there exists an open set U in M, so that ρ can be represented as the kernel of a differential form w , for W defined on U. The idea is that the kernel of a linear map...
  16. W

    Kernels, and Representations of Diff. Forms.

    Hi, All: I need some help with some "technology" on differential forms, please: 1)Im trying to understand how the hyperplane field Tx\Sigma< TpM on M=\Sigma x S1 , where \Sigma is a surface, is defined as the kernel of the form dθ (the top form on S1). I know that...
  17. R

    Indeterminate Forms and l'Hopital's Rule

    Homework Statement Lim as x→∞ of ((2x+1)/(2x-1))^(sqrtx)Homework Equations The Attempt at a Solution When I initially plugged in ∞ for my x, I get (∞/∞)^∞, correct? If so, should I just let y=((2x+1)/(2x-1))^(sqrtx) and take the limit of both sides using ln? That's what I attempted to do...
  18. D

    General physics (or EM) book using vector forms for EM

    So far the best general physics book for EM I've found has been Alonso and Finn. The problem is that I just spent too much time trying to understand electric displacement using the hand-wave magic mathematical definitions they give. The rest of the book seems fine (it gives vector forms for...
  19. J

    I with differential geometry computing connection forms. Please respond

    I need help with Part (b). I finished part (a) and attached it as well. My issue comes from how to apply the definition of connection forms to compute them. The definition states: Let E_1, E_2, E_3 be a frame field on R^3. For each tangent vector v at R^3 at the point p let \omega_{ij}(v )=...
  20. W

    Orientation Forms in Different Codimension.

    Hi, Everyone: A way of defining an orientation form when given a codimension-1 , orientable n-manifold N embedded in R^{n+1} , in which the gradient ( of the parametrized image ) is non-zero (I think n(x) being nonzero is equivalent to N being orientable), is to consider the nowhere-zero...
  21. B

    Two photons forms a particle

    Homework Statement Imagine that we discover a new particle, called P particle by a head-on collision of two photons of energies 500 Mev and 200 MeV. The photons are annihilated in the process. a) what is the mass of the newly discovered particle P? b) what is the kinetic energy of the P...
  22. Physicist50

    Wave and Particle Mass Energy Forms

    I was wondering that since most forms of energy can either be in wave or particle form, (example; photons and electromagnetic wave) and also since mass is also a form of energy, could mass energy also be in wave form, and if so, what would its characteristics be?
  23. J

    Differential forms and wedge products are giving me trouble.

    I'm having problems in my differential geometry class. Does anyone know of a good tutorial or set of notes? The 1-form, 2-form, 3-form stuff is confusing and so is the wedge product. Anyways, here's the problem. After some algebra I arrived at my answer, but I'm unsure of how to incorporate...
  24. D

    First Friedmann Equation forms

    Homework Statement the first friedmann equation is: (\frac{\dot{a}}{a})^2=\frac{8\pi G\rho}{3}-\frac{kc^2}{a^2}+\frac{\Lambda}{3} In the case of a closed Universe (k > 0) containing only non-relativistic matter and no cosmological constant, write the Friedmann equation in terms of, H(a), H0...
  25. Patzee

    Do all life forms need to eat other life forms to exist?

    As you can tell from the question, my science knowledge is lacking. :confused: I can see that mammals, reptiles, etc. must eat other living creatures (mammals, insects, plants, etc.) for energy. But do plants, microbes and other types of life forms all depend on eating other life forms? For...
  26. R

    Integral forms of Momentum and Energy Equations

    Hi I was reading a book that introduced momentum and energy in integral forms and I had some confusion regarding what the terms meant. All integrals below are closed integrals For the momentum equation, the result was: F = d(mV)/dt = ∫∫ρ(V[dot]dS)V + ∫∫∫∂(ρV)/∂tdV From product rule...
  27. D

    What fraction of the kinetic energy is converted to other forms in collision?

    Homework Statement there are 2 blocks along a frictionless track. block 1 has a mass of m1 and block 2 has a mass of m2. Block 1 is initially moving at a speed of v0. it collides and sticks to the initial stationary block 2. (m2=9m1) what fraction of the inital kinetic energ of the system is...
  28. E

    Linear algebra question, quadratic forms.

    A is a square matrix. x, b are vectors. I know for Ax=b, that given b, there are an infinite number of pairs (A, x) which satisfy the equation. I'm wondering if the same is true for xAx=b. in particular, what if (x, A, b) are all stochastic vectors/matrices (i.e the entries of b and x add to...
  29. G

    Why is the gradient of a function considered a one form in Schutz's book on GR?

    So as I have read in Schutzs book on GR, and I'm finding his section on tensors and one forms very confusing. Schutz describes gradients of functions as a one form, I cannot quite grasp why. In calculus I was taught that the gradient was a vector pointing in the direction of the fastest...
  30. D

    Why P^-1AP forms a triangular matrix

    why does (P^-1)AP form a triangular matrix?
  31. J

    The GCD forms a subgroup of the integers

    Let r and s be positive integers. Show that {nr + ms | n,m ε Z} is a subgroup of Z Proof: ---- "SKETCH" ----- Let r , s be positive integers. Consider the set {nr + ms | n,m ε Z}. We wish to show that this set is a subgroup of Z. Closure Let a , b ε {nr + ms | n,m ε...
  32. M

    Does ZFC Imply the Power Set of Naturals?

    Is it true that for every standard formulation T of ZFC, T ⊢ the power set of {naturals}? After all, the empty set axiom and the pairing axiom are in T, and so we get N. Then by the power set axiom we get P(N).
  33. M

    When a star forms where does the Gravity come from?

    Hey guys, in class today we learned about the life cycle of a star and at the very first stage gravity pulls the helium or Hydrogen nuclei at such a speed that they fuse (nuclear fusion). As I understand it there is little gravity in space so where is this extra gravity coming from? Thanks...
  34. A

    Studying Vector calc vs. differential forms, a good textbook?

    Hello everybody, This is my first time on Physics forums. I am a sophomore in high school who LOVES math. I have lots of free time this summer and would like to learn multivariable calculus and/or linear algebra (whichever is a prerequisite for the other, depending on the textbook I choose)...
  35. T

    Convergence of indeterminate forms of a sequence

    State whether the sequence converges as n--> ##∞##, if it does find the limit i'm having trouble with these two: n!/2n and ∫ e-x2 dx now I know they're special forms so the ordinary tricks won't work. Any help or hints?
  36. M

    Finding z^4 in Polar & Cartesian Forms

    Homework Statement Express z=-1+4i in polar for then find z^4 converting to Cartesian form Homework Equations r = sqrt(x^2+y^2) theta = y/x z= r cos (theta) + i r sin (theta) The Attempt at a Solution r= sqrt(-1^2+4^2) = sqrt(17) theta = tan a = 4/1 a = tan^-1...
  37. A

    [Module theory] Prove that something forms a left R module.

    Homework Statement Suppose that R and S are two rings, M, is a (R-S) bi-module and N is a left R-module. Show that M \otimes N has the structure of a left S-module. The Attempt at a Solution Well, M\otimes N is an Abelian group, so it's enough that I define a scalar product on...
  38. M

    Elementary Differential Forms Question

    Let me preface by saying I am a physics major. So I am coming at differential forms from the perspective of physics, i.e. work, flows, em fields, etc. My question is this. My understanding is that a basic 1-form dx, dy, or dz takes a vector v = (v1,v2,v3) and gives back the corresponding...
  39. M

    Differential Forms and Vector Calculus

    So about a hundred years ago there was a live (sort of) differential forms thread hosted by someone named Lethe that was really helpful but short-lived. There have been some other diffl forms threads, too, such as the one centered on Bachman's book, but they all seem to peter out without any...
  40. V

    Identifying the various forms of Energy

    Hi, I’m currently doing research for a science fiction story and was wondering if anyone would be interested in helping me out. I’m trying to understand the various applications of different forms of energy. More specifically, here is what I want to know: If someone was equipped with a...
  41. I

    Best books for learning differential forms?

    Can someone recommend a good textbook for learning differential forms for someone with an understanding of calculus at the level of Spivak? Thanks.
  42. K

    Possible Jordan Forms for 3x3 Matrix with Negative Eigenvalues

    Homework Statement 1. Homework Statement [/b] Enumerate all possible Jordan forms for 3 x 3 systems where all the eigen-values have negative real parts. Do not use specific values. Instead, use possibilities like λ1; λ2; λ3, each with multiplicity 1, or λ (multiplicity 3). Homework...
  43. Matterwave

    Vector Valued Forms: Rank (n,p) Tensors

    Hi, I'm just wondering, a vector valued (or (n,0) tensor valued) p form is the same as a rank (n,p) tensor which is totally anti-symmetric bottom indices right? Is there a difference? A (n,m) valued p form is a (n,m+p) tensor which is anti-symmetric in the lower p indices?
  44. ElijahRockers

    Quadratic Forms & Lagrange Multipliers

    Homework Statement I'm having trouble grasping http://www.math.tamu.edu/~vargo/courses/251/HW6.pdf. Our teacher has decided to combine elements from Linear Algebra, and understanding Quadratic forms with our section on lagrange multipliers. I am barely able to follow his lectures. If I look...
  45. M

    DG - Clifford Algebra / Differential Forms

    Hello Everyone, I'm currently working through a differential geometry book that uses Clifford's algebra instead of differential forms. If anybody has knowledge of both, would you please explain what the differences between the approaches are, and what (if any) are the advantages of each...
  46. Square1

    Indefinite forms and l'hopital

    Homework Statement *indeterminate* oops the limit of x^x as x goes to zero from the right Homework Equations Going to be using L'hopital, and related algebraic manipulations to convert to indefinite form 0/0, infinity/infinity The Attempt at a Solution My understanding is that this limit...
  47. B

    Equivalence of Integral and Differential Forms of Gauss's Law?

    A sphere has charge density \rho=k\cdot r. Using the integral form of Gauss's Law, one easily finds that the electric field is E=\frac{k\cdot r^2}{4\epsilon} anywhere inside the sphere. However, \nabla\cdot E=\frac{k\cdot r}{2\epsilon}, which is half of what should be expected from the...
  48. D

    Complex Numbers - Forms and Parts

    Hi, I have a complex number and understand that the rectangular form of the number is represented by s = σ + jω, where σ is the real part and jω is imaginary. I am having trouble locating them in the number below: I know that "2" is a real number, and the numerator is imaginary...
  49. J

    Linear Equations (General and Standard forms: From Wikipedia)

    Source: http://en.wikipedia.org/wiki/Linear_equation General form:- It says (under the title General Form) "If B is nonzero, then the y-intercept, that is the y-coordinate of the point where the graph crosses the y-axis (where x is zero), is −C/B, and the slope of the line is −A/B."...
  50. J

    Calculation and Uniqueness of Smith Normal Forms

    FYI this is a homework problem which I already have the answer to but would like to clarify some points on. Homework Statement Find the Smith Normal Form of the matrix \left[ \begin{array}{cccc} 6 & 0 & 4 \\ 0 & 6 & 8 \\ 0 & 3 & 0 \end{array} \right] over the ring of integers. Homework...
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