What is Terms: Definition and 1000 Discussions

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  1. H

    EFE Metric: Find a Link to the Full Expansion

    Does anyone have a link to a version of the EFE fully expanded in terms of the metric?
  2. A

    Answer: Limit of Big-O Terms: O(1/x) & O(x)

    I'm a bit confused with limits of big-O terms. What should be the answer for following:- 1) limit of O(1/x) as x->0. O(1) maybe but I'm not sure. 2) limit of O(x) as x-> 0. O(1) or 0?
  3. T

    3x^2 + 2x - k = 0, find 3α^2 - 2β in terms of k

    Homework Statement Let k be a constant. If α and β are the roots of the equation 3x^2 + 2x - k = 0, find the value of 3α^2 - 2β in terms of k. Homework Equations The Attempt at a Solution Obviously, the usual αβ = -k/3 α + β = -2/3 has been written but I couldn't put them...
  4. M

    Expand ψ(o) in terms of eignestates

    if ψ(o)=(1 0)^{T} at time t=0. According to some Hamiltonian, it was found that the corresponding eigenstates are |ø_{1}> = 1/√2(1 i)^{T} and |ø_{2}> = 1/√2(1 -i)^{T} so then we wanted to expand ψ(0) in terms of |ø_{1}> and |ø_{2}>: the author got: 1/√2|ø_{1}> + 1/√2 |ø_{2}> My question is...
  5. C

    Stress-energy tensor explicitly in terms of the metric tensor

    I am trying to write the Einstein field equations $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu} R=\frac{8\pi G}{c^4}T_{\mu\nu}$$ in such a way that the Ricci curvature tensor $$R_{\mu\nu}$$ and scalar curvature $$R$$ are replaced with an explicit expression involving the metric tensor $$g_{\mu\nu}$$...
  6. F

    Help with simplifing an equation in terms of 2 variables

    Homework Statement Hey. I need help simplifying and factoring a differential equation in terms of v and p (velocity(xdot) and position(x) respectively). I need the final answer to be in this form: a = ( )v + ( )p. This is so i can put the governing equation in a state-space and eventually use...
  7. J

    Taylor series in terms of discrete derivative

    All analitic function can be express how: f(x) = \frac{1}{0!} \frac{d^0f}{dx^0}(x_0) (x - x_0)^0 + \frac{1}{1!} \frac{d^1 f}{dx^1}(x_0) (x - x_0)^1 + \frac{1}{2!} \frac{d^2f}{dx^2}(x_0) (x - x_0)^2 + \frac{1}{3!} \frac{d^3f}{dx^3}(x_0) (x - x_0)^3 + ... that is the taylor series of the function...
  8. T

    Find the eigenstates of a basis in terms of those of another basis?

    Homework Statement This isn't exactly a homework question, but I figured this would be the best subforum for this sort of thing. For the sake of a concrete example, let's just say my question is: Express the position operator's eigenstates in terms of the number operator's eigenstates...
  9. C

    Expressing general rotation in terms of tensors

    Homework Statement A general rotation through angle ##a## about the axis ##\underline{n}##, where ##\underline{n}^2 = 1## is given by $$R(a,\underline{n}) = \exp(-ia\underline{n} \cdot \underline{T}),$$ where ##(T_k)_{ij} = -i\epsilon_{ijk}##. By expanding the exponential as a power series in...
  10. T

    Integral by interpreting it in terms of area

    Homework Statement ∫(a= -3 , b= 0) (1 + √9 - x^2) dx Homework Equations ∫(a,b) f(x) dx = lim as n → \infty \sum f(xi) delta x The Attempt at a Solution I tried plugging in my a and b value into the function just as I would with any other function to find the area and i get a number...
  11. T

    Non-canonical terms of scalar fields

    Hello! Well, I guess it's all in the title, really. I was reading about k-essence, and it was described as a scalar field having a non-canonical kinetic term. I did a bit of browsing and couldn't find a clear explanation of what, exactly, a non-canonical kinetic term is. Any help would be...
  12. C

    Representation of e in terms of primes

    We can represent π, in terms of primes by using Euler's product form of Riemann Zeta. For example ζ(2)=(π^2)/6= ∏ p^2/(p^2-1). Likewise, is there a representation of e that is obtained by using only prime numbers?
  13. kaliprasad

    MHB 3 consecutive terms of AP that are perfect square

    find parametetric representation of 3 perfect squares which are successive terms in AP ($x^2$,$y^2$,$z^2$) such that $x^2,y^2,z^2$ are successive terms of AP. find x,y,z
  14. B

    Pure, proper mixed, and improper mixed states in laymen's terms

    This is how one poster tried to explain it to me but for people who have only taken a basic physics course in college it leaves a lot wanting. "If a system is in a pure state, and you know what the pure state is, then your knowledge of the system is complete, and all uncertainty is quantum...
  15. 9

    Convergent limits for sequences: picture terms

    A limit of a sequence is definitely convergent if: If for any value of K there is an N sufficiently large that an > K for n > N, OR for any value of K there is an N sufficiently large that an<±K for n > N My only question is what exactly are K, N, an and n? What values are they? How would...
  16. N

    Finding inverse metric tensor when there are off-diagonal terms

    How do you find the inverse of metric tensor when there are off-diagonals? More specifivally, given the (Kerr) metric, $$ d \tau^2 = g_{tt} dt^2 + 2g_{t \phi} dt d\phi +g_{rr} dr^2 + g_{\theta \theta} d \theta^2 + g_{\phi \phi} d \phi^2 + $$ we have the metric tensor; $$ g_{\mu \nu} =...
  17. S

    What is the median value of an odd-numbered set of letters?

    I wonder what parts of statistics have specific terms existing for them - I see a relevant notion which would be relevant, but not sure if there is a term for it. If variable values can be ordered then it possesses a median. If the values can also be added then they also possesses an average. A...
  18. C

    Geometric Sequence (Only 4 terms and their sums are given)

    Homework Statement "In a geometric sequence, the sum of t7 and t8 is 5832, the sum of t2 and t3 is 24. Find the common ratio and first term." Homework Equations d = t8/t7 or t3/t2 tn = a * rn-1 The Attempt at a Solution So I thought of developing a system of equations then solving...
  19. anemone

    MHB Sum of two trigonometric terms

    Prove that $\tan \left( \dfrac{3 \pi}{11} \right)+ 4\sin \left( \dfrac{2 \pi}{11} \right)=\sqrt{11}$. I know this problem may be stale as it has been posted countless times at other math forums, but I've seen one brilliant method to attack this problem recently, and I'm so eager to share it...
  20. M

    Least amount of terms for sum.

    I was trying to design some GUI for a tool I'm making and I noticed there's a hidden math problem somewhere in there. Not being one to let the opportunity slide, I decided it's worth exploring. Basically there's 3 buttons that add to a variable. What are the best values to put on those...
  21. J

    Rotational in terms of vector calculus

    Hellow! I was noting that several definitions are, in actually, expressions of vector calculus, for example: Jacobian: \frac{d\vec{f}}{d\vec{r}}=\begin{bmatrix} \frac{df_1}{dx} & \frac{df_1}{dy} \\ \frac{df_2}{dx} & \frac{df_2}{dy} \\ \end{bmatrix} Hessian: \frac{d^2f}{d\vec{r}^2} =...
  22. mesa

    Multipliers for series for manipulating signs of the terms

    There are multipliers that can be used when building infinite series that can create several different orders for the signs of consecutive terms by, for example, (-1)^n to get, - + - + - +... but I have been having difficulty figuring out any beyond the following, + - + - + -... + + -...
  23. L

    Sum of 1 + 2a + 3a2 + ... to n terms

    Homework Statement Sum the series 1 + 2a + 3a2 + ... to n terms This series consists of an a.p. (with general term n) and gp general term a^(n-1) right? So the series general term is na^(n-1) So is the sum the sum of each progression times each other? i.e (1-a^n)/(1-a) *...
  24. W

    Transversality of a Vector Field in terms of Forms (Open Books)

    Hi, All: Sorry for the length of the post, but I think it is necessary to set things up so that the post is understandable: I'm going through an argument in which we intend to show that a given vector field [ itex]R_ω [/ itex] (actually a Reeb field associated with a contact form ω) is...
  25. anemone

    MHB Find the sum of the first n terms

    Evaluate the sum $\displaystyle \sum_{i=0}^n \tan^{-1} \dfrac{1}{i^2+i+1}$.
  26. polygamma

    MHB Expressing zeta(3) in terms of a Glaisher-Kinkelin-like constant

    In a previous thread I showed how to express $\zeta'(-1)$ in terms of the Glaisher-Kinkelin constant. http://mathhelpboards.com/challenge-questions-puzzles-28/euler-maclaurin-summation-formula-riemann-zeta-function-7702.html This thread is about expressing $\zeta(3)$ (sometimes referred to as...
  27. M

    Calculate second derivative of a function in terms of another function

    Homework Statement . Let ##f:[a,b] \to [\alpha,\beta]## be a bijective function of class ##C^2## with an inverse function also of class ##C^2## ##g:[\alpha,\beta] \to [a,b]##. a)Calculate ##g''(x)## for every ##x \in (\alpha,\beta)## in terms of ##f## and its derivatives. b)If ##f'(x)>0##...
  28. C

    Lorentz boost matrix in terms of four-velocity

    As I understand it, the value of a 4-vector x in another reference frame (x') with the same orientation can be derived using the Lorentz boost matrix \bf{\lambda} by x'=\lambda x. More explicitly, $$\begin{bmatrix} x'_0\\ x'_1\\ x'_2\\ x'_3\\ \end{bmatrix} = \begin{bmatrix}...
  29. evinda

    MHB Second order differential equation,with constant terms

    Hello (Smirk) Given the x^{2}y''+axy'+by=0,I have to show that with replacing x with e^{z},it becomes a second order differential equation,with constant terms. I tried to do this and I got this: y''+\frac{a}{e^{z}}y'+\frac{b}{e^{2z}}y=0 . But,at this equation the terms aren't constant...
  30. S

    Hydrogen wave function in terms of m_z after m_y measurement

    Homework Statement Given the following wave function for hydrogen: psi(r, t=0) = (1/sqrt(10))*(2*psi_100 - psi_210 + sqrt(2)*psi_211 + sqrt(3)*psi_21(-1)) where the subscripts show n, l, m_z, respectively, and the psi_nlm_z are already normalized. - At t=0, we measure and find l = 1...
  31. N

    Meaning of terms in SU(3) gauge transformation

    Hi All, I'm working through the theory of the strong interaction and I roughly follow it. However I have some questions about the meaning of the terms. The book I use gives the gauge transformation as: \psi \rightarrow e^{i \lambda . a(x)} \psi First question ... What are the a(x)...
  32. ajayguhan

    Expression of bulk modulus of a cube in terms of strain

    In my text it's given when a cube underwents a uniform unit tensile force be applied in all six faces, bulk module=1/3(α-2β) Where α is longitudinal strain and β is lateral strain.is there a derviation for it..? And it states in x direction there will be increase in length and in y, z...
  33. S

    How to Express Function f in Terms of Complex Variable z?

    Let f(x+iy) = \frac{x-1-iy}{(x-1)^2+y^2} first of all it asks me to show that f satisfies the Cauchy-Riemann equation which I am able to do by seperating into real and imaginary u + iv : u(x,y),v(x,y) and then partially differentiating wrt x and y and just show that \frac{\partial...
  34. N

    What is Schwinger terms and what is the origin?

    What is Schwinger terms that related with commutator of currents and what is the origin?Why the infinities appear when we consider the product of operators of fields at the same spacetime point?
  35. C

    Calculating the number of terms in sequences

    How does one calculate the number of terms in the sequence \sum\limits_{a=2}^k \sum\limits_{b=a}^k of 1/(a*b).
  36. S

    MHB Coefficient in a Laurent Expansion in terms of an Integral

    Hi guys, i need your help to go about his question, Question: $$\text{Show that the coefficient }C_n \text{in the Laurent expansion of }$$ $$f(z)=(z+\frac{1}{z}) \text{ about z=0 is given by}$$ $$C_n=\frac{1}{2\pi}\int^{2\pi}_0 \cos(2cos(\theta))cos(n\theta)\, d\theta ,n\in\mathbb{z}$$
  37. G

    Expressing moment of inertia in terms of m,a,r and g

    Homework Statement Find an expression for the moment of inertia (I) of the platform in terms of acceleration of the mass (a), the value of the hanging mass (m), the radius of the spindle (r) and the constant (g). Diagram: http://i.imgur.com/rv3zFYG.jpg Homework Equations F=ma t=Iα...
  38. F

    What Is The Difference Between These Dielectric Terms?

    What Is The Difference Between These "Dielectric" Terms? Can someone please explain to me what the difference between these terms are? 1. Dielectric constant 2. Relative dielectric constant 3. Dielectric loss I came across them on this website: http://www.lsbu.ac.uk/water/microwave.html#pen...
  39. Y

    Schwarzschild metric in terms of refractive index

    This is a spin off from another thread: First there are a couple of mathpages http://mathpages.com/rr/s8-04/8-04.htm and http://mathpages.com/rr/s8-03/8-03.htm that discuss the refractive index model and highlights the differences. The first obvious objection is that the 'medium' must have...
  40. G

    Vector calculus: how to order terms?

    Hi, I need to let an operator act on a scalar function. The operator is however in a very cryptic form, so I would want to work it out a little bit. I get stuck in the process. The operator is: \vec{u}\cdot\left[\vec{L}\times\left(\vec{u}_r\times\vec{L}\right)\right]f Where \vec{L} is...
  41. F

    MHB Dividing vs Subtracting to Solve Equations w/1 Variable

    If you have the equation \frac{dx}{dt}=4(x^2+1) I sometimes get confused if i should should subtract 4(x^2+1) from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but...
  42. B

    MHB Grouping terms to start factoring.

    how would i go about properly grouping terms to start my factoring? 1. $12x^2y^3-24y^3z-6x^6+30y^4-15x^4y+4x^2y+12x^4z+10y^2-8yz$ thanks!
  43. kira506

    What is the 4th dimension n terms of visualization ?

    I want sthg I can visualize in order to understand , I keep asking and am always told time , so how is time a 4th dimension ? I try my best but my mind is too weak to visualize things more complex than disney (so please , I want sthg in that standard ,consider me a curious 6 year old child)
  44. anemone

    MHB Find the sum of the first 11 terms of given series

    Hi MHB, This problem vexes me until my mind hurts. Problem: Find the sum of the first 11 terms of the series \frac{19}{99}+\frac{199}{999}+\frac{1999}{9999}+ \cdots Attempt: I managed only to find the expression of the nth term of the given series and I got...
  45. U

    Find this integral in terms of the given integrals

    Homework Statement If \displaystyle \int_0^1 \dfrac{e^t}{t+1} dt = a then \displaystyle \int_{b-1}^b \dfrac{e^{-t}}{t-b-1} dt is equal to Homework Equations The Attempt at a Solution I used the definite integral property in the second integral \displaystyle \int_{b-1}^b...
  46. D

    Discriminant of cubic equation in terms of coefficients

    1. Background/theory We know that if the equation x3+px2+qx+r=0 has solutions x1, x2, x3 then x1 + x2 + x3 = -p x1x2 + x2x3 + x3x1 = q x1x2x3 = -r 2. Problem statement Find (x1 - x2)2(x2 - x3)2(x3 - x1)2 as an expression containing p,q,r. That is, I'm supposed to find the discriminant of...
  47. G

    Solve x in Terms of c: 3x+cos 2x = c

    Homework Statement 3x+cos 2x = c c is an unknown constant. how do i solve x in terms of c?
  48. E

    The sign of terms in a characteristic equation of a PDE

    This was something I noticed as I was trying to practice solving PDEs using the method of characteristics. The text has the following example: $$\frac{\partial u}{\partial x} + x \frac{\partial u}{\partial y} = 0$$ This should be easy enough. I let p(x,y) = x and solve for \frac{\partial...
  49. S

    Can a 2N by 2N matrix written in terms of N by N matrices?

    I posted this question over at the QM page, https://www.physicsforums.com/showthread.php?t=714076 but I realized I am really looking for a hard Mathematical proof ... A description of a numerical way of proving this would also be very helpful for me. or a reference covering the...
  50. S

    Writing a random 2N by 2N matrix in terms of Pauli Matrices

    Hi, Wasn't sure if I should post this to Linear Algebra or here. My question is really simple: Can a 2N by 2N random, and Hermitian Matrix ( Hamiltonian ) be always written as: H = A \otimes I_{2\times 2} + B \otimes \sigma_x + C \otimes \sigma_y + D \otimes \sigma_z where A,B,C,D are all...
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