What is Delta: Definition and 1000 Discussions

A river delta is a landform created by deposition of sediment that is carried by a river as the flow leaves its mouth and enters slower-moving or stagnant water. This occurs where a river enters an ocean, sea, estuary, lake, reservoir, or (more rarely) another river that cannot carry away the supplied sediment. The size and shape of a delta is controlled by the balance between watershed processes that supply sediment, and receiving basin processes that redistribute, sequester, and export that sediment. The size, geometry, and location of the receiving basin also plays an important role in delta evolution. River deltas are important in human civilization, as they are major agricultural production centers and population centers. They can provide coastline defense and can impact drinking water supply. They are also ecologically important, with different species' assemblages depending on their landscape position.

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  1. F

    Understanding Dirac Delta Function: Time Derivative & Hankel Transformation

    Hi All, I have a problem in understanding the concept of dirac delta function. Let say I have a function, q(r,z,t) and its defined as q(r,z,t)= δ(t)Q(r,z), where δ(t) is dirac delta function and Q(r,z) is just the spatial distribution. My question are: 1. How can I find the time derivative...
  2. H

    Why use stipulations in Epsilon Delta Proofs?

    Homework Statement When constructing an Epsilon Delta proof, why do we need to make a stipulation? For example, in most proofs for limits of quadratic functions, it is stipulated, for example, that δ≤1. Why is this needed anyway? This is my thought process for a quadratic: Prove that lim(x...
  3. F

    Is there a coordinate independent Dirac delta function?

    I have been wondering exactly how one would express the Dirac delta in arbitrary spaces with curvature. And that leads me to ask if the Dirac delta function has a coordinate independent expression. Is there an intrinsic definition of a Dirac delta function free of coordinates and metrics? Or as...
  4. F

    Integrating with a dirac delta function

    Homework Statement I have to integrate: \int_0^x \delta(x-y)f(y)dy Homework Equations The Attempt at a Solution I know that the dirac delta function is zero everywhere except at 0 it is equal to infinity: \delta(0)=\infty I have to express the integral in terms of function...
  5. A

    Fourier series representation of delta train

    The Fourier series of a delta train is supposedly (1/T) + (2/T ) Ʃcos(nωt) ... where T is period and ω=2*Pi/T ...but when I plot this, it doesn't give me just a spike towards positive infinity, but towards negative infinity as well (see attached pic), so this does not seem to converge to the...
  6. J

    Kinematic Equation vs. Delta velocity / Delta Time - Factor of 2?

    I am testing a cylindrical piece of steel dropping down steel pipe in a vacuum system, and came across a problem comparing the kinematic equation and a standard change in velocity over change in time to determine an acceleration. My derivation shows that the kinematic equation is exactly 2...
  7. N

    Laplace transform of the dirac delta function

    Homework Statement L[t^{2} - t^{2}δ(t-1)] Homework Equations L[ t^{n}f(t)] = (-1^{n}) \frac{d^{n}}{ds^{n}} L[f(t)] L[δ-t] = e^-ts The Attempt at a Solution My teacher wrote \frac{2}{s^{3}} -e^{s} as the answer. I got \frac{2}{s^{3}} + \frac{e^-s}{s} + 2 \frac{e^-s}{s^2} + \frac{2e^-s}{s^3}
  8. D

    MHB What is the moral of conflicting definitions of the Heaviside function?

    Integrating the delta function: $$ \frac{4}{\pi^2}\int_0^{\pi}\int_0^{\pi}\delta(x - x_0,y - y_0)\sin nx\sin my dxdy $$ Would the solution be $\frac{4}{\pi^2}\sin nx_0\sin my_0$?
  9. D

    Laplace Transform of Delta Function

    Homework Statement Evaluate the Laplace transform: L{δ(t-∏)tan(t)} Homework Equations The Attempt at a Solution L{δ(t-∏)tan(t)} = ∫ δ(t-∏)tan(t) dt evaluated from 0 to ∞ =tan(∏)e-∏*s = 0 Could someone check my work on this one? I'm suspicious that my transform is just zero...
  10. M

    Significance of delta in expressions.

    Can you always put numbers directly into an expression which has the delta triangle against its variables? For example Faraday's Law is always shown with the delta triangle on top and bottom yet these are dropped when you use it for calculations; which leaves me wondering why they are there in...
  11. T

    Eigenvalues and Eigenfunctions for a Delta Potential Well

    Homework Statement Consider this situation, V(x)=λδ(x) ,-a<x<a. V(x)=∞,x>a or x<-a. How to find the eigenvalue and eigen wavefuntion of the Hamiltonian. Homework Equations i can only reder to stationary Schrodinger equation. The Attempt at a Solution when it is ouside the well(x>a...
  12. F

    Laplace transform, sum of dirac delta

    Homework Statement Homework Equations I really wish they existed in my notes! *cry*. All I can think of is that integrating or in other words summing the dirac delta functions for all t, would be infinite? None the less the laplace transform exist since its asked for in the question and i...
  13. PeteyCoco

    Does this epsilon delta limit proof check out?

    I started learning how to do these things today and boy, they take some interesting logic. Anyway, here's my attempt at one: prove that the limit as (x,y) → (0,0) of [(x^2)(siny)^2]/(x^2 + 2y^2) exists Here's what I did: 0<√(x^2 + y^2) < δ, |[(x^2)(siny)^2]/(x^2 + 2y^2) - 0| < ε...
  14. M

    'Theta function' setting conditions similar to delta function?

    Hi, I'm reading through a paper and have come across what my tutor described as a 'theta function', however it seems to bear no resemblance to the actual 'theta function' I can find online. In the paper it reads: \int^1_0 dz~\theta (s-\frac{4m^2}{z}-\frac{m^2}{1-z}) And apparently this...
  15. R

    ,CFD Simulation of Delta Wing: Questions & Guidance

    I am trying to perform a CFD simulation of a 70 degree sweep Delta Wing at different angles of attack (aoa = 20, 25, 30, 35 degrees). The inlet flow is at 25m/s. I have made a spherical Far-field boundary with the sphere radius of 5 times the root chord length of the delta wing. Because of the...
  16. F

    Prove limits using epsilon delta definition

    Homework Statement http://store2.up-00.com/Sep12/JB498124.jpg 2. The attempt at a solution No attempts because i can't understand how to solve it
  17. R

    Fourier analysis: Impulse Symbol(dirac Delta Function)

    1. what is the even part of δ(x+3)+δ(x+2) -δ(x+1) +1/2δ(x) +δ(x-1) -δ(x-2) -δ(x-3)? 2. δ= 0 x≠0; ∞ x = 0 1/2 (f(x) + f(-x)) 1/2 (f(x) - f(-x)) Knowing the piecewise definition of the delta function, and knowing 1/2 (f(x) + f(-x)) for even parts of a function. I plug this in...
  18. D

    Solving ODE with Heaviside Step and Delta function

    Homework Statement Find the solution of the equation: α(dy/dt) + y = f(t) for the following conditions: (a) when f(t) = H(t) where H(t) is the Heaviside step function (b) when f(t) = δ(t) where δ(t) is the delta function (c) when f(t) = β^(-1)e^(t/β)H(t) with β<α Homework...
  19. D

    Solving ODE with Heaviside Step and Delta function

    Find the solution of the equation: α(dy/dt) + y = f(t) for the following conditions: (a) when f(t) = H(t) where H(t) is the Heaviside step function (b) when f(t) = δ(t) where δ(t) is the delta function (c) when f(t) = β^(-1)e^(t/β)H(t) with β<α My try for all 3 are as follow: 1...
  20. G

    What Do the Lowercase Deltas Stand For?

    Hi! I've got a problem with understanding notation in this lecture: http://www.youtube.com/watch?v=FZDy_Dccv4s&feature=BFa&list=PLF4D952FA51A49E66 For example, at 00:44:13, what does all lowercase deltas stand for? He writes: δA=∫(∂L/∂q)δq + (∂L/(∂q dot))δ(q dot) Why lowecase delta? What...
  21. H

    Complicated delta function integral

    Homework Statement Hi guys ,please look at the integral on the attachement.Does anyone have seen this integral before ? Homework Equations We have the following two properties : ∫δ'(x-x0)f(x) dx =-f'(x0) δ(x^2-a^2)= {δ(x-a) +δ(x+a)}/2a The Attempt at a Solution Please help...
  22. M

    Infinitesimals in integration vs delta x in summations

    Hi, I first had a question regarding infinitesimals. What does it mean when the infinitesimal is at the beginning of the integral? For example: ∫dxf(x) is this the same as ∫f(x)dx ? My second question was how to convert a summation to an integral and a summation into an integral...
  23. O

    Multivariable epsilon delta proofs

    Homework Statement lim (x,y) -> (0,0) xy/sqrt(x^2+y^2) = 0 The Attempt at a Solution my understanding of my actual goal here is kind of poor given ε>0 there exist ∂>0 s.t. 0 < sqrt(x^2 + y^2) < ∂ then 0<|f(x,y) - L| < ε | xy/sqrt(x^2 + y^2) - 0 | < ε (xy * sqrt(x^2 + y^2)) /...
  24. M

    Epsilon Delta Limit Definition

    Homework Statement Prove lim x--> -1 1/(sqrt((x^2)+1) using epsilon, delta definition of a limit Homework Equations The Attempt at a Solution I know that the limit =(sqrt(2))/2 And my proof is like this so far. Let epsilon >0 be given. We need to find delta>0 s.t. if...
  25. T

    Electric Dipoles using Dirac's Delta function

    Homework Statement In the lectures, we considered a dipole, made of two charges ±q at a separation d. Using Dirac's δ function, write the charge density for this dipole. Evaluate the charge (monopole moment), dipole moment, and quadrupole moments Q, p, and Qij in the multipole expansion...
  26. K

    Why we haven't any connection other than Delta or star in 3phase

    why we haven't any connection other than Delta or star in 3phase
  27. J

    Normalization to delta distribution

    Do you know some example of an operator, other than momentum or position, that has (at least partially) continuous spectrum with eigenvalues s, and the corresponding eigenfunctions obey (\Phi_s,\Phi_s') = \int \Phi_s^*(q) \, \Phi_{s'} (q)~ dq = \delta(s-s')~? EDIT For example...
  28. F

    Help with heat equation dirac delta function?

    Homework Statement The question was way too long so i took a snap shot of it http://sphotos-h.ak.fbcdn.net/hphotos-ak-snc7/397320_358155177605479_1440801198_n.jpg Homework Equations The equations are all included in the snapshotThe Attempt at a Solution So for question A I've done what the...
  29. C

    Why Delta PE is Negative Work: Understanding the Relationship and Derivation

    Can someone prove that the change in potential energy is negative work. I have a very basic understanding of the concept. I do not understand where it is derived from.
  30. A

    MHB Prove that lim sin(x)/x = 1 as x goes to 0(Epsilon delta )

    Prove that \lim_{x\rightarrow} \frac{\sin x}{x} = 1 Solution Given \epsilon > 0 want to find \delta such that \left|\frac{\sin x}{x} - 1 \right| < \epsilon for x, |x | < \delta can I use Taylor expansion of sinx ? but Taylor is an approximation of sin(x) around a certain point ...
  31. S

    How do you find delta X using Voy and Vox?

    Homework Statement How do you find delta X with Voy and Vox? Ex. Problem: Vox = 25.202 Voy = 12.097 Vo = 27.95 ∅ = 25.62° Δx = ? Homework Equations I think Kinematic eq. 2 is supposed to be used in this problem, Δx = Vot + 1/2 at^2 The Attempt at a Solution With Video analysis I was given...
  32. H

    Kroenecker delta δ question

    Homework Statement kroenecker delta has one upper and one lower index. except from uppper index and lower index,we have 2 slots for the upper index and 2 slots for the lower index(for a 2 index tensor). Why krenecker delta left or right slot index position doesn't matters? Also why 2 two...
  33. B

    How Does the Kronecker Delta Function as a Substitution Operator?

    Homework Statement http://postimage.org/image/s7m1kohst/ Homework Equations The Kronecker Delta = 1 ; if i=j The Kronecker Delta = 0 ; i (not equal) j The Attempt at a Solution I have no idea what to do from here, or even if I did this first step right...
  34. C

    Proof of lim(1/x) x->0 by negating epsilon delta definition of limit

    Homework Statement I want to show that \lim_{x \rightarrow 0}\frac{1}{x} does not exist by negating epsilon-delta definition of limit. Homework Equations The Attempt at a Solution We say limit exists when: \forall \epsilon > 0, \exists \delta > 0 : \forall x(0< \left| x\right| < \delta...
  35. U

    Validating a Delta Sequence

    Homework Statement Show that \delta_n(x) = ne^{-nx} \quad \mathrm{for}\quad x>0 \qquad = 0 \quad \mathrm{for}\quad x<0 satisfies \lim_{n\longrightarrow\infty}\int_{-\infty}^\infty \delta_n(x)f(x)\mathrm{d}x = f(0) The attempt at a solution The hint says to replace the upper limit...
  36. S

    Dirac delta function / Gibbs entropy

    Homework Statement This is an issue I'm having with understanding a section of maths rather than a coursework question. I have a stage of the density function on the full phase space ρ(p,x); ρ(p,x) = \frac {1}{\Omega(E)} \delta (\epsilon(p,x) - E) where \epsilon(p,x) is the...
  37. C

    Delta dirac function of (x^2)

    Hi I would like to know what is the dirac delta function of x^2, I read somewhere it is equal to delta of x itself but why?
  38. M

    Why we use strictly less than delta and epsilon in definition of limits

    Homework Statement I'm wondering why we can't use less than or equal to for the formal definition of the limit of a function: Homework Equations lim x→y f(x)=L iff For all ε>0 exists δ>0 such that abs(x-y)<δ implies abs(f(x) - L)<ε Why not: lim x→y f(x)=L iff For all ε>0 exists...
  39. F

    Can the Dirac Delta Function be Applied in Curved Space?

    The Dirac delta function is defined as: \int_{ - \infty }^{ + \infty } {\delta (x - {x_0})dx} = 1 Or more generally the integral is, \int_{ - \infty }^{ + \infty } {\delta (\int_{{x_0}}^x {dx'} )dx} But if the metric varies with x, then the integral becomes, \int_{ - \infty }^{ + \infty }...
  40. B

    Divergence of 1/r^2; delta dirac's role

    Homework Statement Given \nabla\frac{1}{r}, show \nabla\bullet\nabla\frac{1}{r} = -4πδ(r), where δ(r) is the delta dirac function.The Attempt at a Solution I've used divergence theorem and also solved the equation itself, so I know that outright solving is zero and the divergence theorem gives...
  41. O

    Proof involving Dirac Delta function

    Prove that x \frac{d}{dx} [\delta (x)] = -\delta (x) this is problem 1.45 out of griffiths book by the way. Homework Equations I attempted to use integration by parts as suggest by griffiths using f = x , g' = \frac{d}{dx} This yields x [\delta (x)] - \int \delta (x)dx next I tried...
  42. T

    Epsilon delta proofs equaling a constant

    Homework Statement Lim x→a of f(x) = c (Where c is a constant) Homework Equations The Attempt at a Solution I have no idea. I am able to do these if I can manipulate fx-L to equal x-a but I am having trouble with this one. Please help me!
  43. D

    Need help with epsilon delta proof of f(x)=x^4+(1/x) as x goes to 1

    Homework Statement Determine the limit l for a given a and prove that it is the limit by showing how to find δ such that |f(x)-l|<ε for all x satisfying 0<|x-a|<δ. f(x)=x^{4}+\frac{1}{x}, a=1. Homework Equations I claim that \lim\limits_{x\rightarrow 1}x^{4}+\frac{1}{x}=2. The...
  44. D

    Epsilon delta proof that x^4 goes to a^4 as x goes to a

    Homework Statement Determine the limit l for a given a and prove that it is the limit by showing how to find δ such that |f(x)-l|<ε for all x satisfying 0<|x-a|<δ. f(x)=x^{2}, arbitrary a.Homework Equations I will incorporate the triangle inequality in this proof.The Attempt at a Solution We...
  45. Z

    Finding the largest value of delta greater than 0

    Homework Statement For f(x) = sqrt(27-x), L=4, x_0 = 11 epsilon = 1, find the largest value of delta > 0 in the formal definition of a limit which ensures that |f(x) - L| < epsilon Homework Equations the formal def. of a limit: lim x->x_0 F(x) = L if, for every number epsilon > 0...
  46. X

    Evaluate expression with permutaion symbol and Kronecker delta

    Homework Statement Evaluate the following expression: \sum_{j}\sum_{k}\epsilon_{ijk}\delta_{jk} Homework Equations \delta_{ij} = [i = j]The Attempt at a Solution I don't have a solution attempt to this one yet, because somehow I completely missed out on what the permutation thing has to do...
  47. X

    Evaluating expression involving permutation symbol and Kronecker delta

    Homework Statement Evaluate the following expression: \sum_{j}\sum_{k}\epsilon_{ijk}\delta_{jk} Homework Equations \delta_{ij} = [i = j] The Attempt at a Solution I don't have a solution attempt to this one yet, because somehow I completely missed out on what the permutation thing...
  48. F

    Solving Epsilon Delta Proof: lim 3 as x->6 & lim -1 as x->2

    Homework Statement lim 3 as x->6 lim -1 as x->2 Homework Equations In the first weeks of a calculus class and doing these epsilon delta proofs. As i am looking at two of the problems i have been assigned: Lim 3 as x->6 Lim -1 as x->2 The Attempt at a Solution...
  49. M

    Eigenvalue of position operator and delta function.

    I'd like to show that if there exists some operator \overset {\wedge}{x} which satisfies \overset {-}{x} = <\psi|\overset {\wedge}{x}|\psi> , \overset {\wedge}{x}|x> = x|x> be correct. \overset {-}{x} = \int <\psi|x> (\int<x|\overset {\wedge}{x}|x'><x'|\psi> dx')dx = \int <\psi|x>...
  50. B

    What is the value of the integral of a delta function over a finite interval?

    Problem arises from next situation. If we have some distribution (of mass for example) on a ring which is given by \begin{equation} \rho=m\delta(\phi) \end{equation} where phi is azimuthal angle. What is the value of integral ? \begin{equation} \int_0^{2\pi} \! \rho \, \mathrm{d}...
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