What is Difference: Definition and 1000 Discussions
A finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.
Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences.
Today, the term "finite difference" is often taken as synonymous with finite difference approximations of derivatives, especially in the context of numerical methods. Finite difference approximations are finite difference quotients in the terminology employed above.
Finite differences were introduced by Brook Taylor in 1715 and have also been studied as abstract self-standing mathematical objects in works by George Boole (1860), L. M. Milne-Thomson (1933), and Károly Jordan (1939). Finite differences trace their origins back to one of Jost Bürgi's algorithms (c. 1592) and work by others including Isaac Newton. The formal calculus of finite differences can be viewed as an alternative to the calculus of infinitesimals.
From the rotation curve of spiral galaxy it is found that the entire mass is not concentrated at the centre but for large distance from the central core it varies linearly with r for which the velocities(rotational) of the objects far from the central core remains nearly constt. and near to the...
Homework Statement
An isolated parallel-plate capacitor of area ##A_1## with an air gap of length ##s_1## is charged up to a potential difference ##\Delta V_1## A second parallel-plate capacitor, initially uncharged, has an area ##A_2## and a gap of length ##s_2## filled with plastic whose...
1. Homework Statement
A proton is released from rest at point B, where the potential is 0 V. Afterward, the proton:
a. Remains at rest at B.
b. Moves toward A with a steady speed.
c. Moves toward A with an increasing speed.
d. Moves toward C with a steady speed.
e. Moves toward C with an...
Homework Statement
Parallel water waves of wavelength 10 m strike a straight sea wall. The wavefronts make an angle 30o with the wall. What is the difference in phases between the waves at two points 5 m apart along the wall?
a. 30o
b. 45o
c. 90o
d. 156o
e. 180o
Homework Equations
Δφ = Δx / λ...
Ok, I am stuck on understanding when to use a part of an equation and when not to.
e = (P/rho) + (Ke/m) + (Pe/m) where P is pressure, Ke and Pe are Kinetic and potential energy divided by mass.
Ok, if we look at P/rho and P is defined as rho(g)(h) then the rho's divide out and we are left...
Homework Statement
A. Two identical speakers, with the same phase constant, are arranged along a 1D track. One speaker remains at the origin. The other speaker can slide along the track to any position x. You are on the track at x=10 m. You hear interference maxima when the adjutable...
Cohererent states are defined as eigenstates of the annihilation operator. Never the creation operator is referred to.
Is this just a convention or is more behind? What is the essential difference between eigenstates of the annihilation- versus the creation operator?
Thank you very much in...
We could have a copper wire at 10,000 V above a copper plate at 0V.
At the end of the wire, one atom of copper. Beneath it: one atom of copper.
What is the difference between the two atoms because of this voltage difference?
Conventionally the current flows from positive to negative. But...
I just got into smart phones, what is the difference between say Samsung J3, J6 or others? I know even in J3, they have different models like the latest is J3-V. The same question can be asked about I-phone 5, 6, 9 and others.
Is J3, J6 equivalent to CPU like I3, I5 and I7? Is the different...
My understanding is that whisky is a distilled product. The "mash" is made of corn, barley, cactus, or other material that is allowed to ferment into ethyl alcohol. Then the mixture is distilled to separate the alcohol from the rest of the mixture. After the alcohol is removed, I believe almost...
In this context the author is deriving the net outflow through 2 surfaces.to do so he is calculating the difference between x components ofthe vector V which is;
so now my question is here the 2 surface are parallel to each other and have same area so their respective x components should be...
Hi guys
I'm into rocks and minerals but I'm not a chemist
I can't really find a definition between ... chemical formula and Idealised chemical formula ?
example below of a mineral sample I purchased a few days ago
part info from ...
https://www.mindat.org/min-3760.html
Chemical Properties of...
I’m understanding that if you prepare a QM system, say 2 electrons in a singlet state and do nothing to the system then when the measurement is made the 2 electrons will still be in the singlet state. If that is true, then I don’t see anything surprising that if Bob measures his electron as up...
Hello all, I'm new to this forum and I'm mucking about with some self-made physics conundrums, and I need some help!
So, What I am aiming for is a roughly cylindrical vessel (it can, and I think probably has to, be tapered to achieve the effect) with the air being pumped out of one end, and a...
Homework Statement
Hi, this is more of a review question and I'm just looking at solutions of natural cubic spline equations and some will give the cubic spline as:
1. s(x) = a + bx + cx^2 + dx^3
on Wolfram
while other pages will give:
2. s(x) = a + b(x - t) + c(x-t)^2 + d(x-t)^3
where...
Homework Statement
My main conceptual issue here surrounds positives and negatives as they apply to electric potential difference. I will post two questions that illustrate my confusion, if that's ok.
1) The electrons in an old TV picture tube are accelerated through a potential difference of...
Hi all,
I am a bit new in this, am trying to learn DE, dynamical systems, & chaos. I am looking into some answers for the following questions:
1) Is it always possible to derive a difference equation for every differential equation, and if so how do we do that?
2) Consider Lorenz system...
Hi guys!
Does anyone know why the lattice parameters of a crystal calculated with PBE-D3 functional are lower than those calculated with PBE?
Thanks in advance! :)
Homework Statement
I'm trying to do a problem two ways, and things aren't consistent, finding the electric potential difference in a linearly varying field.
The electric potential difference between two points is often summarized in texts as ΔV = Vf - Vi = - ∫ E⋅ds where the lower bound of...
Homework Statement
Consider a particle of mass m moving in a one-dimensional double well potential
$$V(x) = -g\delta(x-a)-g\delta(x+a), g > 0$$
This is an attractive potential with ##\delta##-function dips at x=##\pm a##.
In the limit of large ##\lambda##, find a approximate formula for the...
My question here is regarding fracture of materials. I have problems in understanding some concepts. Now, for static loading, there is a property called KIC (fracture toughness). By equating our stress from the static load to this KIC, we get the maximum length of the crack which does not...
The picture above has thrust density as a column and I am not too sure what that is. Can anyone explain to me what the difference between thrust and thrust density? Thank you for your answers!
Is there really much of a difference between an astronomy PhD and an astrophysics PhD? There seems to be a lot of overlap in the fields, and it seems that both can qualify you for many of the same careers, it just depends on the PhD focus.
For an example, I'm very interested in almost all areas...
Could anyone please explain how can I know mathematically whether the logarithmic spiral curve spirals inward or outward? In which sense does the outward spiral spirals?
Thank you very much for your help
I've recently come across this problem:
Answer true or false. If light shines through 2 slits, will the diffraction pattern always be within the interference pattern.
I don't understand this question, however. How can the interference and diffraction pattern be separated in this situation...
Hi all
I was hoping someone could help explain the difference between Young's Modulus and Second Moment of Area.
I know that Young's modulus is a measure of how elastic a material is and is calculated by Stress/Strain.
I know that the Second Moment of Area can be defined as a objects...
Homework Statement
Homework Equations
Finite difference method
The Attempt at a Solution
I have tried two different approaches, but still i am wrong in the question. Can anyone guide me how to attempt this question?
Thank you
What is the basic difference between the following math courses?
Single Variable and Multivariable Calculus
Discrete Math and Applied Math
Euclidean and Non-Euclidean Geometries
Trigonometry and Rational Trigonometry
Linear Algebra and Abstract Algebra
for continues signal (function) we have Bernstein inequality :
$$
|{df(t)}/dt| \le 2AB\pi
$$
where A=sup$|f(t)|$ and B is Bandwidth f(t),
the question is:Is there a relationship for discrete function x[n] like this?
$$
|x[n] -x[n-1] | \le\ \mu\ W
$$
where
$$
X[k] = \sum\limits_{k =...
Define $f(x)=sinx$ on $[0, 2\pi]$. Find two increasing functions h and g for which f = h−g
on $[0, 2\pi]$.
I know that if f is of bounded variation in $[a,b]$, it is the difference of two positive, monotonic increasing functions. However, we didn't do any examples of this in class. Is there a...
Hi All
I am trying to understand a stress / strain curve for a ductile material.
But I am struggling with understanding the difference between the Elastic Limit and the Yield Point. I define these terms as:-
Elastic Limit - Is the point on the stress/strain curve where the material will...
Homework Statement
Derive the relationship bewteen x_{max}, A_{+}, A_{-} and \phi
Homework Equations
x(t) = e^{\gamma t}(A_{+}e^{i \omega_d t} + A_{-}e^{-i \omega_d t})
x(t) = x_{max} e^{\gamma t} cos(\omega_d t + \phi)
The Attempt at a Solution
I know the e^{\gamma t} cancels and for the...
Homework Statement
An Electron with an initial speed of 500,000m/s is brought to rest by an electric field
a)did the electron move into a region of higher or lower potential? I
b) what was the potential difference that stopped the electron?
Homework Equations
ΔV=ΔU/q
ΔU=-W
The Attempt at a...
Homework Statement
What is the speed of a proton that has been accelerated from rest through a potential difference of -1000V?
Homework Equations
ΔV=potential difference
V=U/q
Conservataion of energy
U=qEd (d is distance the proton is moving...i think)
The Attempt at a Solution
Here is my...
This is a gendenke experiment.
You(A) and your friend (B) are on earth. Now your friend sits on a spaceship that can fly at speed of 0.1c. He flies for 5 year straight ahead(away from earth) and then returns back slowly.
The answer that i get is B would have aged. Assuming this answer is right...
Homework Statement
What's the difference between Oxygen Tension And Partial Pressure
Homework Equations
...uh...rules of grammar ?
The Attempt at a Solution
If I knew the solution I wouldn't be here now would I ?
Here are a few links
https://en.m.wikipedia.org/wiki/Blood_gas_tension...
Homework Statement
My textbook is no help, my teacher is no help, so I've found myself here. I am having a difficult time understanding the differences in
1.Electric Potential energy
2. Potential Difference
3. Electric potential
Im sure this question has been asked tons of times but I need...
I am working on modelling of a heat storage tank. More specifically, I need to find out the transient temperature variation through the tank height.
My question is about the plume entrainment considering the case that hot water is injected from the bottom part of a heat storage tank. This...
I’m in an honors calc-based physics 1 course at my college and I can’t audibly understand my professor. I tried looking for tutorials online, but I have no idea if what I’m looking at is calc-based physics or alg-based physics, and I don’t want to learn the wrong methods. Is there a difference...
The potential difference between two points is given ans the negative of integral of E(vector) <dot product> dl(vector) from initial to final points.
Therefore, integral integral of E(vector) <dot product> dl(vector) from initial to final point should give the negative of potential difference...
I want to find the probability density function (pdf) of the difference of two RV's,
p_{\Delta Y} = p_{(Y_1 - Y_2)},where y = \sin \theta, and where \theta_1 and \theta_2 are random variables with the same uniform distribution p_{\theta}=\mathrm{rect}\left(\frac{\theta}{\pi}\right). This has...
Lagrangian Mechanics uses generalized coordinates and generalized velocities in configuration space.
Hamiltonian Mechanics uses coordinates and corresponding momenta in phase space.
Could anyone please explain the difference between configuration space and phase space.
Thank you in advance for...
I couldn't get a good explanation differentiating phase and grain.From what I understood, a collection of unit cells arranged in the same orientation is called grain.A collection of grains with similar structure is called phase.Is this interpretation right?
Homework Statement
What is the Difference between delta G and delta G°?
I have encountered them in various equations but their exact meaning and difference is never mentioned.°
I was reading up on the nature of time and found this: "
In one sense, "time" is the time that is in the equations of physics. That's the t in the equations of the paper, it's the parameter that describes how the states of all systems in the universe change."
Does this explain coordinate time...