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.
I am hesitant to write this post. I am a bit overwhelmed that many members have questions of a higher level. They may be reading scientific journals. My question is very basic. I might be called stupid.
Coming to the question. Is angular momentum same as spin of an electron?. But I read that...
I am looking over the supplies on University Wafer until I notice the following:
link: https://order.universitywafer.com/default.aspx?cat=Borofloat%2033%20Glass&diam=100mm
They sell quartz, fused silica and Borofloat glass as different products. I thought quartz and fused silica are the same...
Hello
I have a quarter wave plate for 550 nm but i can't determine which it is a zero quarter wave plate or multiple.
How can I find m in this formula :
delta phase =m*2 Pi +Pi/2
?
Thank you.
Homework Statement
How would i go about finding the electric field and potential difference when there is a constant charge density between the capacitor rather than a vacuum?
Homework Equations
int E dot dA = Qencl/epsilon0
V ab = int E dot dl
The Attempt at a Solution
to be honest I am not...
Homework Statement
Is there any difference between these 2 terms, if yes how are they different?
\begin{align}(\nabla\cdot\nabla\vec A)\vec B &= (\nabla\vec A\cdot\nabla)\vec B\end{align}
Homework Equations
From what i know about dot product, it is commutative, so does this property apply here?
I am trying to figure out the difference between a carbon sink and a carbon reservoir. The definition for a carbon sink from wikipedia is that “carbon sinkis a natural or artificial reservoir that accumulates and stores some carbon-containing chemical compound for an indefinite period. ” And the...
I am trying to figure out the difference between a carbon sink and a carbon reservoir. The definition for a carbon sink from wikipedia is that “carbon sink is a natural or artificial reservoir that accumulates and stores some carbon-containing chemical compound for an indefinite period. ” And...
Gravity causes spacetime to warp. Relative speed also causes an apparent warp from the point of view of the stationary observer.
But warp due to relative speed will cause rods to contract, rods will effectively measure shorter for the stationary observer. Accordingly we should also infer that...
Difference between Calculus 4th edition and Calculus 3rd edition by Michael Spivak?
I currently possesses Calculus 3rd edition by Michael Spivak in it's electronic form. However, I am considering buying a hard copy and have the option of buying either a used 3rd edition or a new 4th edition...
A difference matrix takes the entries of a vector and computes the differences between the entries like
[x1 - 0 ] = difference from 0 and x1: 1 step
[x2 - x1] = difference from x2 and x1: 1 step
[x3 - x2] = difference from x3 and x2: 1 step
assuming we had a vector x in Ax = b
So why now when...
I'm new to quantum physics, and this might be a stupid question. What is the difference between Photons and the Higgs Boson? I know that neither of them interact with the Higgs field. And that when CERN found the Higgs Boson, it decayed into other particles INCLUDING photons. So what's the...
I have a container with one inlet and one outlet. I have the area of the inlet, Ai, velocity vi of the air coming in, and mass flow mi (assume a plane with an air inlet to a bay). I don't know anything about the outlet (just that there is one). What I need to do is calculate the size of an extra...
Inside a conductor, as opposed to inside an insulator, charges are free to move around and reposition themselves, which causes that, if we wait a long enough time, the electric field inside them will be zero.
But in an empty space there's nothing (by definition) that can stop charges from...
At first, we need some state parameters(like P/T/V) to fully describe a system. And the order parameter is also a parameter which could describe the property of the system.
However, in the Laudau theory, why it said that order parameter is an external parameter(not a independent variable)? Is...
On the wiki-pages it says that in the LHC protons travel 3m/s slower than c.
I was curious what it would be for heavy-ions; is it maybe 15m/s because their energy is ~5 x lower (7 vs. 2.76 Tev) ?
And a small question on the side, does Gravitation assistance have a bigger impact on speeding up...
V=Vo √1-(x^2/a^2)
X is the distance of the spring's stretch, but how would you rearrange the equation if you are looking for Amplitude? They both use the same units (meters) as far as I am concerned. Help would be appreciated, thanks; I am still a beginner with Physics.
We studied random walk starting from a probability conservation : p(x,t)=p(x+dx,t+dt)+p(x-dx,t+dt)
Which means the particle can go left or right by dx in time dt.
The solution of the differential equation starting from a delta is a gaussian, which means the particle could go apparently at...
Would anybody pleas tell me what's the difference between fine and coarse measurement? I am reading a paper named "Electronic distance measurement-An introduction" in which fine measurement and coarse measurement is mentioned. here is the exact paragraph:
"The transmitter includes a master...
Homework Statement
Neutrinos with energy of about ##1 GeV## are measured in an underground detector and compared with simulations of neutrinos produced in the atmosphere. Measured flux of upward going muon neutrinos ##(\nu_\mu + \bar \nu_\mu)## is half compared to simulations while measured...
Homework Statement
Our setup:
Connect the transformer to an LRC-series circuit(L= 2mH with iron core,C=1mF and R=10Ω). Use the 2V and 6V outputs of the transformer, the effective voltage supplied by the transformer will then be 2 V.
Use the digital multimeter to measure the effective...
Homework Statement
Find the potential difference Va-Vb between points a and b.
Homework EquationsThe Attempt at a Solution
Each capacitors left plate will have difference amount of positive charge and right plate will have negative charge. After that i don't know how to proceed.
Homework Statement
What is the difference between this statement being expressed in z-notation and the notation shown? What are the benefits of the two and how do you do the conversion?
Nevermind about answering the question itself.
if X ~N(mu,sigma) show that P(|X-mu|<= 0.675*sigma) = 0.5...
i want to know the basic difference between simple harmonic wave and stationary wave.
and also why stationary wave is type of distructive interference.
if stationary wave is a type of distructive interference so why stationary wave exist.
I read in a book "Optoelectronic Integration: Physics, Technology and Applications" edited by Osamu Wada.
Ballistic Conduction and Superconductivity are both electron transport that are not affected by the collisions and scatterings.
Ballistic conduction or Ballistic transport occurs when the...
I only memorized these trigonometric differential identities :
`sin(x) = cos(x)
`cos(x) = -sin(x)
because I can convert tan(x) to sin(x) / cos(x) and
sec(x) to 1 / cos(x) .. etcAnd there is no need to memorize some integral identities such as :
∫ sin(x) dx = -cos(x) + C
∫...
Me and my grandfather got into a "debate" (more like one-sided argument) on whether objects fall at the same rate on Earth independent of air resistance or not. He claims that "If you drop 2 objects from an airplane -- like a car and a marble, both objects would hit the ground at the same...
Homework Statement
Why is is that when we look in a mirror we expect to see a reflection equally as bright as the real image, but when we stand in front of a cliff and clap our hands we don't hear an echo as loud as the original sound?
Homework Equations
R = (z2 - z1)/(z2 + z1)
The Attempt at...
I had these code in this forum but comes out error as below, any suggestion?
Error 1 error C4430: missing type specifier - int assumed. Note: C++ does not support default-int c:\users\username\documents\visual studio 2010\projects\fdm 001\fdm 001\explicit 001.cpp 27
Error 2...
I understand how to do calculations involving potential difference but I've never been able to find any information that helps me understand what is physically happening to cause it.
My assumption is that for a PD to occur, there must be a build up of charge to cause the difference in...
What is the difference between a vector and a vector space? I get that a vector is an object with both magnitude and direction, but am confused by the term "vector space". Does a vector space simply refer to a collection of vectors? Thanks!
In our textbook it is written that -voltmeter measures the electrode potential difference between 2 half cells (in an electrochemical cell) (electrode potential refers to the potential difference between electrode and its salt solution in which it is dipped)
it should come-voltmeter measures...
As far as I know only 2 % of human genome can make the proteins (protein-coding DNA) while the major part of DNA mainly produces mRNAs that regulate other genes (regulatory RNAs).
I would like to know – are these two kinds of mRNAs comparable in size, that is in the amount of their nucleotides...
Was wondering what is the difference between the 2nd and 3rd ed of Physics by Resnick and Halliday?
I know for the most part, at least for mathbooks, the earlier edition the better, and that there is ussually few changes in newer edition.
However, I already own the 2nd edition (Blue Cover) and...
I understand how to find a difference quotient, but afterwards it asks me to then evaluate or approximate each limit, is that just by plugging in the given limit or is there another step?
Homework Statement
In a TV tube, an electric potential difference accelerates electrons from a rest positive towards a screen. Just before striking the screen, the electrons have a wavelength of 1.0⋅10-10. Find the electric potential difference.Homework Equations
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Should I use these...
Homework Statement
A Michelson interferometer is illuminated with a laser with a wavelength of 514.5nm. A Haidinger fringe pattern is photographed with a lens of focal length 55mm. The diameter of the two adjacent circular fringes in the image are 1.53mm and 2.62mm.
How far would the mirror...
Homework Statement
A Michelson interferometer is illuminated with a laser with a wavelength of 514.5nm. A Haidinger fringe pattern is photographed with a lens of focal length 55mm. The diameter of the two adjacent circular fringes in the image are 1.53mm and 2.62mm.
How far would the mirror...
I noticed that uniform continuity is defined regardless of the choice of the value of independent variable, reflecting a function's property on an interval. However, if on a continuous interval, the function is continuous on every point. It seems that the function on that interval must be...
I realize this question has arisen before in the following thread: https://www.physicsforums.com/threads/difference-between-heat-and-work.461711/ but I felt there may be more room for discussion. I feel that the nature of the effect of heat on physical systems is a rather deep one. If the flow...
Homework Statement
I just need help understanding what establishes a positive charge on the top conductor in C1:
http://imgur.com/fppHtMN
My book says that first there is a positive potential difference, Vab
Homework EquationsThe Attempt at a Solution
So since Vab is positive, a is at a...
Homework Statement
Given the following difference equation;
x(k+2)-x(k+1)+0.25x(k)=u(k+2)
where
x(0)=1; x(1)=2; u(k)= 1 for k=1,2,3,…
Homework Equations
Z- transformation
The Attempt at a Solution
To be able to solve this difference equation, I think I need to transform it into z domain...
Hello,
I realized this semester I will receive an A- in Quantum 2 which I am not feeling so happy about. Currently, my major gpa is roughly about a 3.93-3.94 in physics and about a 3.9-3.92 in math. I feel slightly like a failure as I am unable to maintain a 4.0. Do I still have a shot to being...