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.
Hi today I was watching a demonstration of using explosives in demolition and emergency rescue and they did one where they wrapped explosive cord around a steel I beam and cut it in half then said this was a shearing force which sounded right to me but then they took a concrete post similar...
Homework Statement
What is the difference between the Centre of Pressure and Centroid
Homework EquationsThe Attempt at a Solution
My understanding is that the centre of pressure acts on a centroid. So, how come they can be on different positions for a submerged surface?
Hi guys,
I consider the qm-derivation of the electronic states of hydrogen.
There are two different derivations (I consider only the coulomb-force):
1) the proton is very heavy, so one can neglect the movement
2) the proton moves a little bit, so one uses the relative mass ##\mu##
The...
I am simulating electrons inside a cylindrical well like the one shown on the first figure.
My current work has been on solving the Schrodinger equation numerically for the above potential and then finding corrections to the solution such that it is consistent with Poissons equation.
To do so...
What is the difference between scalars and one-dimensional vectors? I know that we represent the set of all two-dimensional vectors as ##\mathbb{R}^2##, so doesn't this mean that we would represent the set of all one-dimensional vectors as as just ##\mathbb{R}##? However, doesn't this also refer...
Homework Statement :[/B]
Determine whether there exists an integer x such that x^2 + 10 is a perfect square.
Homework Equations :[/B]
N/A
The Attempt at a Solution :[/B]
Assume x^2 + 10 = k^2 (a perfect square).
Solve for x in terms of k:
x = ±sqrt(k^2 - 10)
Since k is an integer and k^2 -...
Hi,
I have written some codes for the finite difference solution of diffusion equation (\frac{\partial c}{\partial t}= D {\nabla^2 c}, where c is the species concentration and D is the diffusion coefficient) as follows:
DO k= 1, tsteps+1
DO i = 2, zsteps
DO j = 2, rsteps...
Homework Statement
I've attached a url with a picture of the problem setup and diagram
https://instagram.com/p/7nYNXTscre/
Homework Equations
I used the equation V = KΣiqi/ri to solve for potential at A and B
The Attempt at a Solution
For Va I used K((Q/d)+ (2Q/(d^2+d^2)^.5))
I just plugged...
It is my first time learning about power in circuits. From reading my electric circuits text, I understand that when current enters the positive terminal of a circuit, power is being "absorbed" and when it enters the negative, it is "supplied". The book doesn't really go in depth on what those...
The problems states: An inverted hemispherical bowl of radius R carries a uniform surface charge density σ. Find the potential difference between the north pole and the center.
I was able to do the problem and got the correct answer the book gives, which is (Rσ/2ε0)(√2 - 1). My professor...
I am trying to solve the following eigenvalue differential equation numerically:
∇2ψ = Eψ
, where the coordinate system is polar coordinates and the boundary condition is ψ(R,Φ)=0, where R is the radius of the disk i am working on.
To solve it I am using a finite difference scheme, but there...
When I connected the positive terminal of the battery to one terminal of the bulb and the other terminal (of the bulb)to the ground the bulb did not glow, even when a potential difference exists?
Electricity travels from higher potential to lower potential then why don't we get an electric shock while holding aa high potential wire without touching the Earth ( we are also at lower potential)
In difference between column the second point says one talks about similarity and the other of size.I think there should be term"smaller "or "similar" (point is both should mention the same thing)
please guide
Hello Forum,
Consider a simple DC circuit composed of a battery (say 2V), conducting wires and a single resistor R=2 Ohm
The potential difference across the resistor will be exactly 2V only if the wires were superconductors (zero resistance). But wires do have some small finite resistance so...
When an neutrino is observed, it becomes a point particle, but it has mass. Is that mass not concentrated into a point? Why doesn't it collapse down to a micro black hole? What's the difference between a neutrino and a micro black hole of the same mass? I know it has 1/2 spin and other...
1)I am confused why do we take vectors along y-axis and x-axis in motion on a plane? What's essence of learning vectors functions.
2)And in textbooks, they have given that motion in a straight line has 2 directions only. Hope many do motion on a plane has?
Please give me simple and detailed...
At some point in the history of technology something happened whereby some devices that operate by electricity became known as "electronic" devices while others remained merely "electric" devices. The latter are obviously simpler, but it's not clear to me where the cut off between the two should...
Hi All
A mathematical structure : is A set with an Object ( structure ) and there are generally two types of mathematical structure , which are algebraic structure and space ( geometric structure )
Eaxmples of algebraic structure are rings , fields , modules vector spaces ... act
Examples of...
Hi PF!
I was wondering if anyone could help me with a finite difference question? The problem I am doing is a 1-D space and time problem, so ##z## (space variable, from left to right) and ##t## (time) are my independent variables and my dependent variable is ##h##, the height, governed by a PDE...
...real science and corporate backed bias.
I've been having a debate over several issues with a, well he works for the same company, but we don't see each other, so I don't know if I should call him a coworker or not.
He refuses to do any fact checking, one recent thing (about 5 mins ago) he...
Hey!
How are the two m=0 spin states (<up,down> + <down,up>) and (<up,down> - <down,up>) physically different? I realize that according to the math, the first one has a total spin of ##2 \hbar## while the second has a total spin of ##0##. But wouldn't you, intuitively, expect both states to...
I know that manifolds are topological spaces that locally look like euclidean spaces near each point of and open neighbourhood
And non-euclidean spaces are the curved spaces or simply don't match the 5th euclid's axiomThanks .
Homework Statement
So i was in a course yesterday and the "teacher" told us the following (which i had a hard time believing/understanding)
There is a load connected to a transformer. Applied potential difference is 230V. The load is malfunctioning and the insulation isn't working anymore. The...
Notion of differentiability (analyticity) for function of complex variable is normally introduced and illustrated by comparison with function of single real variable.
It is stated that there are infinite number of ways to approach any given point of complex plane where function is defined, not...
Homework Statement
A conducting sphere of radius a is surrounded by a neutral conducting shell of radius b (b > a).Connections are provided as shown in diagram. Initially, the sphere has a charge Q. The switch S1 is opened and then closed. The switch S2 is then opened and closed. Finally, the...
I know the two steel grades: M2 tool steel and 1.3343 steels are similar. But the M2 has Mn element while 1.3343 has W elements. what would be the differences with such elements ?
Hello,
recently I became interested in some basics of material science and there was one thing that I did not really understand.
What is the difference (or what are things in common) between creep and strain rate sensitivity?
I read about it in connection with indentation.
- To measure the...
Q6c)
Why is the phase difference between two points in a stationary wave equals to zero?
I understand that a stationary wave is formed by two progressive waves which have the same amplitude, frequency, wavelength and speed, but traveling in opposite directions.
Hello,
How do I take into account the difference in stiffness when fabricating a part (for example, an L-bracket) from sheet metal or using an extrusion?
In particular, where I work, it is "common knowledge" that extrusions are stiffer. How do i factor this in the stress and strain...
Hello everyone..I have some difficulties in understanding the potential difference in a circuit with a transistor. Kindly refer to the picture provided. I understood that potential difference across Ry can be obtained from the formula in the picture. The potential difference across Rx plus Ry...
In case of power transformer,what is the difference between electrical fault and thermal fault?
I want to know that if internal fault is occurred in power transformer then on what basis we can differentiate electrical and thermal fault?
Hey guys, I have a problem that I really have no idea what to do.
It was discussed in class that we do not need to know how to integrate or use the dot product-- any of the complex stuff.
1. Homework Statement
The electric field in a given region in space is given by (3 i - 1 j) x 10^5 N/C...
Homework Statement
If 3000V is applied to the teltron tube with EHT voltage, what would be the potential difference between the parallel plates in the teltron tube?
Homework EquationsThe Attempt at a Solution
Since one end of the plate is positive, the other end is negative, 3000V-(-3000V)=6000V
Homework Statement
Homework Equations
V=IR
W=VQ
The Attempt at a Solution
The answer is B, though I thought that electric potential difference is the ratio of energy to charge? Why is the answer stating the ratio of energy to current instead?
Obviously there are MANY differences, but I'm curious about one in particular.
In an article I read, the creator used NiMH batteries because of their high charge density, but also because they do not require a charge controller and voltage regulator in the circuitry. Why is this, and is there...
The question is based on the image below but is not the same. The question is as follows:
Assume the capacitor is charged, so that there is a charge q on the top plate and a charge -q on the bottom plate. Determine the magnitude of the potential difference across the k2 region, answering in...
This has been causing some confusion to me as the two concepts seem very similar, if not the same (especially when taking special relativity into account).
As far as I understand, even in classical physics (i.e. even before considering QFT and the like), one requires that interactions are...
Sorry... This question may be very basic. As a self taught, I understand that the mass will bend the space around it such that any other mass entering the bent space will immediately be pushed towards the center because of the bent space. Higher the mass, higher will be the bent (if that is the...
A plant cell is usually larger in size. An animal cell is comparatively smaller in size. 2. It cannot change its shape. An animal cell can often change its shape. 3. A mature plant cell contains a large central vacuole. An animal cell often possesses many small vacuoles. 4. Plastids are present...
I understand that Contravariant vectors have an upper index and co-variant vectors use a lower index. But why is one preferred over another in a specific physical situation?
I am just struggling with which form is preferred, and why one would bother trying to raise or lower the index in a...
Hi all,
I am confused about the terms: Vibration, oscillation and waves. Is vibration and oscillation same or are they different?
My understanding is vibration is associated with flexible/deformable bodies and oscillation for rigid bodies. Waves not really having an idea!
Any examples of...