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.
Say 2 cars are traveling side by side at 10 m/s in some flat, wide open space. Relative to each other they are stationary. Relative to someone on the ground they are both moving at 10 m/s. Now say you're in 1 of the cars and you see the other car accelerate, changing his velocity by 10 m/s in...
What's actually details in difference of any cooking oil (vegetable, palm oil, etc) before and after exhaustive/heavy cooking ?
As only heard not clear or reliable folks' says, the many unsaturated bonds turns to be saturated afterward..
The need arose as it's quite affirmed that the former is...
A general free field Lagrangian in curved spacetime (- + + +), is given by:
L = -1/2 ∇cΦ ∇cΦ - V(Φ)
when the derivative index is lowered, we obtain:
L = -1/2 gdc∇dΦ ∇cΦ - V(Φ)
then we can choose to replace V(Φ) with something like 1/2 b2 Φ2 so:
L = -1/2 gdc∇dΦ ∇cΦ - 1/2 b2 Φ2
** I will...
Hey! :giggle:
From two populations of small and medium enterprises, we collect two random and independent samples of size $n_1 = 64$ and $n_2 = 36$ enterprises respectively. If we calculate for the companies of the first sample average sales of $9$ thousand euros and a variation of $4$, while...
Hello,
I'm seriously confused on several things around how concretely
batteries create potential difference in order to force the electrons
circulate trought the circuit wire.
Almost all explanations I found (wikipedia, diverse tutorials, intro scripts, etc.) explain it in nearly
the same...
Let's discuss whether the energy under a finite difference (FD) scheme is conserved. Take the simplest vibration eq mx''+kx=0, which one will use a FD scheme to solve. The energy is mx'^2/2+kx^2/2. Whether the energy is conserved doesn't depend on the FD scheme for the ODE but upon the FD scheme...
What is the difference between an absolutely continuously differentiable function and a wave? Are all absolutely continuously differentiable equations waves?
is this method accepted?
2V is split equally between the 2 5kohms resistor because they are of equal resistance.
2V=5kohms
2kohms= 0.8V
3kohms=1.2V.
p.d across P and Q= 1V-0.8V=0.2V
Hello, can anyone help me out with this?
If i want to lift an object that weights 100kg and I am going to do it with a 101kg of force (990,81 N ).
Then my acceleration would be;
a = F/m
a= 990,81N / 101kg = 9,9081 m/s2
but gravity is pulling it down so then I am acually accelerating it with...
My attempt:
I think ##x## is the path difference so by using trigonometry, I got ##x=d \sin \theta##
But my teacher said the answer is ##d \cos \theta##
What is my mistake? Thanks
Edit: Sorry, I found my mistake. My ##x## is not the path difference
I understand phase voltage (phase to neutral) well, but I'm still confused by what exactly the potential difference is between any 2 phases in 3 phase power. If you were to try to find the potential difference where 2 sine wave phases cross, then at that instantaneous point, the potential...
When we have a resistor in electronic conductors, potential difference is created via surface charges which accumulate on conductor surface.
What about electrolytes?
I am not sure if electrolytes can create potential difference in the same way since surface in electrolytic conductors isn't as...
Hello!
I need to calculate the limit of this function ## f(x) = (x^2-9)*e^{-x}## for + and - ## \infty ## Now for + infinity I did this
$$ \frac{(x^2-9)}{e^x} $$ apply L'Hospital since we have infinity divided by infinity; $$\frac{2x}{e^x} $$ Apply L'Hospital again $$ \frac{2}{e^x} $$ the...
Molecules and superconductors bind due to overlaps of the wave functions of the electrons.
1. What is the difference between these two then?
2. Why can't we look at molecules as a macroscopic wave function?
I am practice stick fighting for self defense. I have a question I don't know how to judge. Say if I have a 6oz and a 12oz stick both 28" long. I swing them to hit an object, assuming I have the same strength, obviously the velocity is faster with the lighter stick and slower with the heavy...
I have found the difference in the magnitude from the counts to be -.073 using -2.5log(11347/10606) but I m unsure if this is right or how to calculate the uncertainty
I was watching a video about jet engines, and it was obvious for me and for the instructor that if we compress air at high speed from the gas turbine inlet, then after multiple stages collide with the turbines blades inside, the body will move in the sense of difference in velocity, so forward...
Hello Community,
i have BLDC motor with General parameters are 3 Phase motor with 4 Poles, 36V, 7.3A rated current, 4000RPM rated speed.
you can check datasheet on link below
The first question is how many Pair of Poles does this motor have? 2 or 4?
For example the motor bellow...
Read the book and conducted research on the internet. Came to conclusion that this was an isolated system because the girl was being accelerated by gravity but answer is non isolated. Can someone please help me grasp this concept better.
This is the analytical working out. I substituted the value of 306mm ( the maximum length of the beam) to find the maximum deflection along the Z-axis. Which came out to be -2.39mm. But according to Ansys the average deflection is 0.3mm and the maximum deflection is 0.8mm.
This is the Ansys Values.
The 2 Bowling Balls
Ball(a) & Ball(b)
(a) is in acceleration of 10m/s^2
(b) is in at fixed position in a gravitational field where g=10m/s^2
In both cases the observer is:
- perpendicular to the vector of acceleration
- distant enough to be in empty flat space
Question : In an instantaneous...
I did (1300)(9.81)(0.67) and got 8544.51 N/m^2 but unsure if that was the correct route to take. Please confirm or deny if I was approaching it in the correct way!
Hello,
I was wondering if someone could help clarifying this question.
The question asks to estimate the energy state difference between the vibrational ground state of S0,v=0 and the first excited vibrational ground state S0,v=1 of the spectra below.
The given solution: S1,v=1 -> S0,v=1 at...
I tried following the formula but it wasn’t correct. I’m sure I could get it if I had an example as I’m sure this must be a simple question for other people I was just unsure if I was doing it correct.
Attempt at solution:
I wanted to try and solve this with dimensional analysis. I reasoned that I would chose the following dependent variables:
- [V] : Volume ( of the block)
- [Q] : Heat ( the radioactive decay would cause some heating of the water)
- [R]: Radiation
- [Cv]: Heat capacity...
I am working on an equation that is supposed to model two dependent variables Y and Z using four parameters a, b, c, and d (for regression) and a single independent variable X. What I am doing is that given a set of values for X, I am going to regress a, b, c, and d to fit Ycalc and Zcalc to...
I have no clue how to do this, so I did my best guess of it.
Friction is μN, N being the normal force.
The normal force when it is in contract with the pole should be V2/R, R being the radius of the pole.
So ΔT = μV2/R
The answer provided is μTΔθ
Homework Statement:: Discuss the limitation of the Explicit Finite Difference Model.
Relevant Equations:: no formula
Hello there, I have to discuss the limitations of using the Explicit Finite Difference model to calculate a 2D Heat Diffusion through an aluminium place, however, I really...
We have to submit a Matlab (my worst module) assignment to show the heat transfer on a plate. However, I have the 2 codes almost done but I am struggling to write the report. To calculate the temperature on a 2D aluminum plate we need to use the Explicit Finite Difference Method. The problem...
[Moderator's note: Spun off from a thread in the QM forum to separate out the interpretation discussion.]
Yes, but I was hoping that you could give a precise specification of the difference. (In my opinion, @vanhees71 never specified the difference precisely.)
I want to locate an infrared signal using Angle on arrival (AoA), I have elected to use Phase Interferometry to achieve this, I am however struggling to understand how the phase difference (∆ϑ) is found. Can someone explain how I could find this?
They say wave function is different to quantum field. Then what is the difference between EM wave and EM field?(By the way :Is that EM wave the wave function of photons?).It seem to me EM wave is the wave of EM field?
I am struggling with tensor notation. For instance sometimes teacher uses
\Lambda^{\nu}_{\hspace{0.2cm}\mu}
and sometimes
\Lambda^{\hspace{0.2cm}\nu}_{\mu}.
Can you explain to me the difference? These spacings I can not understand. What is the difference between...
Emf between the center of the disc and its rim
= ##- \frac{d \phi}{dt }##
= ##-B.A \frac{d \cos (\omega t)}{dt}##
=##\mu_0 \frac{N}{L} I A \omega \sin (\omega t)##
Potential difference across the ends of the solenoid = ##10\mu_0 \frac{N}{L} I A \omega \sin (\omega t)##
Is this correct? How to...
Just recently, I finally upgraded my 7+ year old computer. I was able to find a good deal on a HP Omen, with a Geforce RTX 2060 graphics card.
So, not only was I able to upload the latest build of Blender, but I was able to go back and tweak some renders I had done with the old computer.
For...
Hi everyone,
I'm currently working on the problem listed above.
I'm pretty new to electrodynamics, and I'm learning on my own through a book. I was wondering if someone can please help me through this problem. Here are my thoughts:I think I need to use Faraday's Law of Induction for part (a)...
I'm trying to prove the associative law of symmetric difference (AΔ(BΔc) = (AΔB)ΔC ) with other relations of sets.
A naive way is to compare the truth table of two sides. However, I think the symmetric difference is not a basic one, it is constructed form other relations, that is AΔB =...