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.
Hello! I just started reading something on differential geometry and I am not sure I understand the Difference between diffeomorphism and homeomorphism. I understand that the homeomorphism means deforming the topological spaces from one to another into a continuous and bijective way (like a...
I would like to know the difference between this two concepts, specially the difference between the geometry deformations of space-time that they descript. As far as I know the Schawrzschild metric can be represent by Flamm’s paraboloid, but this shape is not the same that the deformation of...
Hi. This might be really basic. But I am really struggling to grasp the difference between electrical currents such as AC and DC and RF. For the case of AC current, it alternates currents at a certain frequency.. which makes me wonder how AC and RF are different.
Also, if you could, could you...
when the external electrical potential difference is applied across the conductor ,electrons flow in the direction opposite to the current.Whether the number of free electrons in the conductor decrease?
Homework Statement
What is the heat generated on closing the switch?
Homework EquationsThe Attempt at a Solution
[/B]
On closing the switch, the potential difference across each capacitor should change which would cause it to charge and hence cause heat loss through the capacitors.
But...
Hello! I hope someone could help me to solve mu doubt, I am very confused and I don't find answers in internet. My question is about pendulums. I know the angular frecuency of a pendulum is give by the equation w= sqrt(g/L). But also i know the angular velocity (also named with "omega") can be...
I have a little question. I want to know if there is a process in which I can find equilibrium solutions to some system of difference equations. For example, if I have something crazy like
$$\begin{cases} x[n+1]=(x[n])^2y[n]+z[n]e^{-ax[n]} \\
y[n+1]= z[n]x[n]+x[n+1]y[n+1]\\
z[n+1]=...
In my goal to self study up to Calculus, I've utilized the very useful Insights page on what books are best for a real intuitive understanding in basic high school mathematics such as Algebra, Geometry, Trigonometry. I purchased all the recommended books and I was wondering what some of the...
Hello Guys...
I know this is simple but this two concepts confuse me a lot. Like in vacuum distillation Pressure is reduced to increase the difference in boiling point between two components and steam distillation is where steam is introduced in the mixture to reduce the vapor pressure. So what...
I= Current flowing
V1= Voltmeter 1
V2= Voltmeter 2
My question is that if there would be any difference between the readings of V1 and V2?
We know that: By Ohm's law: V= I.R
also:
Combined resistance of R1 and R2 will be:
1/RCombined Resistance of R1 and R2= 1/R1+1/R2
The reading in V2...
Homework Statement
Homework EquationsThe Attempt at a Solution
[/B]
A)
Mean velocity is defined as <v> = total distance traveled/ total time taken = πR/Γ = 0.5 m/s
B) How is part a) different from part b)?
I think what Irodov means by mean velocity is mean speed in part a.
It is mean...
Homework Statement
A transverse wave that is propagated through a wire, is described through this function: y(x,t) = 0.350sin(1.25x + 99.6t) SI
Consider the point of the wire that is found at x= 0:
a) What's the time difference between the two first arrivals of x = 0 at the height y =...
1. Amazon link: https://www.amazon.com/dp/0131118927/?tag=pfamazon01-20
ISBN: 978-0131118928
This is the book that my class syllabus suggests based off ISBN number, however it is $119.00 to buy off Amazon.
2. Amazon Link: https://www.amazon.com/dp/1107179866/?tag=pfamazon01-20
ISBN...
Homework Statement
In the circuit shown, what is the potential difference VPQ?
Homework Equations
No relevant equations given in question
The Attempt at a Solution
Tried kirchhoffs law.
Tried to find equivalent battery and resistance but that doesn't seem to be possible.
Hey guys,
I am having issues with understanding the physical nature of pure and mixed states. Maybe you can help me out?
1) A pure state - superposition is a state that consists of different states at the same time. It's like having several waves, each one belonging to an Eigenstate of the...
This is about signal processing, moving averages & superposed / standing waves. This is an online system: causal (univariate) time series analysis.
Suppose you have a sinusoid of period n (i.e. n=40, so its frequency is 0.025). If you calculate a "weighted moving average" (WMA) on this sinusoid...
Hello! I am reading some introductory stuff on Klein-Gordon equation and I see that the author mentions sometimes that in a certain context the K-G equation "is a classical field equation, not a quantum mechanical field equation". I am not sure I understand. What is the difference between the...
In quantum mechanics there is a no cloning rule, so you cannot have two things that are exactly the same. So that must mean that all particles are different. So what kind of unique properties can individual electrons or protons have?
Homework Statement
A battery of emf 2V and internal resistance 0.1ohm is being charged with a current of 5 ampere.
In what direction will the current flow inside the battery?What is the potential difference between the two terminals of the battery?
Homework Equations
If a battery of emf E and...
What is the correct way to expand (p3-p4)2 where p3 and p4 are 4-vectors, with metric gmu nu=diag[1,-1,-1,-1], p = [wp, p], where p is 3-vector, and wp= (p2+m2)(1/2)
I was wondering what the differences are between CMS and ATLAS when it comes to their channels. I know they detect for the H →γγ, H → 4l, H → eνμν channels, but I was wondering how they differ in their detection for these channels.
I was also wondering if there were any noticeable...
Hello. I am inquiring about how a pressure difference between a hot room (roughly room temperature) and a cold room (roughly the temperature of a standard refrigerator) can cause a force inside the cold room when exposed to its hotter counterpart. More specifically, I would like to apply this...
Hello! I read in my complex analysis book that holomorphic and analytic "do not always mean the same thing", but in the complex plane they do. In which case they don't mean the same thing? More specifically what does holomoprhic function means outside the complex plane (such that you can define...
See the Wikipedia article on Penrose-Hawking singularity theorems: https://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems.
It says that
A singularity in solutions of the Einstein field equations is one of two things:
1. a situation where matter is forced to be compressed to a...
Hello! I see that all theorems in complex analysis are talking about a function in a region of the complex plane. A region is defined as an open, connected set. If I am not wrong, the real line, based on this definition, is a region. I am a bit confused why there are so many properties of the...
Factor x^6 - y^6 as a difference of cubes.
Solution:
(x^3 - y^3)(x^3 + y^3)
I now proceed by applying the difference and sum of cubes accordingly, right?
Factor x^6 - y^6 as a difference of squares.
Solution:
(x^3 - y^3)(x^3 + y^3)
The problems states to use the difference of squares.
I can apply the difference of cubes to the left factor and the sum of cubes to the right factor but how do I continue using the difference of squares?
So I know that linear mixed models model has coefficients that are fixed and random. From what I understand, the fixed coefficients are still good since the random slopes/intercepts capture between subject heterogeneity. Which I suppose help estimate the crossectional effects better( i.e the...
Wikipedia's article on rifles in the American Civil War mentions this:
Is it true that smoothbore guns have a flatter trajectory than rifles? Can someone explain the physics of why that would happen?
Factor (a + b)^3 - 8c^3.
Is this the difference of cubes?
Formula:
x^3 - a^3 = (x - a)(x^2 + ax + a^2)
Let x = (a + b)
Let a = 8
(a + b - 8)((a + b)^2 + 8(a + b) + 64)
Correct?
and Homework Statement
Ok, so I am doing As physics at the moment and have been left confused by stationary waves.
I have read that between adjacent nodes/ even numbers the phase difference is always 0 and between numbers of does it is pi radians. So in the attatched image why is my textbook...
In
https://en.wikipedia.org/wiki/Galilean_transformation
it is shown that translation is different from uniform motion.
So, isn't translational motion another name for uniform motion?
Hello there,
I'm confused on several things such as the potential difference it provides and how it pushes the charges through the wire or conductor or circuit.
So when a battery comes into contact with a wire, the positive charges flows from high potential through the circuit to the low...
What is the difference between valence factor and n-factor for oxidants and reductants? Take ##H_2O_2## as an example. What is the difference between the n-factor and valence factor for this compound?
Also, how do I find the n-factor for any oxidant or reductant?
Hi. I am trying to simulate this paper since apparently I have a lot of time.
Scrolling down to the last page, he simulated a transient 2D heat conduction plate with composite slabs on it. Darkest one is copper, lighter one is steel, lightest one is glass.
If you look closely, the authors said...
Q1:
So I'm trying to extract the electrical properties of a single phase induction motor. First off, how am I supposed to measure the phase difference between the start and run windings? I have L and R of start and run windings too!
Q2:
I have a torque vs slip curve up until 130% of rated load...
We have a good cholesterol (HDL) and bad cholesterol. It just occurred to me that do we have a similar thing in glucose too. Good glucose after a proper digestion and bad glucose in improper digestion?
Homework Statement
There are two similar atmosphere ISA +30C and ISA tropical Maximum, they have identical:
Mean Sea level conditions, same basic shape of temperature profile and same lapse rate in troposphere. The difference is the altitude of the tropopause and hence a different temperature...
Hi, the solution of my exercise says that the potential difference in the capacitor C1 is zero.
Can you please explain me why it's the case ?
Thank you.
Homework Statement
Create two 5x5 arrays, A & B, and ask the person to fill them out. Save those numbers in matrix_a.txt & matrix_b.txt respectively. Then, save the sum and difference of those numbers in sum.txt & diff.txt respectively.
Basically we need to create two arrays, fill them out...
Homework Statement
An inductor (Xl = 40.2 ohm) is connected in series with a resistance (30 ohm) and and an AC source ( 10V , 80Hz) and the current flows in this circuit is 0.2 amp. How could you reduce the phase difference between current and voltage to zero without changing the value of...
Homework Statement
The article “Variance Reduction Techniques: Experimental Comparison and Analysis for Single Systems” (I.Sabuncuoglu,M. Fadiloglu, and S. Celik, IIE Transactions, 2008:538–551) describes a study of the effectiveness of the method of Latin Hypercube Sampling in reducing the...
Homework Statement
State the phase relationship between
x and y
x and z
(shown in photo)
The Attempt at a Solution
I got the phase difference between x and y to be 135 degrees and then between x and z to be 45 degrees. However the mark scheme gives the answers 180 degrees and 0 degrees. Please...
Hello! I am not really sure I understand the idea of tensors and the difference between them and normal matrices, for example (for rank 2 tensors). Can someone explain this to me, or give me a good resource for this? I don't want a complete introduction to GR math, I just want to understand the...
Hi guys,
I am a little confused on the difference between an Algebra and a vector space. I´m guessing there´s a fairly simple distinction. Any guidance would be much appreciated, I accept both hand wavy and hardcore axiom based responses :)
Cheers
So I have this PDE:
d2T/dr2 + 1/r dT/dr + d2T/dθ2 = 0.
How do I implement dT/dr || [r = 0] = 0? Also, what should I do about 1/r?
This is actually the first time I am going to attack FDF in polar/cylindrical coordinates. I can finite-difference the base equation fairly decently; I am just...
Hello everyone.
Iam trying to get my head around the difference between real and complex numbers, but Iam having a hard time...
I read that the difference is that a complex signal contains phase information.
If I look at a real signal --> x(t) = Acos(wt + Θ)
and compare...