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.
There is another topic for this but I didn't quite see it and I don't know how I've gone so far through my course not asking this simple question. So what's the difference?
My thought process for hydrogen. I know it can have quantised values of energy, the energy values are the Eigen values of...
And a cartesian axis system in physics?
I thought about that and my answer is that a cartesian axis system is the same as a inertial frame of reference, is that true?
Moved from non-homework section, so the homework template is missing.
Distance difference between A and B must be 0.25 or 0.75, find length of A and B in any possible value within radius of circle.
Is there a name of theory to find this problem?
here's my try. for A at any point on...
Homework Statement
The electric field in a region of space has the components Ey = Ez = 0 and Ex = (4.00 N/C·m) x. Point A is on the y axis at y = 3.60 m, and Point B is on thex axis at x = 3.00 m. What is the potential difference VB − VA?
Homework Equations
Vb- Vi = -∫ba E * dS
The Attempt...
Homework Statement
Two identical parallel-plate capacitors, each with capacitance 10.0 μF, are charged to potential difference 50.0 V and then disconnected from the battery. They are then connected to each other in parallel with plates of like sign connected. Finally, the plate separation in...
Homework Statement
why the author ignore the pressure difference at point 1 and point 2 in the energy equation ?pressure at pont 1 must be higher than pressure 2 , right ? as the height of P1 is higher
Homework EquationsThe Attempt at a Solution
Homework Statement
Assume an ideal diode with ##V_t=0.6##v, find the potential differences across the diode V_ab and across the resistor V_bc as the forward bias voltage is varied from 0 to 10v. Hint: equivalent circuits may be useful
Embedding the image wasn't working so...
Two different waves are starting froms points A,B respectively and going to a point C such that
$$AC - BC = 2\lambda$$
which corresponds to a phase difference of 4π
AC is given 7λ and BC is given 5λ
Now the second wave(BC) would need to have an initial phase of 4π so that the two waves can...
I believe this question will be a no-brainer for many members. I want to conceptually grasp how do atoms (and molecules) behave using QM in contrast to the classical physics model. Now there's uncertainty principle and atoms don't have a fixed position and momentum, and that's fine, I know it's...
I am trying to build up a kind of mind map of the following:
Module (eg. vector space)
Ring (eg Field)
Linear algebra (concerning vectors and vector spaces, from what I understood)
Multilinear Algebra (analogously concerning tensors and multi-linear maps)
Linear maps & Multilinear maps
The...
Hey all, for a function approximation program t run fast enough i need to solve for where the function (represented by a NDDP) is at a minimum (necessary trust me), althogh I have no idea how to go about differentiating it, i tried to break it up from its's general formula (the pi operators and...
Hey all, since I was programming a polynomial interpolater i found it easier to use the expanded divided difference $$ f[x_0 ,...,x_n] = \sum_{j=0}^{n} \frac{f(x_j)}{\Pi_{k}^{n,j \neq k} (x_j - x_k)} $$ , it works, but I can find no proof, any help/ references appreciated.
Second question: how...
I am currently working on something and I would like to know something. When we connect two tanks and we have water flowing into Tank 1.
Is it possible to make a connection between Tank 1 and Tank 2 so the water level in Tank 2 is higher than water level in Tank 1?
Dear all,
Consider the connection of two electrical circuits. Both circuits, Z1 and Z2, are stable and only one of them is non-passive. I.e., the eigenvalues are located in the LHP but Re{Z2(jw)}<0 in a frequency range.
For studying the closed-loop stability, you represent the linear system by...
Homework Statement
I apologize, this is not really a homework problem. I have an exam coming up, and I need to be able to explain the difference between a stationary/non-stationary quantum state in a qualitative way, and in what cases these states have time dependent probabilities. I am hoping...
say we have some wavefunction |psi> and we want to find the probability of this wavefunction being in the state |q>. I get that the probability is given by P = |<q|psi>|^2 since we're projecting the wavefunction onto the basis state |q> then squaring it to give the probability density.
However...
Homework Statement
Two waves travel next to each other for 100cm.
Wave A passes through a glass container containing liquid. The thickness of the glass in total is 1cm and the width of the liquid is 10cm. The glass has n = 1.52 and the liquid has n=1.33.
Wave B passes through a vacuum and...
I've been trying to figure out why my DC subtraction amplifier is not working, and am completely baffled. I have set up an op amp with no feedback resistors with voltages applied to both the inverting and non-inverting inputs as specified below. I previously had the op amp setup with a 10x gain...
Are spacetime and the gravitational quantum field (still hypothetical) separate entities? Would the gravitational field be more fundamental, one of the various entities from which spacetime as a whole is composed?
Gravitons, which are believed to transmit the force of gravity, would surely be...
Homework Statement
In a Young’s two-slit experiment a piece of glass with an index of refraction and a thickness is placed in front of the upper slit. (a) Describe qualitatively what happens to the interference pattern. (b) Derive an expression for the intensity of the light at points on a...
Pretty much as said; what is the practical distinction between Statistical Physics and Statistical Mechanics? The Wikipedia page for Statistical Physics has Statistical Mechanics as a subsection, but virtually all other subsections just talk about prominent figures, institutions, and...
Homework Statement
Homework EquationsThe Attempt at a Solution
(Sorry my poor English). I just don't understand why should the minimum path difference be 0.75 wavelengths for angles below the centerline instead 0.25 wavelenghts as it is for angles above the centerline.
Homework Statement
Given the electric field E = (2x−y2)ax + (3z−2xy)ay + 3yaz, and the piecewise linear path joining the points A(−2,1,−1), P(2,1,−1), Q(2,3,−1) and B(2,3,1), find −∫E⋅dl from A to P − ∫E⋅dl from P to Q − ∫E⋅dl from Q to B along the straight line segments.
Homework Equations...
I have a difference equation which is given as:
ΔP = e^P [1]
where we can re-write ΔP as: Δ P = P_2 - P_1, where the subscripts indicate two distinct discrete time indices.
What I would like to do: is to convert this into a continuous time expression and solve it, if possible.
In order...
It is said that a coherent light beam is described by a single wave because all the individual waves add up in phase to produce a single big wave.
It is also said that entangled light is described by a single wavefunction...
I believe it is an important topic for us to learn about. There are frequent mistakes, people confuse many times classical correlations with quantum entanglement on their blogs and forums and only peer-reviewed papers give the true answers.
Classical correlations exist between the quanta of a...
Homework Statement
A dipole is centered at the origin, with its axis along the y axis, so that at locations on the y axis, the electric field due to the dipole is given by
E vector = 0, 1/4πε0 * 2qs/y^3, 0 V/m
The charges making up the dipole are q1 = +6 nC and q2 = -6 nC and the dipole...
Homework Statement
In what direction is your friend from the starting point after skiing 3km east and then 1.5km north?
Homework Equations
angle = tan-1(1.5km/3km)
= 26.6 degrees
The Attempt at a Solution
they want the answer in terms of degrees "north of east "
not sure what the rules are...
Matter has a wavefunction associated to it. But what about light? Does it have both a electromagnetic wave described by Maxwell's equation and a wavefunction described by Schroedinger's equation?
Or is the electromagnetic wave considered to be the wavefunction of the photon?
I read somewhere...
1. The problem statement, all variables and given/known dat
What is the difference between Newton's 2nd and 3rd law of motion? Are they related as in if I applied force so that an object accelerates, would it exert the same amount of force towards me?
Homework Equations
F=ma
Hi! I am having problem in understanding the difference between phase and group velocity clearly. In my textbook phase velocity is given by ω/κ while group velocity is by dω/dκ. What is the difference between these two terms?
Thank you!
On Wikipedia, an article appear from which I quoted below. Here is something called Bose-Einstein correlation due to interference of wave character that I confuse with quantum entanglement.
I want to know if these BEC correlations are entangled or separable states...
Hi Experts,
I'm preparing piezo electric generator project, but when I'm searching for piezo disc for my project, i came across different sizes of piezo electric disc, but i didn't found any datasheet,
My question is what's the output voltage/power difference between different diameter...
what is the definition of phase lag and phase difference in waves and how are these 2 related?please explain in simple words and with real life examples.
Please explain phase,phase lag and phase difference from scratch.
One condition for wave interference is that the sources of the waves must be coherent, which means they emit identical waves with a constant phase difference.
I can understand that identical waves means they have the same wavelength. However, I don't understand what is a constant phase...
how to calculate phase difference for spherical waves?how to say whether they are in phase or out of phase?
in sinusoidal we can easily say whether they are in phase or out of phase just by looking at it,but how to do the same for spherical waves?
Okay guys
I am a beginner (in electrostatics as i just started studying it)
I am thorough with kirchhoffs rules/laws
But one thing which bugs me is this doubt
So in the book that i am reading
It says that even if the potential difference is zero,current flows through a wire
I don't get how
I...
what is phase difference and how to visualize it?
i can understand it pretty well for sinusoidal waves,but how to visualize it for other type of waves like spherical waves,plane waves etc?
What is the difference between "Physics" (1 volume, 1156 pages) and "Fundamental University Physics" (3 volumes) by Alonso Finn? Is the former 3 volumes bound as one or a revised edition?
Homework Statement
Q: Two conducting balls of radius 0.1 m are situated 3m apart in free space. Electrons are transferred from one ball to another at a rate of 10^13 per second. How long does it take for a p.d of 100 kv to develop?
Homework Equations
where ε0 is the electric constant...
Homework Statement
Find the potential difference ##V_A– V_B## for the circuit shown in the figure.
Homework Equations
Kirchhoff's laws.
The Attempt at a Solution
If we assign potentials to junctions starting by setting ##A=0## Current ##i_1## flow through each vertical resistances and ##i_2...
Homework Statement
There is a spring with 2 masses with a combined mass of 0.69kg. The vertical oscillation has a frequency of 1.5Hz. The amplitude of the oscillation is 30mm.
Now this spring is attached to a horizontal support rod that can be made to oscillate vertically.
how do i work out...
Homework Statement
When two same lamps are connected with the same battery. Their lighting will be greater when they are connected in series or parallel?
Homework Equations
Series U=U1+U2+U3+...
I=I1=I2=I3...
Parallel U=U1=U2=U3...
I=I1+I2+I3+...
The Attempt at a Solution
The answer is when...
Homework Statement
This is from an exam for my current course in "Mechanics 2", from a couple of years ago, which means that the correct answers are given for checking results, but without further explanations. I'm confused about part (c) where my results do not correspond with the given...
This is a 2 part question and I guess it applies to the brushed case as well.
1.What is the difference between an electronic speed controller (ESC) and a brushless motor controller show below:
ESC:
http://www.robotshop.com/en/lynxmotion-12a-multirotor-esc-1a-bec-with-connectors.html
Brushless...
electrons in terms of absorption.
To move from a lower to a higher energy level, an electron must gain energy. Oppositely, to move from a higher to a lower energy level, an electron must give up energy. In either case, the electron can only gain or release energy in discrete bundles.
Now let's...