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.

View More On Wikipedia.org
Recent contents Top users
  1. Jonathan1218

    Mathematical difference between permutation&combination

    I know to calculate a combination with n options and r selections while repetition is allowed you are supposed to do (n+r-1)! / r!(n-r)! and the purpose of r! as a denominator is to act as a ratio to eliminate same outcomes but of different orders and is what makes us calculate the combination...
  2. P

    I Tachyon and antiparticle difference

    What is the difference between tachyons and antiparticles?
  3. HCverma

    What's the difference between neutral and stable?

    What's the difference between neutral and stable? As an example of H2. Here two H atoms combine and make an H2 molecule. Now two H atoms are neutral as they have the same number of protons and electrons. So the H2 molecule is neutral. on the other hand. Two H atoms combine through a covalent...
  4. J

    B When Difference between Kelvin and Celsius are negligible

    This question is more for practicality than anything else, and I realize it may be partly subjective. At what temperatures can the 273 degree difference between Kelvin and Celsius scales be ignored? I'm thinking for examples regarding stars and very high temperatures. Surely once you get to 15...
  5. J

    I Difference between an electromagnetic field and a photon?

    So I'm kind of confused. The way I understand it, an electromagnetic field is just a regular electric field viewed from a relativistic point of view, meaning that since we see the charges moving relative to us, we feel like the particles and the fields created by them come closer together (I...
  6. HCverma

    What is the difference between 'equivalent' and 'equivalence'?

    What is the difference between 'equivalent and equivalence'?
  7. lordlarddallas

    Potetial Difference between center and point r

    Homework Statement A cylindrical conductor of length L and radius R, L » R, carries a charge Q. 1. Neglecting boundary effects; evaluate the potential difference between a point at distance r from the center of the cylinder, and the center. Assume r to be of the same order of magnitude as R but...
  8. Krushnaraj Pandya

    Potential difference across capacitors

    Homework Statement The figure shows part of a complete circuit. The potential at point A is greater than that of B by 19 volts what is the potential difference in volts across the three microfarad capacitor? Homework Equations All relevant to electric circuits The Attempt at a Solution From...
  9. T

    Difference between Vav and Vrms

    Homework Statement [/B] I encountered this problem during my exam. A coil of 50 turns, each with area 0.02m2 is rotated in a uniform magnetic field of magnitude 0.4T. The coil is rotated at a frequency of 60Hz. Given the average power generated is 50W, what is the resistance of the...
  10. S

    Difference between angular velocity and angular frequency

    I have seen so many questions and confusion about the difference between angular velocity/speed and angular frequency. Usually, answers were always given in the context of uniform circular motion (angular speed) and simple harmonic oscillation (angular frequency), but this is what causes the...
  11. R

    Difference between color / temperature?

    What is the difference between a red object at room temperature and a heated red object (Metal for example). They are both red except one is cooler then the other? Why aren't the red objects in my room not hot like the heating of a metal?
  12. R

    Potential difference between charged parallel plates

    So we know that the E-field between two parallel plates is constant and that the potential difference between the plates is just the E-field times the distance between the plates. Let's say we're moving a positive charge from a negatively charged plate to a positively charge plate ( or near)...
  13. Krushnaraj Pandya

    Potential difference in uniform electric field

    Homework Statement There is a uniform electric field=100 V/m inclined at 45 degrees with the x axis. My doubt boils to which is greater? V(0,0) or V(10√2,0) (since my answer has the wrong sign) Homework Equations All electrostatics formulas The Attempt at a Solution The work done to move a...
  14. Quentin_alex

    What could be causing this microstructural difference?

    Hello, I have two rebar samples of virtually identical chemical composition of 0.27 wt%C, 1.2 wt%Mn and 0.033 wt%V that are A706 grade. The rolling mill parameters are essentially the same yet I am seeing differences in pearlite size upon microscopy. The billets used to make the bars are...
  15. M

    Difference between flash point, fire point and self ignition temperatures

    Is there any difference between setting petrol on fire directly(by contacting it with burning stick) and heating petrol in a vessel, increasing its temperature above itself ignition temperature and making it burn spontaneously? What is the difference between flash point,fire point and self...
  16. HCverma

    Difference between 1 mole of CH4 and 1 molecule of CH4?

    Is there any difference between 1 mole of CH4 and 1 molecule of CH4? or they mean the same thing?
  17. F

    A What is the difference between second quantization and QFT?

    Please teach me the difference between second quantization and QFT?
  18. D

    Binary Representation: Log or Ln?

    What is the difference between log and ln?? [Thread moved to General Math forum by moderator]
  19. S

    I Difference between parallel and antiparallel spins?

    What is the difference between parallel and antiparallel spins for a pair of nucleons? My understanding is that nucleons have a strong tendency to pair - proton with proton, neutron with neutron, proton with neutron. When they pair their spins either: cancel (spins pair antiparallel) pairing...
  20. S

    I What's the difference between Euclidean & Cartesian space?

    What's the difference between Euclidean & Cartesian space?
  21. M

    What is the difference between nozzle (or a ventury) and flow control valve?

    In both the cases, the flow cross section area of the pipe is reduced.But in case of nozzles the velocity increases,pressure reduces and the flow rate is maintained.But in case of flow control valve, flow rate changes.(Assuming the fluid to be incompressible) Why is there a difference between...
  22. M

    Throttle Valve vs Carburetor: Exploring the Difference

    In carburetors, at the throat or ventury, the area decreases and so velocity of air increases (by continuity equation.).This is reason for suction of fuel from the float chamber.But in case of throttle valve, when the valve closes(area of flow reduced), the quantity of air fuel mixture passing...
  23. avner yakov

    What the difference between pin and pn diodes i-v curve?

    For my understanding there should be no big difference in i-v curve between regular p-n junction and p-i-n junction, the only difference i can think about is do to the bigger resistance of the intrinsic layer. The curve should look the same only the current will rise little bit slower, because...
  24. Chris Lyddon

    What's the difference between pushing/lifting a weight?

    Hi, I am working on a project where the normal process has been to push a single linear plain away from a given area. I am now considering lifting the single linear plain away but wondered about the physical dynamics when comparing pushing to lifting something. In the image:- A. Represents...
  25. Kenneth Boon Faker

    B What is the difference between a wave and a field?

    I've been reading about Quantum Field Theory. It strikes me that since the 1920's, physicists have changed the name "wave" to "field". I can't tell the difference between today's "fields" and what was described a "wave" in quantum theory in the early 1900's. So in quantum physics, is there a...
  26. S

    I Difference between Constructive proof and Existential Generalization?

    What is the difference between Constructive Proof of existence and Existential generalization? Logically they seem to be the same because, for a given predicate and specific member of the predicate's domain, you are concluding the general statement about the predicate.
  27. Ravik Rocha

    Difference between real and virtual objects? (optics)

    I do know the difference between real and virtual images. I would like to know the difference between real and virtual objects. I need some examples. See this picture
  28. opus

    Please explain the difference between these fractions w/ radical

    Homework Statement For the solution to a given problem, in the second to last step I had: ##-\frac{\sqrt 6}{4} + \frac{\sqrt 2}{4}## I stated next that the solution was ##-\frac{\sqrt{6}+\sqrt{2}}{4}## I was told this was incorrect and that the correct solution is...
  29. J

    I What is the Difference between the lottery and QM?

    It seems to me that so far in quantum mechanics, because we have yet to establish probability patterns for, say, what the spin of a photon is, we have made it some mystical thing that we can only know by measuring it. I don't really buy that; is the result of a lottery impossible to know until...
  30. H

    Difference between two vectors

    Homework Statement In most problems involving projections I'm given a vector and the equation of a line either in parametric form or in symmetric form (ie. parametric: <0t+3, -t-4. 3t+2> or symmetric form: x=3, (y+4)/-1, (z-2)/3). However, when asked to use these in a problem I get confused...
  31. C

    Calculating Electric Potenial Difference

    Homework Statement In a TV tube, an electric potential difference accelerates electrons from a rest position towards a screen. Just before striking the screen, the electrons have a wavelength of 1.0 x10-11m. Find the electric potential difference.[/B] Homework Equations λ = h/mv Ek = qΔV The...
  32. K

    Intro Physics Difference Between 3rd and 10th Editions of Halliday/Resnick?

    Hi, So I'm trying to self-study AP Physics C and found the first volume of Halliday/Resnick's Fundamentals of Physics on my parent's shelf, 3rd edition (from 1988). They also have the 2nd edition of University Physics, volume 2 (E&M). I do, however, have a copy online of the extended 10th...
  33. M

    A copper wire and an iron wire - Potential difference

    Homework Statement A copper wire and an iron wire of equal length l and diameter d are joined, and a potential difference V is applied between the ends of the composite wire. Calculate the potential difference (in volts) across the iron wire. Assume that l = 2.00 m., d = 0.30 mm., and V = 156...
  34. N

    Electric Potential Difference Problem

    Homework Statement Two charges, A (-3 C) and B (+4 C), are placed 2.40 m apart. Point X is 30 cm from A, and Point Y is 30 cm from B. What is the electrical potential difference going from X to Y? Homework Equations W = △Vq The Attempt at a Solution Teacher gave answer as 6.9 x 10^4 V I am...
  35. M

    Kinetic Energy vs Flow Work: Exploring the Difference

    As per work energy principle, the energy spent in moving an object is stored as kinetic energy.Flow work is done to make the fluid move.Why is it not included in kinetic energy (i.e) why kinetic energy and flow work are considered seperately?
  36. F

    I Difference between A and B irreps

    In my understanding, in group theory the one-dimensional irrep A differs from the one-dimensional irrep B in the symmetry under rotation about the principal axis: A is when the state is symmetric and B is when the state is antisymmetric under that rotation. However, I find in the character...
  37. A

    How Is Electric Potential Difference Measured Without Specific Distances?

    Hello, I'm struggling to understand how the electric potential difference is measure especially when a distance is not given. For instance in Serway, on the explanation of the Van de Graaff Generator the authora write, "Van de Graaff generators can produce potential differences as large as 20...
  38. Mr Davis 97

    I Find the constant value of the difference

    I know that the following two functions have the same derivative: ##\arctan (x-1)## and ##2 \arctan (x-1 + \sqrt{(x-1)^2+1})##. Out of curiosity, how can I find the constant value at which they differ? I tried to add ##\pi / 2## to arctan(x-1) but I'm not sure if that works or not...
  39. J

    Difference between diluting and adding

    Homework Statement Place 20.0 g NaOH(s) in a flask and dilute to 1.00 L with water. Place 20.0 g NaOH(s) in a flask and add 1.00 L of water. How exactly do these two statements differ? Wouldn't adding 1.00L of water to 20.0g of NaOH dilute it anyways? Homework Equations none? The Attempt...
  40. K

    I Difference between Schrodinger's equation and wave function?

    Is there a difference between Schrodinger's equation and the wave function? In the beginning of the second edition by David J. Griffiths he compares the classical F(x,t) and Schrodinger's equation and I am having trouble understanding the connection.
  41. caters

    Difference between cast iron and high carbon steel?

    I don't understand the difference between cast iron and high carbon steel. They both are an iron-carbon alloy and they both have a high amount of carbon within the iron metal. Both will oxidize at the same rate without a coating to protect the metal. Stainless steel will oxidize, it just takes...
  42. Mr Davis 97

    I Explanation for parity difference for # of simple graphs

    http://oeis.org/A000088 This is a list that gives the number of simple graphs on n unlabeled vertices. Could someone conversant in graph theory explain why the number of simple graphs on 4 unlabeled vertices, which is 11, is the only one that seems to be odd (nontrivially), while the rest seem...
  43. C

    Find the phase difference (in radians)

    Homework Statement In a Newton's rings apparatus, find the phase difference (in radians) when an air wedge of 500nm thickness is illuminated with red light (lambda = 640nm). t = 500nm lambda = 640nm radians = degrees × pi / 180° Answer) 13 Homework Equations 2pi x path difference / lambda...
  44. T

    B Gravitational difference between a black hole and a star

    How come the gravity of a stellar- mass black hole is strong enough to trap light but the gravity of a stellar-mass star (eg the sun) is not strong enough to trap light ?
  45. Simonel

    I The difference between a family of sets and an indexed family of sets

    What is the difference between family of sets and indexed family of sets ??
  46. P

    Finite difference conjugate heat xfer: internal flow

    Hi. I have been trying to solve this problem that has been keeping me up at night for a coupe weeks at least. If anyone can help me, I would be greatly appreciated. Hot air enters a cylindrical duct. The duct has some R-value and radiation and convection is being accounted for on the outside...
  47. A

    Is there an Entropy difference between a cold and hot body

    Hello, If two bodies, who say start with ##T_{cold}=T_c## and ##T_{hot}=T_h## and then they are brought in contact with one another and then after some time they both have the same temperature. What would be the entropy of the entire system? Also another quick question, I've looked at some...
  48. axer

    Calculating Potential difference (X Ray tube)

    Homework Statement If the electrons hit the tungsten target with an energy of 75 keV, find the potential difference. Homework EquationsThe Attempt at a Solution I tried this: (W=eV) V=W/Q V=eV/Q V=75,000/1.6*10-19 V= 4.6*1023 V, This seems wrong because all examples in my...
  49. Ranku

    I Gravitational difference between a black hole and a star

    A star or a planet is a material object, while a black hole is an 'immaterial' spacetime object. Does the material or 'immaterial' nature of an object make any difference in how it curves or travels through spacetime as it manifests gravitation (apart from the powerful gravitation near a black...
  50. S

    Difference between emission due to absorption and reflection

    What is the difference between the photon interaction mechanisms in emission due to absorption and reflection?
Back
Top