# 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.

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1. ### I One difference between GR and quantum mechanics

I wanted to ask about a potential difference between general relativity and quantum mechanics phenomena - that we are observing them at different moments in time. Because causality has a speed limit (##c##), every point in space where you observe it from will be the closest to the present...
2. ### Phase difference between two light waves of the same frequency

the diagram. i found that the phase difference between them is 100º but how is the answer 260 can someone please explain?
3. ### Inversion of Control: OS vs Software Development | Explained

Hi. What is the difference between Inversion of Control in Operating system and IoC in Software Development? Thanks.
4. ### Difference between -3² and (-3)² ?

What is the difference between these to. -3² and (-3)² ? I know - x - = + I am told -3²= -9 not +9 -3² means -3 x -3 = 9 I am told (-3)² = 9
5. ### I What is the distinction between invariance and covariance?

What is the difference between these two concepts? An equation is said to be "invariant" under some operation if the form of the equation doesn't change. However, isn't that exactly what "covariance" in physical laws means—that the form of the laws remains unchanged when applying an operation to...
6. ### My Python Library For Finite Difference Method

I recently made a Python library for modelling (very basic) finite difference problems. The Github readme goes into details of what it does and how it works, and I put together a Google Colab with some examples (diffusion, advection, water wave refraction) with interactive visuals. I'd love to...
7. ### Potential difference between 2 points in a capacitor circuit

In the given circuit, a transient current will flow and when this current finally stops at equilibrium, the charges ##q_1## and ##q_2## are assumed to deposit at the capacitor plates as shown below. The dashed line indicates an isolated system that will have it's total charge conserved. If I...
8. ### Difference between Boss seal industrial vs military fittings SAE specs

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9. ### Difference between "usermod -aG" and "usermod -G" options in linux?

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10. ### B The Difference Between Wavefunction & Superposition: Exploring Photon Behaviour

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11. ### B Entropy & Information Content: Examining the Difference

What does entropy in the following sentence means? Does it mean the same as the term "information content" before it? Is entropy more technical a term than information content? He remembered taking a class in information theory as a third-year student in college. The professor had put up two...
12. ### Does the absence of the term "valley" make a difference?

TL;DR Summary: the peaks and valleys vs. the peaks A. He felt this interminable wave was an abstract view of the universe: one end connected to the endless past, the other to the endless future, and in the middle only the ups and downs of random chance—without life, without pattern, the peaks...
13. ### Experiment about diode related to temperature and potential difference

(a) I know some of the apparatus needed for the experiment, such as DC power supply, ammeter, voltmeter, maybe rheostat. But I don't know how to change the temperature of diode. What is the correct and safe way to change the temperature of diode? Thanks
14. ### I Electric potential and potential difference

Electric potential = "absolute potential" Textbooks usually connect both ends of two capacitors, of different voltages, in parallel. What would happen if we only connect one end of the capacitors? Perhaps we would have to solve for Maxwell's coefficients of potential for these two cases (to...
15. ### What is the pressure difference?

TL;DR Summary: Which gas has a higher pressure and why? School has provided answer which I disagree. Like to hear comment from others.
16. ### A Need help implementing finite difference method for BPM

I am trying to apply finite difference scheme for Beam propagation method by following this paper. I was wondering if anyone can share their code if they have implemented this method. I can share my code which is not working as expected and can get some insights if possible.
17. ### Calculating ΔE Difference for 2 Samples of Monatomic Ideal Gas

Question: Two samples of a monatomic ideal gas are in separate containers at the same conditions of pressure, volume, and temperature (V = 1.00 L and P = 1.00 atm). Both samples undergo changes in conditions and finish with V = 2.00 L and P = 2.00 atm. However, in the first sample, the volume is...
18. ### Proof of angle in path difference formula for two slits

For this I am trying to prove that angle theta between PQ and QO is equal to theta highlighted so that I know I can use theta is the path difference formula. I assume that the rays ##r_1## and ##r_2## are parallel since ##L >> d## My proof gives that the two thetas are equal, however I am...
19. ### Studying Huge difference in the cost of education in UK and Germany

I have searched for almost all courses and all universities and found that the fees of universities in UK is more than 10 times than those of Germany (if I were to convert both of those national currencies in my country's currency). Had education been some market product, I would have instantly...
20. ### B Quantum Connection vs Entanglement: What's the Difference?

quantum connection vs. quantum entanglement Do they mean the same? Are there any differences? Is the second one more common/newer/more standard than the first one? Could someone please answer these questions or recommend something to read?
21. ### Are lost volts the difference between EMF and terminal potential difference?

Are lost volts the difference between EMF and terminal pd?
22. ### Finding charge on a capacitor given potential difference across two points

For this part(b) of this problem, The solution is However, I tried solving (b) like this: Since ##Q_{total} = 363 \times 10^{-6} C## then ##Q_1 = 181.5 \times 10^{-6} C ## since the equivalent upper capacitor is in series with the equivalent bottom capacitor so should store the same amount...
23. ### Finding the potential difference in a circuit

The solution chooses the centre wire to determine the potential difference, where Va−(0.909 A)(2.00 Ω)=Vb and Vb - Va = -1.82 If I choose the top wire (passing through the 12 V battery and 4 Ω resistor), Va - 12 + (1.636 A)(4.00 Ω)=Vb, and Vb - Va is different (= -5.46 V). Why would this path...
24. ### Acceleration of Uranium 238 ion through a potential difference

I don't understand why the Uranium 238 ions are accelerated I think ##\Delta V = -2000 V## to accelerate since the ion would be accelerated by more postive charges so ## V_i > V_f ##
25. ### Heat loss from the temperature difference

Hello, My house has some heat loss. As an example I know the outside door temperature. How can I calculate the heat loss delta if I reduce the door temperature by 1 degree? I know that there is a formula to calculate a heat loss based on the U-value of a fabric. But I can't get those values...
26. ### Vote for a PhysicsForum member who made a difference

There is still time to vote for PF members who made an impact in 2022. Vote for up to 3 members in each category. https://www.physicsforums.com/forums/2022-pf-member-awards.363/
27. ### The Difference in Paths: Exploring Central Force & Gravity

When we throw a ball in a projectile motion, the ball follows a parabolic path due to gravity. And we see that earth moves in an elliptical path around the sun due the same force of gravity. So why two paths are different due to the same force? Explain using the idea of central force
28. ### Am vs Fm variable capacitor receiver, what is the difference?

What is the difference between a variable capacitor in a AM receiver and a variable capacitor in a FM receiver? I understand that Am is amplitude modulation and that the signal is carried over a changing amplitude and that the frequency is constant. And the opposite in FM signals. And a variable...
29. ### Difference between average position of electron and average separation

Hi, I asked this question elsewhere, but I didn't understand the answer. It seems to be easy to understand, but for some reason I'm really confuse. I'm not sure how to find the average position of an electron and the average separation of an electron and his proton in a hydrogen atom. To be...
30. ### Finding time difference between two arriving wave fronts

For part(b), The solution is, However, where did they get the formula shown in red from? Many thanks!
31. ### Difference between Granite in different grades

Hi guys, There are different grades of Granite (grade 0, 00 and 1). From what I have researched online, the grades are defined by the flatness tolerance. I would like to know besides of flatness, is there any differences in its material properties in different grades? I'm not familiar with the...
32. ### Difference between scalar and cross product

Hi! For example, how do you tell whether to use the scalar or cross product for an problem such as, However, I do know that instantaneous angular momentum = cross product of the instantaneous position vector and instantaneous momentum. However, what about if I didn't know whether I'm meant to...
33. ### I Is there a difference between an ultracool dwarf and a brown dwarf？

After reading the introduction of ultracool dwarf and brown dwarf in Wikipedia, I can't see the difference between them. Besides, do they all belong to the main sequence stars?
34. ### Can’t tell the difference between a “good” school and a top 5 private school

I’m not sure what I was expecting to be honest. Definitely not an entire campus population of geniuses but I’ve spent the past 2 months here (albeit as a research tech taking grad classes, not a student) and I guess I was expecting to, I dunno, be humiliated with everyone’s brilliance as well as...
35. ### Order of Magnitude Difference: Solving with Torricelli & Bernoulli

Solving with Torricelli I get Vt = 6x10^-3 m/s Solving with Bernoulli I get Vt = 6x10^-4 m/s, a whole order of magnitude smaller. How can it be correct? I know that Torricelli is an approximation, but the solution given by the book uses Torricelli which doesn't seem right to me.
36. ### I Time difference caused by length contraction

The goal is to calculate the difference in the passage of time between two ends of a cabin which is accelerating upwards due to length contraction. To help in the calculations we can consult: https://arxiv.org/pdf/1807.05338.pdf There is an old problem called the 4/3 problem which has been...
37. ### B Phase Difference of Current & Voltage: Capacitors, Inductors & Complex Numbers

how does capacitors and inductors cause phase difference between current and voltage? how does complex number come into play to explain the relation between phase of current and voltage?
38. ### What is the difference between TIC and alkalinity?

Hey there, What is the difference between Total Inorganic Carbon (TIC) content and alkalinity? When I am reading it says that the TIC consists of: - H2CO3 / aquous CO2 - HCO3- - CO32- And it says that alkalinity consists of all acid-neutralizing compounds, portayed as CaCO3, but consisting...
39. ### I Difference between Working distance and object distance

So I have a problem understanding the difference between working distance and the object distance of a lens. For me it is also unclear what the difference between image distance and back focal length. If I want to enlarge the image by 6. How can I calculate the focal length, object distance...
40. ### I Difference Between Lorentz Transformation & Special Relativity

Sorry for the extra question. Just have a lot of questions lately and I know some people around here are annoyed with that.
41. ### Computing for Dummies Q: What is difference between server and data center?

I've been looking this up and don't seem to have a great understanding. Can someone confirm or correct that my understanding is accurate. Is a data center simply a large collection of individual servers? If not, how do they differ? Thanks.
42. ### I Is electromotive force always equal to potential difference?

In the case motional emf, there is a static magnetic field and a rectulgular loop that goes into the field region, then current is produced. There is no electric field, but there is an emf. However, Griffiths states that emf is equal to the potential difference between the source endpoints. But...
43. ### I Difference between relative risk and odds ratio

Hello! I was studying odds ratio and its relation to relative risk. By what I understood, the statistics that is indeed important for us and that have a nice interpretation for the context is relative risk (I was also wondering if odds ratio has any interpretation). But relative risk sometimes...
44. ### I What is the difference between the resistance force and the friction coefficient?

Hi I have been wondering what is the difference between resistance force and friction coefficient. While doing research online I could not find a clear answer. Maybe someone here will now:bow:
45. ### What is the difference between DFT and TD-DFT in Gaussian 09 software?

Homework Statement:: difference between DFT and TDDFT in Gaussian 09 software? Relevant Equations:: hello , I hope this message finds you well Please I want to know what is the difference between DFT and time‐dependent density functional theory TD-DFT and why we use it in the measurement of...
46. ### B Differences in Predictions between SR and LR?

SR interpreted as having no absolute frame of reference and an absolute frame type version of SR, where the speed of light is isotropic only in one undetectable frame are considered equivalent, since they use the same math. But here is a scenario in which I don't see how the physical predictions...
47. ### I Difference Between Locally Flat & Locally Inertial?

Are they equivalent to each other?Thank you.
48. ### MHB Difference of angles in a triangle

In a triangle ABC, let D and E be the intersections of the bisectors of the angles ABC and ACB with the sides AC and AB, respectively. Knowing that the measures in degrees of the angles BDE and CED are equal to 24 and 18, respectively, calculate the difference in degrees between the measures of...
49. ### A Range of Difference: Bounds for Length of Stay

Ok, so I'm given hotel data :{Arrival Date, Departure Date}, each in terms of nth day of the year , and I want to estimate whether the range/difference, aka, the length of stay is below a bound. Say a week ( 7 days) for definiteness. I'm thinking of using either the distribution of the range...
50. ### MHB What is the difference between activity and event in "simulation"?

I am studying about components of a system. Activity-: It is What entities do to cause changes is activity. It is represented by time period of a specified length. Event-: Event is defined as an instantaneous occurrence that might change state of the system. Endogenous events occurs within...