2011年9月26日 · Actually I've never seen that use of it. I'm not saying it's wrong, but it's unusual. But in elementary math texts, [itex]\Delta[/itex]x means the amount of change in the variable x.

2013年1月30日 · δy/δx is the gradient of the line between two ponts on the curve y=f(x) which are close together ∂y/∂x is the gradient of the tangent through a point on the surface y=f(x,z,...) in the direction of the x axis. The lower case delta just indicates a small change - …

2016年7月24日 · The ##\delta x## denotes rather a variation in variational calculus, e.g., in the Lagrange formalism of classical mechanics, where you have an action functional ##A[x]=\int_{t_1}^{t_2} \mathrm{d} t L(x,\dot{x}).## Then ##\delta x## …

2012年5月8日 · The delta function doesn't really have a well-defined meaning outside of an integral, so as far as we're concerned, if integrating f(x) against [itex]\delta(x-a)[/itex] or [itex]\delta(a-x)[/itex] gives you the same result, then [itex]\delta(x-a) = \delta(a-x)[/itex].

2014年4月13日 · But there we have [itex]\delta'(-x)=-\delta'(x)[/itex]. I think if you want to see why the Dirac delta is an "even" distribution is to go back to the definition: [itex] \int_{I(0)} \delta(x) f(x) dx = f(0) [/itex] where [itex]I(0)[/itex] is a neighbourhood of 0. Now let's see what happens if we use [itex]\delta(-x)[/itex] instead:

2012年10月6日 · The Dirac delta is a map whose input is a function and output is the value at the origin. In symbols: ##f \mapsto f(0)##.

2013年9月17日 · Suppose that at time ##t_0## a car starts at a point ##x_0## and travels to point x arriving at time t. Then the average velocity of the car over its trip is ## \Delta x/ \Delta t = \frac {x-x_0}{t-t_0}## -- that is the change in distance divided by the change in time. This tells you nothing about the velocity at any given moment.

2008年3月2日 · Homework Statement I would like to prove that \\delta(ax)={\\delta(x) \\over {|a|}}. My problem is that I don't know how the absolute value brackets arise. Homework ...

2004年10月3日 · It can also be written as dx/dt or delta x/delta t. [meaning velocity is a small change in position per small change in time] a is acceleration. [ how fast the velocity is changing] It can also be written as dv/dt or delta v/delta t. [meaning acceleration is a small change in velocity per small change in time] x(t) is position as a function of time

2004年8月12日 · There is a simple way to settle the issue. The inequality becomes equality for the SHO in its ground state. So if anyone wants to calculate the the standard deviations [itex]\sigma_x=\sqrt{ <x^2>-(<x>)^2} [/itex] and similar for p, …