Dirac-Delta Functions and Double Integrals

[zheng89120]

Homework Statement

show that $\delta$(x-ct)$\delta$(x+ct) = $\delta$(x)$\delta$(t)

P.S. sorry I mean't:

show that 2C*$\delta$(x-ct)$\delta$(x+ct) = $\delta$(x)$\delta$(t)

Homework Equations

calculus and Dirac-delta properties

The Attempt at a Solution

$$d/dx \int_{-\infty}^x\delta(x-ct)\delta(x+ct) = \delta(x)\delta(t) dx$$

P.S. sorry I mean't:

$$2C*d/dx \int_{-\infty}^x\delta(x-ct)\delta(x+ct) = ...$$

there are a couple of really weird steps that somebody else used after the above

 

[Mark44]

Homework Statement

show that $\delta$(x-ct)$\delta$(x+ct) = $\delta$(x)$\delta$(t)

Homework Equations

calculus and Dirac-delta properties

The Attempt at a Solution

$$d/dx \int_{-\infty}^x\delta(x-ct)\delta(x+ct) = \delta(x)\delta(t) dx$$

there are a couple of really weird steps that somebody else used after the above

Why are you taking the derivative? How is the Dirac delta function defined?

 

[I like Serena]

Hi zheng89120!

Do you know how to calculate for any generic function f(u,v):
$$\iint f(x-ct, x+ct) 2c \delta(x-ct) \delta(x+ct) dxdt$$

And do you also know how to calculate this double integral after a parameter transformation to (u, v), where u=x-ct and v=x+ct?