recategorized by
0 votes
0 votes

The Dirac-delta function $\left ( \delta \left ( t-t_{0} \right ) \right )$ for $\text{t}$, $t_{0} \in \mathbb{R}$, has the following property

$$\int_{a}^{b}\varphi \left ( t \right )\delta \left ( t-t_{0} \right )dt=\left\{\begin{matrix} \varphi \left ( t_{0} \right ) & a< t_{0}< b\\ 0 & \text{otherwise} \end{matrix}\right.$$

The Laplace transform of the Dirac-delta function $\delta \left ( t-a \right )$ for $a> 0$;

$\mathcal{L}\left ( \delta \left ( t-a \right ) \right )=F\left ( s \right )$ is

  1. $0$
  2. $\infty$
  3. $e^{sa}$
  4. $e^{-sa}$
recategorized by

Please log in or register to answer this question.

Answer:

Related questions

1 answers
0 votes
go_editor asked Mar 1, 2021
If the Laplace transform of a function $f(t)$ is given by $\frac{s+3}{\left ( s+1 \right )\left ( s+2 \right )}$, then $f(0)$ is$0$$\frac{1}{2}$$1$$\frac{3}{2}$
0 answers
0 votes
gatecse asked Feb 22, 2021
If $y(x)$ satisfies the differential equation $(\sin x) \dfrac{\mathrm{d}y }{\mathrm{d} x} + y \cos x = 1,$subject to the condition $y(\pi/2) = \pi/2,$ then $y(\pi/6)$ is...
0 answers
0 votes
gatecse asked Feb 22, 2021
The ordinary differential equation $\dfrac{dy}{dt}=-\pi y$ subject to an initial condition $y\left ( 0 \right )=1$ is solved numerically using the following scheme:$$\fra...