$x(t)*h(t) = h(t)*x(t)$ (Commutative)

$x(t)*[h_1(t)+h_2(t)] = [x(t)*h_1(t)] + [x(t)*h_2(t)]$ (Distributive)

$x(t)*[h_1(t)*h_2(t)] = [x(t)*h_1(t)]*h_2(t)]$ (Associative)

If $y(t) = x(t)*h(t)$, then $A_y = A_x \times A_h$.

$x(t-a)*h(t-b) = y(t-a-b)$.

$x(t)*h(-t) = y(t)$.

$x(at)*h(at) = \frac{1}{a} y(at)$.

$Ax(t)*Bh(t) = ABy(t)$.

$\frac{d^n x(t)}{dt^n} * \frac{d^m h(t)}{dt^m} = \frac{d^{m+n} y(t)}{dt^{m+n}}$.

$y(t) = \int_{-\infty}^{t} x(\tau)d\tau$. Running Integration. Area of $x(t)$ from $-\infty$ upto $t$.

$x(t)*u(t) = \int_{-\infty}^{t} x(\lambda)d\lambda$.
Rectangular pulse: Same duration (Triangle). Different duration (Trapezoidal).
$y(t) = \int_{-\infty}^{\infty} x(\tau)h(t-\tau)d\tau$.
Timeline Method:
- S-1: Given $x(t)$ and $h(t)$.
- S-2: Plot $x(\tau)$ and $h(t-\tau)$.
- S-3: Make timeline of $x(\tau)$ vs $\tau$ and $h(t-\tau)$ vs $\tau$.
- S-4: Vary $t$ and determine the integration.
Graphical Method: $y(t) = \int_{-\infty}^{\infty} x(\tau)h(