ភាពខុសគ្នារវាងកំណែនានារបស់ "បំលែងឡាប្លាស"

:<math>F(s) = \mathcal{L} \left\{f(t)\right\}=\int_{0}^\infty e^{-st} f(t) \,dt </math>
 
ដែល <math> \int_{0}^\infty e^{-st} f(t) \,dt </math> ត្រូវបានគេហៅថា'''អាំងតេក្រាលឡាប្លាស'''។
 
== រូបមន្តគ្រឹះ ==
{| class="wikitable" align="ceenter"
|-
! អនុគមន៍ដើម f(t)
! បំលែងឡាប្លាស F(s)
|-
| <math>e^{at} f(t) \,</math>
| <math>F(s-a)</math>
|-
| <math>f(at) \,</math>
| <math>\frac{1}{a} F(\frac{s}{a}) ; \quad a > 0</math>
|-
| <math>f'(t) \,</math>
| <math>sF(s) - f(0) \,</math>
|-
| <math>f''(t) \,</math>
| <math>s^2 F(s) -sf(0) - f'(0) \,</math>
|-
| <math>t^kf(t) \,</math>
| <math>(-1)^kF^{(k)}(s) \,</math>
|-
| <math>f*g \,</math>
| <math>F(s)G(s) \quad ; \mathcal{L} [g(t)] = G(s) </math>
|-
| <math>1 \,</math>
| <math>\frac{1}{s}</math>
|-
| <math>t \,</math>
| <math>\frac{1}{s^2}</math>
|-
| <math>t^n \,</math>
| <math>\frac{n!}{s^{n+1}}</math>
|-
| <math>e^{at}t \,</math>
| <math>\frac{1}{(s-a)^2}</math>
|-
| <math>\sin \omega t \,</math>
| <math>\frac{\omega}{s^2 + {\omega}^2} \,</math>
|-
| <math>\cos \omega t \,</math>
| <math>\frac{s}{s^2 + {\omega}^2}</math>
|-
| <math>\sinh \omega \,</math>
| <math>\frac{\omega}{s^2 - {\omega}^2} \,</math>
|-
| <math>\cosh \omega t \,</math>
| <math>\frac{s}{s^2 - {\omega}^2} \,</math>
|-
| <math>t \sin \omega t \,</math>
| <math>\frac{2\omega s}{(s^2 + {\omega}^2)^2}</math>
|-
| <math>t \cos \omega t \,</math>
| <math>\frac{s^2 - {\omega}^2}{(s^2 + {\omega}^2)^2}</math>
|-
| <math>e-{at} \sin \omega t \,</math>
| <math>\frac{\omega}{(s - a)^2 + {\omega}^2}</math>
|-
| <math>e^{at} \cos \omega t \,</math>
| <math>\frac{(s - a)}{(s - a)^2 + {\omega}^2}</math>
|}
 
== លក្ខណៈនិងទ្រឹស្តីបទ ==
៩៤៦៩

កំណែប្រែ