Laplace Transform
Definition
Basic Transforms
Linearity
Shifting Theorems
First Shifting Theorem (s-domain):
Second Shifting Theorem (t-domain):
where is the Heaviside step function.
Transform of Derivatives
Solving ODEs
Example: , ,
:
Inverse Laplace Transform
Partial Fractions
For rational , decompose into partial fractions and invert each term.
Convolution Theorem
Dirac Delta Function
Applications
Heaviside Step Function
Periodic Functions
for with period .