Laplace Transform
Source lecture(s): PHY621 Lec4
Physical Meaning
Converts time-domain functions to complex frequency \(s\)-plane representations.
Variable Definitions
| Symbol | Meaning |
|---|---|
| \(s\) | complex frequency |
| \(f(t)\) | time-domain function |
Assumptions
\(f(t)=0\) for \(t<0\) (unilateral); region of convergence required.
Derivation
Direct from integral definition; table entries follow by integration-by-parts.
Applications
RC/RL/RLC circuits, control theory, initial-value problems.
Connections to Other Equations
- fourier-integral
- convolution