Laplace Transform
Definition
Turning calculus into algebra — it converts differential equations into solvable algebraic ones, beloved by engineers.
Technical definition
F(s) = ∫₀^∞ f(t)e^(−st)dt. Differentiation becomes multiplication by s — ideal for circuits and control systems with initial conditions.
Example
Analyzing an RLC circuit's switch-on transient: Laplace turns the differential equation into algebra; solve it, then transform back.
Common confusion
The Laplace transform doesn't solve the physics for you — it changes the language of the math. You still need correct equations and boundary conditions.