System Analysis in the s-Domain

Trace the development of the Laplace transform from Euler and Lagrange through Heaviside's operational calculus.

Derive the bilateral Laplace transform from the Fourier transform and define its region of convergence (ROC).

Analyze system stability and causality based on the location of poles and the ROC in the s-plane.

Apply the unilateral Laplace transform to solve linear time-invariant (LTI) differential equations with initial conditions.

Characterize analog LTI systems using their impulse response, frequency response, and transfer function.

Derive the relationship between a system's transfer function and its frequency response.

Analyze analog filter characteristics including magnitude response, phase response, and group delay.