Week 02
Laplace Transforms and Transfer Functions
I follow the saved course materials and calculations from modeling through stability, root locus, and frequency response.
What I connect in this unit
The Laplace transform turns a differential equation into an algebraic relation, but it does not erase initial conditions by itself. A transfer function is the zero-initial-condition input-output ratio, while poles, zeros, and denominator order summarize the dynamics.
Concept map
- Initial conditions
- Poles and zeros
- Transfer functions
- System order
Technical anchor
After separating the initial-condition terms, define G(s)=Y(s)/U(s). Denominator roots identify natural-response modes, whereas numerator roots mark frequencies or modes suppressed by the chosen input-output path.
How I review it
Write the initial-condition response and the zero-state transfer function separately, then check whether any apparent pole-zero cancellation hides a physical system order.
Connection to the full course
Unit 2 of 12. Unit numbers organize the concepts found in the materials and do not reproduce an attendance schedule.