By the end of this section, you should be able to

1. Place 1st-order systems into standard form

2. Identify the defining parameters of system

3. Sketch response of system due to step input

This section introduces first-order systems and the practical analysis tools that let you predict dynamic behavior with only a few parameters. You will practice placing first-order transfer functions into standard form, including the constant-numerator form and the form with an s term in the numerator, so the model structure is easy to read and compare across problems. From that standard form, you will identify the defining parameters of the system, especially steady-state gain and the time constant, and connect them to what you see in response plots. You will also build the habit of reading the model first and calculating second: the single pole location tells you whether the response is stable and how quickly the transient decays, and the step response shape is the familiar exponential rise or decay that shows up in many engineering systems. By the end of the section, you should be able to sketch the qualitative response to a step input without doing a full inverse Laplace transform, and you should be able to explain which parameter changes make the response faster, slower, larger, or smaller. Use the table of contents below to jump to the standard-form notes and lecture code, and return to this section whenever you need a fast, reliable way to interpret first-order dynamics.