ยง10.1: Parametric Equations
Introductory resources for reading, graphing, and interpreting curves defined by $x=f(t)$ and $y=g(t)$. The focus here is on basic graphing, eliminating the parameter, and understanding orientation and motion along the curve.
Library, Handouts & Tools
| Resource Name | Type | Description | Link |
|---|---|---|---|
| OpenStax: Parametric Equations | Textbook Notes | Clear textbook-style introduction to parametric equations, their graphs, and how a parameter traces a curve in the plane. | Read Notes |
| Paul's Notes: Parametric Equations and Curves | Study Guide | Good for basic graphing strategy, eliminating the parameter, and remembering that the parametric curve may trace only part of the rectangular graph. | Read Notes |
| Paul's Notes: Practice Problems | Practice | Extra problems on eliminating the parameter, sketching the curve, and identifying any restrictions on the graph. | Practice |
| Desmos: Parametric Equations Help | Tool Guide | Quick reference for entering a parametric curve in Desmos as an ordered pair and adjusting the parameter interval. | Open Guide |
| Desmos: Parametric Graphing Example | Interactive | A simple ready-made Desmos example you can edit to experiment with curves, domains, and tracing direction. | Open Graph |
Video Lectures
| Topic | Source | Description | Link |
|---|---|---|---|
| Video Calculus Series (Parametric Overview) | Houston ACT | The UH Video Calculus page explicitly includes a parametric description of curves in the plane; for this section, use it only for the introductory parametric material. | Open Page |
| Parametric Equations Intro | Khan Academy | Short introduction to what parametric equations are and how $x$ and $y$ are both written in terms of a parameter. | Watch |
| Curves Defined by Parametric Equations | Asher Roberts | A full section-style video focused on reading and graphing basic parametric curves for a Stewart-style section 10.1 treatment. | Watch |
Focused Practice Path
| Skill | Best Resource | What to Focus On | Link |
|---|---|---|---|
| Read the setup | OpenStax | Understand that a curve is traced by points $(x(t),y(t))$ as the parameter changes. | Start Here |
| Eliminate the parameter | Paul's Notes | Practice rewriting the pair of equations as one rectangular equation and then checking whether you get the full graph or only part of it. | Review |
| Graph and orient the curve | Desmos | Adjust the $t$-interval and watch how the point moves so you can match the graph to the direction of motion. | Try It |
| Do extra problems | Paul's Practice | Use these after notes/video to get repetition with sketching and identifying restrictions. | Practice |