Intro to Plane Curves & Parametric Equations | Calculus 2 Lesson 38 - JK Math

Introduction to Plane Curves & Parametric Equations (Calculus 2 Lesson 38) In this video we learn about plane curves and parametric equations. We discuss what plane curves are, and why we cannot represent them with regular equations in terms of x and y (rectangular equations). Then we discuss what parametric equations are and how they can be used to accurately represent plane curves. We look through examples of sketching graphs of plane curves using parametric equations by creating a table of parameter values and x- and y- coordinates as well as by eliminating the parameter. Finally we take a look at how to find a set of parametric equations given certain requirements or a rectangular equation. 🖥️ Join My Membership Site: https://www.jkmathematics.com/plus This video series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture! Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first! Video Chapters: 0:00 What are Plane Curves? 0:25 Why do we need Parametric Equations? 2:51 What are Parametric Equations? 7:41 Example - Sketch a Plane Curve: x=t^2-3, y=2t, [-1,3] 18:19 Example - Sketch a Plane Curve: x=2*sqrt(t), y=4t 23:44 Example - Sketch a Plane Curve: x=t, y=t^2 27:28 Example - Sketch a Plane Curve: x=a*cosθ, y=a*sinθ 37:55 Example - Finding Parametric Equations: Horizontal Line 39:49 Example - Finding Parametric Equations: y=4-x^2, t=0 at (1,3) 42:29 Example - Finding Parametric Equations: Circle at origin, r=4 45:14 Example - Finding Parametric Equations: y=6x-5 47:06 Example - Finding Parametric Equations: y=x^3 48:21 Outro 📝 Examples Video: https://youtu.be/BA1iDRWlYoA ⏩ Next Lesson: https://youtu.be/uc6XaNRi62E 📺 Calculus 2 Playlist: https://youtube.com/playlist?list=PLHdRLeAbIZE7KQ922piyRIDAj30XYcOIu 📺 Calculus 1 Playlist: https://youtube.com/playlist?list=PLHdRLeAbIZE6krGDQthaQRpLZFLD4ob54 🌐 Visit My Website: https://www.jkmathematics.com ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://amzn.to/3XuUcB9 Non-Graphing Calculator: https://amzn.to/46hHJ7E Financial Calculator: https://amzn.to/3CRe9s4 Graphing Paper: https://amzn.to/46mAfAr College Rule Paper: https://amzn.to/3NOJaTN My Favorite Pencil: https://amzn.to/3NOFMIB My Favorite Erasers: https://amzn.to/3PumUQB Calculus Workbook: https://amzn.to/3r8SnNP ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://amzn.to/3PzfI5F Calculus 3: https://amzn.to/46rSy76 Financial Mathematics: https://amzn.to/3ppIVW0 ⚡️My Recording Equipment⚡️ iPad Air: https://amzn.to/3phEug1 Apple Pencil (Gen 2): https://amzn.to/3Nl45MM Tablet Desk Stand: https://amzn.to/4420rPh External Hardrive: https://amzn.to/44pkEyh (Commissions earned on qualifying purchases) Find me on social media: Facebook: https://www.facebook.com/jkmathematics Twitter: https://twitter.com/jk_mathematics Instagram: @jk_mathematics Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! -Josh from JK Math #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.