Lecture 9: Parametric Equations. Objectives Be able to use parametric equations to describe the motion of a point Be able to find the arclength of a curve.

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Presentation transcript:

Lecture 9: Parametric Equations

Objectives Be able to use parametric equations to describe the motion of a point Be able to find the arclength of a curve described by parametric equations as well as the area underneath such a curve. Know how to find the curvature of curves in 2D and 3D. Corresponding Sections in Simmons 17.1,17.2,17.5

Parametric Equations

Example: Projectile motion

Example: Circular Motion

Velocity and Acceleration

Arclength with Parametric Equations

Example: Arclength of a Circle

Area with Parametric Equations

Curvature

Curvature Cont.

Curvature of a curve