Parametrized Curves, Multivariable Calculus

Parametrizing curves in (x,y) and (x,y,z)-space with vector-valued functions r(t). As a curve is a one-dimensional object, it requires exactly one parameter "𝑡" for its complete description. We explore various examples of curve parametrization, including circles, line segments, and intersections of surfaces. (Unit 2 Lecture 3)

Key Points
1. Parameterization of Curves: Using a vector-valued function to describe a curve in a space.
2. One-Dimensional Nature of Curves: A curve, despite existing in a multi-dimensional space, is fundamentally one-dimensional.
3. Unit Circle Parameterization: Utilizing trigonometric functions to describe circles in different planes.
4. Line Segment Parameterization: A method to parametrize a straight line segment between two points.
5. Parabolic Curve Parameterization: Setting one variable as the parameter to describe a parabolic curve.
6. Intersection of Surfaces: Using a common variable as a parameter to describe the intersection of two surfaces.

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@bevinmaultsby
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