Section 5.3 *Vector-Valued Functions
Vector-valued functions allow us to represent a set of parametric equations defining a curve in the \(xy\)-plane or in space as a single function of time. The outputs of vector-valued functions are vectors, as their name clearly indicates. The vector output can be said to point to the location of a particle that is traveling along the curve it defines.
Subsection 5.3.1 Parameterizing the graph of a function, \(y=f(x)\)
- From left-to-right:
- From right-to-left:
Subsection 5.3.2 Various Parameterizations of a path
Subsection 5.3.3 Synchronized Space Curves
- Piecewise-defined vector-valued functions:
- Synchronizing motion along multiple curves at the same time: