Calculus › Section M · Vector-valued functions › Topic M.1
Vector-valued functions
A curve in space cannot be the graph of y = f(x): a loop fails the vertical line test before it leaves the page. Pack the coordinates into a vector, and one function r(t) carries position, path and direction all at once.
In this topic
- Why curves need vectors
- The definition
- Worked example: sketching a plane curve
- Worked example: the helix
- Curves as intersections of surfaces
- Orientation and choice of parameter
- Algebra and limits, component by component
- Continuity
- Worked example: a horse on a carousel
- Common mistakes to avoid
- Key takeaways
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Standards: 9 (BC)