Calculus › Section P · Vector analysis › Topic P.5
Parametric surfaces
One parameter swept a curve; two sweep a surface. The cross product of the two sweep directions then hands you the surface's normal and its area element — the tools the final theorems need.
In this topic
- Curves have a big sibling
- Tangent vectors and normals
- The area element
- Worked example: the sphere's area
- Worked example: a cone
- The graph case, recovered
- Choosing an orientation
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP