Difference between revisions of "Multivariable calculus"
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**[[cross product]] | **[[cross product]] | ||
*Arc length, area and volume | *Arc length, area and volume | ||
| + | **recognizing shapes of different functions | ||
**area between curves | **area between curves | ||
**volume of intersecting solids | **volume of intersecting solids | ||
| + | ***disk, circular ring and cylindrical shell formulas | ||
*[[Vector fields]] | *[[Vector fields]] | ||
**[[gradient]] | **[[gradient]] | ||
| Line 38: | Line 40: | ||
**partial derivatives | **partial derivatives | ||
**[[Jacobian]] | **[[Jacobian]] | ||
| − | * | + | *[[Power series]] |
| − | **[[Taylor | + | **[[Taylor series]] |
== See also == | == See also == | ||
Revision as of 15:23, January 9, 2010
Multivariable calculus is a college-level topic of study that typically includes:
- Vector space
- equations of planes, finding lines perpendicular to planes
- dot product
- cross product
- Arc length, area and volume
- recognizing shapes of different functions
- area between curves
- volume of intersecting solids
- disk, circular ring and cylindrical shell formulas
- Vector fields
- gradient
- divergence
- curl
- line integral
- conservative field
- defined by line integral, contour integral, curl, and gradient
- surface integral
- isolating singularities
- Green's Theorem
- solving integrals split into separate expressions for dx and dy
- finding area enclosed by a contour
- Stoke's Theorem
- solving contour integrals when curl over capping surface can be found, and vice-versa
- Divergence Theorem
- solving volume integrals for divergence when enclosing surface integral can be found, and vice-versa
- multiple integrals
- substitution
- curvilinear coordinates
- Maxima
- Lagrangian multiplier
- parameterization
- related rates (e.g., filling volumes)
- continuity
- limits
- differentiability
- L'Hopital's Rule
- partial derivatives
- Jacobian
- Power series