Difference between revisions of "Multivariable calculus"
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(added conservative field) |
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**[[dot product]] | **[[dot product]] | ||
**[[cross product]] | **[[cross product]] | ||
| + | *Arc length, area and volume | ||
| + | **area between curves | ||
| + | **volume of intersecting solids | ||
*[[Vector fields]] | *[[Vector fields]] | ||
**[[gradient]] | **[[gradient]] | ||
| Line 17: | Line 20: | ||
**[[Green's Theorem]] | **[[Green's Theorem]] | ||
***solving integrals split into separate expressions for ''dx'' and ''dy'' | ***solving integrals split into separate expressions for ''dx'' and ''dy'' | ||
| + | ***finding area enclosed by a contour | ||
**[[Stoke's Theorem]] | **[[Stoke's Theorem]] | ||
***solving contour integrals when curl over capping surface can be found, and vice-versa | ***solving contour integrals when curl over capping surface can be found, and vice-versa | ||
| Line 27: | Line 31: | ||
**[[Lagrangian multiplier]] | **[[Lagrangian multiplier]] | ||
**[[parameterization]] | **[[parameterization]] | ||
| − | ** | + | **related rates (e.g., filling volumes) |
*[[continuity]] | *[[continuity]] | ||
**limits | **limits | ||
Revision as of 15:18, 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
- area between curves
- volume of intersecting solids
- 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
- sequences