Difference between revisions of "Multivariable calculus"
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'''Multivariable calculus''' is a college-level topic of study that typically includes: | '''Multivariable calculus''' is a college-level topic of study that typically includes: | ||
| − | *[[ | + | *[[Vector space]] |
**equations of planes, finding lines perpendicular to planes | **equations of planes, finding lines perpendicular to planes | ||
**[[dot product]] | **[[dot product]] | ||
**[[cross 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]] | *[[Vector fields]] | ||
**[[gradient]] | **[[gradient]] | ||
| Line 11: | Line 16: | ||
**[[line integral]] | **[[line integral]] | ||
***[[parameterization]] | ***[[parameterization]] | ||
| + | **[[conservative field]] | ||
| + | ***defined by line integral, contour integral, curl, and gradient | ||
**[[surface integral]] | **[[surface integral]] | ||
| + | ***isolating [[singularity|singularities]] | ||
**[[Green's Theorem]] | **[[Green's Theorem]] | ||
| + | ***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 | ||
**[[Divergence Theorem]] | **[[Divergence Theorem]] | ||
| + | ***solving volume integrals for divergence when enclosing surface integral can be found, and vice-versa | ||
*[[multiple integrals]] | *[[multiple integrals]] | ||
| + | **substitution | ||
**[[curvilinear coordinates]] | **[[curvilinear coordinates]] | ||
*[[Maxima]] | *[[Maxima]] | ||
| − | **[[Lagrangian multiplier]] | + | **with constraints ([[Lagrangian multiplier]] and [[Hessian]]) |
| − | **[[ | + | **[[parametrization]] |
| + | **related rates (e.g., filling volumes) | ||
*[[continuity]] | *[[continuity]] | ||
**limits | **limits | ||
| + | **[[differentiability]] | ||
**[[L'Hopital's Rule]] | **[[L'Hopital's Rule]] | ||
| + | **partial derivatives | ||
| + | **[[Jacobian]] | ||
| + | *[[Power series]] | ||
| + | **[[Taylor series]] | ||
== See also == | == See also == | ||
*[[Calc3.1]] | *[[Calc3.1]] | ||
| − | [[ | + | [[Category:Vector Analysis]] |
| − | [[Category: | + | [[Category:Calculus]] |
| − | [[Category: | + | [[Category:Mathematics]] |
Latest revision as of 20:18, July 29, 2016
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
- with constraints (Lagrangian multiplier and Hessian)
- parametrization
- related rates (e.g., filling volumes)
- continuity
- limits
- differentiability
- L'Hopital's Rule
- partial derivatives
- Jacobian
- Power series