Topical Overview
From Vectorcalcumb
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=[[Vector Functions]]= | =[[Vector Functions]]= | ||
<m>F : \\bbR^m \\right \\bbR^n</m> | <m>F : \\bbR^m \\right \\bbR^n</m> | ||
| + | *Things more complicated than Linear Transformations | ||
| + | *Structure of <m> \\\\bbR^n </m> | ||
| + | **[[Metric Spaces]] | ||
| + | **[[Topology]] | ||
| + | *Calculus of Vector Functions | ||
| + | **[[Limits]]<m>\\right</m>[[Continuity]]<m>\\right</m>[[Differentiability]] | ||
=[[Vector Fields]]= | =[[Vector Fields]]= | ||
| + | <m>F : \\bbR^n \\right \\bbR^n</m> | ||
| + | *Gradient Fields | ||
| + | *<m>F : (\\gradient f)(p) \\in \\bbR^n</m> | ||
| + | *Maxima & Minima | ||
| + | **Free | ||
| + | **Constrained | ||
| + | *Lagrange Multiplier | ||
| + | *divergance, circulation | ||
| + | **div | ||
| + | **curl | ||
| + | |||
=[[Integrals]]= | =[[Integrals]]= | ||
| + | *[Multiple Integrals] | ||
| + | *[Line Integrals] | ||
| + | *[Surface Integrals] | ||
| + | |||
=[[Integral Vector Calculus]]= | =[[Integral Vector Calculus]]= | ||
| + | *[Stoke's Theorem] | ||
| + | **[Green's Theorem] | ||
| + | *[Gauss's Theorem] | ||
| + | |||
=[[Manifolds]]= | =[[Manifolds]]= | ||
| + | *[[Parameterized Manifolds]] | ||
| + | *[[Differential Forms]] | ||
| + | *[[Integrals on Manifolds]] | ||
| + | <m>int{partial M}{} omega = int{M}{} d omega</m> | ||
Current revision as of 03:19, 9 February 2006
Contents |
[edit] Vector Functions
<m>F : \\bbR^m \\right \\bbR^n</m>
- Things more complicated than Linear Transformations
- Structure of <m> \\\\bbR^n </m>
- Calculus of Vector Functions
- Limits<m>\\right</m>Continuity<m>\\right</m>Differentiability
[edit] Vector Fields
<m>F : \\bbR^n \\right \\bbR^n</m>
- Gradient Fields
- <m>F : (\\gradient f)(p) \\in \\bbR^n</m>
- Maxima & Minima
- Free
- Constrained
- Lagrange Multiplier
- divergance, circulation
- div
- curl
[edit] Integrals
- [Multiple Integrals]
- [Line Integrals]
- [Surface Integrals]
[edit] Integral Vector Calculus
- [Stoke's Theorem]
- [Green's Theorem]
- [Gauss's Theorem]
[edit] Manifolds
<m>int{partial M}{} omega = int{M}{} d omega</m>
