Current revision as of 03:19, 9 February 2006

[edit] Vector Functions

<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

<m>F : \\bbR^n \\right \\bbR^n</m>

<m>int{partial M}{} omega = int{M}{} d omega</m>

@@ Line 1: / Line 1: @@
 =[[Vector Functions]]=
-<m>F : R^m \\arrow \\; R^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]]=
+<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]]=
+*[Multiple Integrals]
+*[Line Integrals]
+*[Surface Integrals]
 =[[Integral Vector Calculus]]=
+*[Stoke's Theorem]
+**[Green's Theorem]
+*[Gauss's Theorem]
 =[[Manifolds]]=
+*[[Parameterized Manifolds]]
+*[[Differential Forms]]
+*[[Integrals on Manifolds]]
+<m>int{partial M}{} omega = int{M}{} d omega</m>