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	=[[Integrals]]=		=[[Integrals]]=
		+	*[Multiple Integrals]
		+	*[Line Integrals]
		+	*[Surface Integrals]
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	=[[Integral Vector Calculus]]=		=[[Integral Vector Calculus]]=
	=[[Manifolds]]=		=[[Manifolds]]=

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Revision as of 03:14, 9 February 2006

Contents 1 Vector Functions 2 Vector Fields 3 Integrals 4 Integral Vector Calculus 5 Manifolds

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

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

Manifolds