From Vectorcalcumb

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

[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

[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

• Parameterized Manifolds
• Differential Forms
• Integrals on Manifolds

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