lecture11: extensions: several independent variables

Topics covered

• Several independent variables
• Notation
• Formalisms
• The problem
• Solution
• The First Variation
• Green's theorem
• Green's theorem in use
• Euler-Lagrange equation
• Simple example
• Simple example: solution
• Example: vibrating string
• Example: Plateau's problem
• Surface area minimization
• Approximate solutions
• Example
• Example: solution
• But this is hard...
• Plateau's laws %
• appendix