Lecture 14

Introduction to the
Calculus of Variations

  1. Calculus of Variations [MathWorld]
  2. Brachistochrone Problem [solved by Newton in 1696 as a challenge]
  3. Tautochrone Problem
  4. Euler-Lagrange Equations for minimizing an integral.
  5. Plateau's Problem
  6. Minimal Surface problem
  7. Hilbert's 23d Problem
  8. Principle of Least Action from Fundamental Concepts of Physics
  9. Lagrangian and Hamiltonian Mechanics

References:
  1. References [EricWeisstein.com]
  2. Resources [FuturesEdge.org]
  3. EZ Calculus of Variations [Utah]
  4. Maple Worksheets [MapleApps.com]
  5. Journal [Springer Verlag]
  6. Preprints [Pisa]
The Bernoulli Family:
    The Bernoulli's
  1. Jakob Bernoulli brother of Johann [1654-1705]
  2. Johann Bernoulli brother of Jakob [1667-1748]
  3. Nicholas Bernoulli son of Johann, brother of Daniel [1695-1726]
  4. Daniel Bernoulli son of Johann, brother of Nicholas [1700-1782]