MP7 · Calculus of variations
A 19-module path through mp7 · calculus of variations, in study order from foundations to the frontier.
Modules
- Functionals and Function Spaces
- First Variation and Stationarity
- Fundamental Lemma of the Calculus of Variations
- Euler-Lagrange Equation
- Beltrami Identity and First Integrals
- Natural and Essential Boundary Conditions
- The Brachistochrone Problem
- Functionals of Several Functions and Higher Derivatives
- Constrained Variation and Lagrange Multipliers
- Isoperimetric Problems
- Geodesics as Variational Problems
- Hamilton's Principle of Stationary Action
- Lagrangian Mechanics
- Cyclic Coordinates and Conserved Momenta
- Noether's Theorem
- The Rayleigh-Ritz Method
- Variational Principles for Eigenvalue Problems
- Second Variation and Sufficiency Conditions
- Variational Problems in Multiple Dimensions and Field Theory