Calculus of Variations

Author

Affiliation

Enrico Bertolazzi

University of Trento, Department of Industrial Engineering

Prerequisites, objectives, and expected outcomes

Prerequisites: multivariable calculus, integration by parts, and basic ODE boundary-value problems.

Objectives: compute first variations, derive Euler–Lagrange equations and natural boundary conditions, and handle integral and path constraints.

Expected outcomes: the reader can translate a functional minimization problem into necessary conditions, distinguish fixed and free endpoint data, and check a candidate extremal.

Variational Foundations
Fundamental Lemma
Euler–Lagrange Equations
Higher-Order Functionals
Isoperimetric Constraints
Path Constraints
Summary
Worked Exercises (companion volume)

Contents