Linked from

The 36 pages that link to Calculus of variations, each with the reason it gives.

• Lagrangian mechanicsNarrower topic: Lagrangian mechanics applies variational methods to the action integral.

• Noether's theoremNarrower topic: Noether's original reasoning uses variations of the action under infinitesimal transformations.

• Euler–Lagrange EquationNarrower topic: The equation is a central tool for finding stationary functions in this broader subject.

• Isoperimetric inequalityNarrower topic: Variational methods derive the circle as an area-maximizing boundary.

• Fermat's principleNarrower topic: The principle is a physical application of finding stationary values of travel time.

• Minimal surfaceNarrower topic: Area stationarity is a variational condition on a surface.

• Optimal controlNarrower topic: Its earlier methods supplied the mathematical ancestry for optimizing trajectories.

• Hamilton's principleNarrower topic: The principle applies variational calculus to the action functional.

• Morse theoryNarrower topic: Morse developed foundational methods while studying critical points in variational problems.

• Isoperimetric problemNarrower topic: It supplies the variational framework for optimizing an integral subject to another integral condition.

• Jakob BernoulliNarrower topic: Bernoulli’s isoperimetric work helped launch this field.

• Direct method in the calculus of variationsNarrower topic: The direct method addresses minimization problems formulated in this broader subject.

• Noether's second theoremNarrower topic: Noether’s theorem is derived by varying an action functional.

• Sobolev inequalityNarrower topic: Variational problems motivated function-space estimates that control minimizing sequences.

• Brachistochrone curveNarrower topic: It turns the least-time path into an optimization problem over possible curves.

• Fundamental lemma of the calculus of variationsNarrower topic: The fundamental lemma supplies the pointwise inference used throughout variational proofs.

• Pontryagin's maximum principleNarrower topic: The maximum principle extends variational ideas to systems with explicit controls and constraints.