Linked from

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

• Leonhard EulerRelated: Euler helped formulate its central methods for finding curves that minimize or maximize quantities.

• GeodesicRelated: It derives geodesics as stationary paths of length or related functionals.

• 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.

• Joseph-Louis LagrangeBroader topic: Lagrange developed systematic techniques for solving variational problems.

• 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.

• Principle of least actionRelated: It supplies the method for varying paths and deriving motion equations.

• 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.

• Action (physics)Related: It supplies the method for varying trajectories in the action principle.

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

• Johann BernoulliRelated: Johann and Jacob helped establish this field through problems involving shortest paths and curves.

• Mathematical analysisRelated: It extends differentiation from numbers to functions and underlies many optimization problems.

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

• Fréchet derivativeRelated: First variations are derivatives of functionals, often formulated as Fréchet derivatives.

• History of calculusBroader topic: It extended calculus from choosing numbers to choosing entire paths and functions.

• 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.

• Analytical mechanicsRelated: It supplies the method behind variational principles in mechanics.

• Geometric analysisRelated: Variational principles produce minimal surfaces and curvature equations.

• Hilbert's problemsRelated: Hilbert's twenty-third problem urges progress in this broad research area.

• Constantin CarathéodoryRelated: Carathéodory gave a rigorous treatment of variational problems and their extremals.

• 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.

• Bernoulli familyRelated: The brachistochrone challenge drew Johann and other Bernoullis into this emerging field.

• Hopf–Rinow theoremRelated: Compactness and minimizing geodesics help establish existence of length-minimizing curves.

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

• Carathéodory's existence theoremRelated: Carathéodory's broader analytical work connected differential equations with variational methods.

• Virtual workRelated: Virtual-work equilibrium is closely connected to stationary-action variational methods.

• Wirtinger's inequalityRelated: The inequality supplies coercive bounds for energies of periodic variations.

• Jean TaylorRelated: Area-minimization questions place Taylor’s geometric results within this broader framework.

• 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.