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- In November 1967, he defended a doctorate at Moscow University named "A Periodic Problem of Variational Calculus", focused around Fet's theorem about two closed geodesic arcs, which became classical.
- Fet was a well-recognized topologist and specialist in variational calculus in the large.
- His interests included Sturm–Liouville theory, integral equations, variational calculus, and Fourier series.
- In direct collocation method, we are essentially performing variational calculus with the finite-dimensional subspace of piecewise linear functions (as in trapezoidal rule), or cubic functions, or other piecewise polynomial functions.
- He outlined his "δ-algorithm", leading to the Euler–Lagrange equations of variational calculus and considerably simplifying Euler's earlier analysis.
- A fairly universal way of performing these derivations is by using the techniques of variational calculus, the main objects used in this being Lagrangians.
- on Variational Calculus.
- This is the main assumption of variational calculus. Here it is a theorem. This property is the source of the name "convenient", which was borrowed from (Steenrod 1967).
- He is known for his pioneering research of wetting transitions, and analytical thermodynamic derivations of the Cassie and Wenzel equations using the variational calculus.
- For example, the problem of determining the shape of a hanging chain suspended at both ends—a catenary—can be solved using variational calculus, and in this case, the variational principle is the following: The solution is a function that minimizes the gravitational potential energy of the chain.
- He won the 1999 Fermat Prize, jointly with Fabrice Bethuel, for several important contributions to the theory of variational calculus.
- The problem of finding optimal functions for such changes is studied in variational calculus and in optimal control theory.
- This is shown, using variational calculus, in standard textbooks like the classical reference text of Landau & Lifshitz.
- Jon T. Pitts (born 1948) is an American mathematician working on geometric analysis and variational calculus. He is a professor at Texas A&M University.
- The GNAMPA group supports and coordinates research in Differential Equations and Dynamical Systems; Variational Calculus and Optimisation; Real Analysis, Measure theory and Probability; and Functional and Harmonic Analysis.
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