differential equations

The Floer homology: topology and differential equations

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Floer’s homology has now established itself as a fundamental bridge between topology and the in-depth study of differential equations. Originating from the developments in symplectic geometry at the end of the 20th century, this theory has decisively changed the understanding of manifolds, particularly those of infinite dimension. Designed as an analogue of Morse theory in … Read more

Solution of differential equations: simplified methodologies

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Résolution d'équations différentielles : méthodologies simplifiées

IN BRIEF Differential equations: fundamental in applied mathematics. Homogeneous solutions: functions of the form x ↦ λe−A(x). Cauchy problem: method of variation of the constant. Linear equations: of order 1 and 2, rewritten in canonical form. Numerical resolution: approach for solutions by series. Variation method: development of particular solutions. Applications: usefulness in various industrial fields. … Read more