variational-calculus

synthetic differential geometry Introductions geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry Differentials Tangency The magic algebraic facts Theorems Axiomatics Models smooth algebra (-ring) differential equations, variational calculus Chern-Weil theory, ∞-Chern-Weil theory Cartan geometry (super, higher) Let and be two smooth manifolds of…

I was reading Gelfand&Fomin Calculus of Variations book, in which I found this Lemma 2 If $\alpha(x)$ is continuous in $[a, b]$, and if $$\int_a^b \alpha(x) h'(x)\, dx = 0$$ for every function ...