This theory, which has major importance in mathematical physics, was developed between 1829 and 1837. Sturm and Liouville examined general linear second order differential equations and examined properties of their eigenvalues, the behaviour of the eigenfunctions and the series expansion of arbitrary functions in terms of these eigenfunctions.
Ang teorya, na kung saan ay may malaking kahalagahan sa matematika physics, ay binuo sa pagitan ng 1829 at 1837. Sturm at Liouville napagmasdan pangkalahatang pahaba second-order ng kaugalian equation at napagmasdan pag-aari ng kanilang mga eigenvalues, ang pag-uugali ng eigenfunctions at ang serye pagpapalawak ng arbitrary function sa mga tuntunin ng mga eigenfunctions.