Simone变分法是讨论泛函极值的工具，所谓泛函，是指函数的定义域是一个无限维的空间，即曲线空间。在欧氏平面中，曲线的长的函数是泛函的一个重要的例子。一般来说，泛函就是曲面空间到实数集的任意一个映射。
函数的微余早分定义式为f(x+Δx)-f(x)=f'(x)Δx+o(x);那么泛函的微分有类似的定义：Φ(γ+h)-Φ(γ)=F+R,此处F为h的函数，R=o(h^2).注意，这里和微分不同的是h不一定是无穷小量。 泛函是可微的，其微分（变分）是参考文扮行献：
1）钱伟长，《变分法及有限元（上册）》，科学出版社， 1980年8月第一版
2）Shen Xiaoming(沈孝明)，Mixed Compatible Element and Mixed Hybrid Incompatible Element Variational Methods in Dynamic of Viscous Barotropic Fluids，Proceedings ofthe second international confernce on fluid mechanics(Bejing,1993):511-516;
APPLIED MATHEMATICS AND MECHANICS(English Edition)，Vol.15，No.6，JUN.1994：561-569
3）沈孝明，粘性流动的最大功率消耗原理不成立——论自然条件不参加变分兼论变分的定义和运算法则，北京大学学报，1990，26(3)：291-293
4）Shen Xiaoming(沈孝明)，Deformation Power and Complementary Power and so Forth of Compressible Viscous Fluid Floows and Their Applications in Variational Principles，《Some new trends on fluid mechanics and theoretical physics》，Chair man of Editiorial commitee:C.C.Lin(林家翘)，Peking UnivercityPress，Frist Edition 1993:305-307
5）沈孝明，粘性流体动力学有限元变分原理，上海力学，1997，18(3)：201-206
6）沈孝明，非线性弹性体大变形问题的竖缺雀新广义变分原理，上海力学，1988，9(4)：66-72 1.Venables, John, The Variational Principle and some applications. Dept of Physics and Astronomy, Arizona State University, Tempe, Arizona (Graduate Course: Quantum Physics)2.Williamson, Andrew James, The Variational Principle-- Quantum monte carlo calculations of electronic excitations. Robinson College, Cambridge, Theory of Condensed Matter Group, Cavendish Laboratory. September 1996. (dissertation of Doctor of Philosophy)3.Tokunaga, Kiyohisa, Variational Principle for Electromagnetic Field. Total Integral for Electromagnetic Canonical Action, Part Two, RelativisticCanonical Theory of Electromagnetics, Chapter VI
