In / if you wanted to have equations numbered within sections---that is, have equation numbers (1.1), (1.2), ..., (2.1), (2.2), ..., in sections 1, 2, and so forth---you could redefine theequation as suggested in the / manual [5, .3, § C.8.4,]:
\renewcommand{\theequation}{\thesection.\arabic{equation}}
This works pretty well, except that the equation counter won't be reset to zero at the beginning of a new section or chapter, unless you do it yourself using setcounter. To make this a little more convenient, the amsmath package provides a command numberwithin. To have equation numbering tied to section numbering, with automatic reset of the equation counter, the command would be
\numberwithin{equation}{section}