In the Gauss - elimination for a solving system of linear algebraic equations, triangularization leads to

If a function is continuous at a point its first derivative

The expression curl $$\left( {grad\,f} \right)$$ where $$f$$ is a scalar function is

The one dimensional heat conduction partial difference equation $$\,\,{{\partial T} \over {\partial t}} = {{{\partial ^2}T} \over {\partial {x^2}}}\,\,$$ is