Definition of partial derivatives;
        Notation for partial derivatives;
        Instantaneous rates of change;

        Geometric interpretation of partial derivatives;
        Definition of the planes tangent to surfaces;
        Find the planes tangent to surfaces;
        Higher-order partial derivatives;

        Examples.

Section 13.5 Topics:

        Existence of extreme values;
        Necessary conditions for local extrema;
        Types of absolute extrema;

        Finding local extrema;
        Finding global extrema;

        Highest and lowest points of surfaces;
        Applied maximum-minimum problems;

        Examples.