Approximations and Intentions
Planar Approximations and Intentions
For now we see only a reflection as in a mirror; then we shall see face to face. Now I know in part; then I shall know fully, even as I am fully known.
Sometimes, analysis of a given relationship in multivariable settings is complex--too complex to be worth the effort of exact calculation. Instead, it is sufficient to use an approximation for the relationship that matches some but not all of the essential characteristics of the original relationship.
This is modeled below by the planar approximation for the lumpy surface. To calculate values of the lumpy surface, we instead find a simple function (here a plane) that in a small window around the point the values will agree within some tolerance for error.
A Planar Approximation to a Lumpy Surface
