MATH 2ZZ3 Study Guide - Midterm Guide: Tangent Space, Conservative Vector Field, Directional Derivative
2 Oct 2016
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If ( ) is a differentiable function of x and y, and then. The maximum value of the directional derivative is when || || and occurs when u has the same direction as (when cos=1. Where ( ) is a point on the graph on the plane. When there is something given for x and y, then you sub it in, so that it is in terms of t. Path independence for a conservative field such that ( ) Because f is conservative there is a potential function such that. Where c is the constant or constants that need to be added to make to get. We can see that y2 is the missing term in the first equation so we sub that in for c to get such that, If the vector field is conservative, than the it is = 0.
