Monday, April 24, 2017

lecture 36: conservative vector functions

On Friday we used the fundamental theorem from calculus I to construct a fundamental theorem for line integrals involving $\vec{F} \cdot d\vec{r}$ (14.3). The fundamental theorem only works if the vector function is conservative: $\vec{F} = \vec{\nabla}f$. We'll create a test to tell whether a generic vector function is conservative, and we'll figure out how to construct the potential function $f(x,y,z)$ for a conservative vector function.