Media Summary: Remember inverse functions? There's a nice derivative rule associated to these... Finding an inverse can be tough in the case of a nonlinear multivariate function. So, what so we do? Taylor expand everything in ... We can integrate as well as differentiate, and that shows up most clearly when computing arclength of a curve. The good news is ...
Calcblue 1 Ch 7 2 - Detailed Analysis & Overview
Remember inverse functions? There's a nice derivative rule associated to these... Finding an inverse can be tough in the case of a nonlinear multivariate function. So, what so we do? Taylor expand everything in ... We can integrate as well as differentiate, and that shows up most clearly when computing arclength of a curve. The good news is ... Our ruminations on inverse lead us to the obvious derivative rule for inverses. Thank you chain rule! Here's a simple example of the Inverse Function Theorem to a system of (stubborn) nonlinear equations. Why have we not done any calculus yet? Where are the derivatives and integrals? It's time to start thinking about calculus, starting ...
Time for some calculus! Let's start with some generalizations of the product rule for derivatives of dot products and cross products. What do we do with vectors? One source of utility comes from basic vector algebra. Let's consider how to add and rescale vectors.
