The circumference of a sphere is measured to be 24 cm, with a possible error of 0.25 cm. Use the differential \(dV\) to estimate the maximum error in the calculated ...

So by imagining a pseudo Bose-Einstein condensate tailor made for each nonlinear problem, this algorithm deduces a useful linear approximation. “Give me your favorite nonlinear differential equation, ...

While I do spend lots of time pushing the idea of linear approximations on my students, we do need nonlinear functions to describe most interesting physical phenomena. The tradeoff for that is ...

The area \(A\) of a square of side length \(s\) is \(A=s^2\text{.}\) Suppose \(s\) increases by an amount \(\Delta s=ds\text{.}\) Draw a square and then illustrate ...