MATH 2450 Lecture 2: Lecture 2 Lines in Space

We can put the ODE: [D(D^2 + tD)]y(t) in the form: a) [D(D^2 + tD)]y'(t) b) [D(D^2 + tD)D]y(t) c) [D^3 + tD^2 + D]y(t) d) [D^3 + tD^2]y(t)

Let T : D* rightarrow D be defined by T(s, t) = (s/3 - 2t/3, (delta + t)/3), where D* = {(s, t) : 2 4, -3 t 0}. Evaluate

Let u(t)=2ti+sin tj-cos tk and v(t) = I + t^2j - tk. Compute each of the following: d/dt(u(t).v(t)) d/dt(u(t) x v(t))