2008-02-25

Today's nonsense
- Homework due today. Homework due tomorrow. Pg846 #12-24even,30,32,34,50,52,54,58-68even
- Used yoyo drive?
- Professor Lewin video in physics earlier today (lecture #15 on momentum, has that insert during the middle of the video about his labeling of the variables).

Differentiation of Vector-Valued Functions

ex) Find r'(T).
a) VectorR(T) = T^{^(2)} i - 4 j
And the derivative of that is going to be just 2Ti.
This could easily have been written as < T^{^(2)}, -4, 0 > ---> <2T,0,0>

A curve is smooth or an open space interval, I, if VectorR = F(T)j + g(T)i + h(T)k if f ', g ', and h ' are continuous and VectoR ' (T) != 0 (as in, it does not equal the zero vector. So write VectorZero) for any value of T in the interval I. If you cross two vectors and get zero, that's the VectorZero, but if you dot two vectors and get zero, that's the scalar zero.

ex) The integral from zero to 1 of (T^{^(1/3)} i + 1 / (t + 1) j + e^{^(-T)} k ) dT
= ((3/4)T^{^(4/3)} i + ln(T+1)j - e^{^(-T)} k from 0 to 1
=