The Levi-Civita tensor
October 25, 2012
In 3-dimensions, we define the Levi-Civita tensor, ijk , to be totally antisymmetric, so we get a minus
sign under interchange of any pair of indices. We work throughout in Cartesian coordinate. This means that
most
PROBLEMS, SECTION 5
Use the preliminary test to decide Whether the fellmving series are divergent or require
further testing. Careful: De not 333-" that a series is ccnvergent; the preliminary test cannct
decide this.
1 4 g 16 25 36 ﬁ ﬁ «E J3
1' _ _ _
PROBLEMS, SECTION 1
1.
2.
In the bouncing ball example above, ﬁnd the height of the tenth rebound, and the
distance traveled the ball after it touches the ground the tenth time. lCompare
this distance with the total distance traveled.
Derive the formula (
PROBLEMS, SECTION 4
For the following series, write formulas for the sequences an, Sn, and R. and ﬁnd the
limits of the sequences as n. —> GO [if the limits exist).
DC“ 1 ‘3‘” 1
1. — 2. Z—
1 2 III 5
1 1 1 1
3. 1—— ——— —
2+4 8+16
5 Z 2n1n51ntﬁ‘i3} Hint: