Igor Kriz
Regular problems:
1.
Compute the following integrals:
(a) 
(b) 
(c) 
.
2.
Using integration of rational functions, compute:
(a) 
(b) 
.
3.
Suppose 
is such that
||f(t)||=1 (the Euclidean norm 
) for every t.
Prove that 
for every 
.
4.
Define for 
,
.
Similarly, for 
,
, let 
. (This is called the Laplacian.)
Prove that
Challenge problems:
5.
Integrate:
(a) 
(b) 
(c) .
6.
Put f(0,0)=0, and
if 
. Prove that
(a) 
are continuous in 
;
(b) 
and
exist at every point of
and are continuous except at (0,0);
(c) 
