The worksheet
Problem 1. Evaluate S curl F dS if S is the surface x2 + 4y 2 + z = 4, z 0 oriented upward
and F = (x + sin z )i + zeyz j + z k. What would do you use here, Stokes or Divergence theorem
Final practice problems
Solutions of all problems must by accompanied by relevant explanations. Show your
work, but not to others.
Problem 1. Let E be a simple region in 3 dimensional space and S its
Midterm 2, Math 53
July 11th, 2008
Solutions of all problems must by accompanied by relevant explanations. Show
your work, but not to others. Simplify your answers where possible.
Problem 1. Find the
Midterm 2 practice problems
Solutions of all problems must by accompanied by relevant explanations. Show your
work, but not to others.
Problem 1. Find the limit if it exists or prove that it doesnt ex
Midterm 1, Math 53
July 11th, 2008
Solutions of all problems must by accompanied by relevant explanations. Show
your work, but not to others. Simplify your answers where possible.
Problem 1. Consider
Midterm 1 practice problems
Solutions of all problems must by accompanied by relevant explanations. Show your
work, but not to others.
Problem 1. Eliminate the parameter to nd a Cartesian equation of
PRACTICE MIDTERM 2 SOLUTIONS
PEYAM RYAN TABRIZIAN
1. (a) State carefully: The Mean Value Theorem
Mean Value Theorem: Let f be a function that satises the following two
hypotheses:
1) f is continuous o
Lecture notes for Math 115A (linear algebra)
Fall of 2002
Terence Tao, UCLA
http:/www.math.ucla.edu/tao/resource/general/115a.3.02f/
The textbook used was Linear Algebra, S.H. Friedberg, A.J. Insel, L