Math 2144 Homework 1: Due Thursday January 26
Problem 1. Find the local maximums, minimums and saddle points for the following two
functions.
f (x, y ) = x4 + y 4 4xy + 2
g (x, y ) = (1 + xy )(x + y )
Problem 2. Find the point (or points) where the graph
Math 2144 Homework 5: Due Thursday February 16
Problem 1. Evaluate the following double integrals.
/2
2
x sin y dy dx
0
0
2
xyex y dA where D = [0, 1] [0, 2]
D
D
x
dA where D = [0, 1] [0, 1]
1 + xy
y 2 exy dA where D = cfw_(x, y ) | 0 y 4 and 0 x y
D
x
Math 2144 Homework 4: Due Thursday February 9
Problem 1. Let (t) = 2 sin t, t, 2 cos t , 0 t , parameterize a curve C in R3 .
Calculate
xyz ds
Problem 2. Let C be the line segment in R3 from the point (0, 0, 0) to the point (1, 2, 3).
Write down two param
Math 2144 Homework 3: Due Thursday February 2
Problem 1. Find the maximum and minimum values of f (x, y ) = x2 y subject to the constraint x2 + 2y 2 = 6.
Problem 2. Find the maximum and minimum values of f (x, y, z ) = xyz subject to the
constraint x2 + 2
Math 2144 Homework 2: Due Friday January 27
The problems in this homework concern the chain rule. In the rst problem, I give you a
standard abstract situation and ask you to verify two forms of the chain rule.
Problem 1(a). Let f (x, y ) : R2 R and g (s,
Math 2144 Homework 6: Due Thursday February 23
Problem 1. Use Greens Theorem to evaluate the following line integrals. In each case,
assume that the curve C is positively oriented.
xy 2 dx + 2x2 y dy where C is the triangle with vertices (0, 0), (2, 2) an
Math 2144 Homework 7: Due Thursday March 8
Problem 1. Evaluate
/2
y
x
cos(x + y + z ) dz dx dy
0
0
0
Problem 2. Evaluate
xy dV
E
where E is bounded by y = x2 , x = y 2 , z = 0 and z = x + y .
Problem 3. Evaluate
xyz dV
E
where E is the solid tetrahedron
Math 2144Q Section 1 Spring 2012
Reed Solomon
Oce: 214 MSB, 486-2341.
Email: david.solomo[email protected]
Web Page: www.math.uconn.edu/solomon
Oce Hours: Tuesday and Thursday 11:00-12:30
Grading: You will be graded on homework (50%), one midterm exam (25%) and
Math 2144 Homework 10: Due Thursday April 5
Problem 1. Solve the following dierential equations and determine the interval on which
your solution is valid. (Remember that to be a solution, y (x) must be dierentiable and hence
continuous.)
dy
= (1 2x) y 2
Math 2144 Homework 9: Due Tuesday March 27
Problem 1. Use Stokes Theorem to evaluate
S
curl F dS where
F (x, y, z ) = x2 z 2 , y 2 z 2 , xyz
and S is the part of the paraboloid z = x2 + y 2 that lies inside the cylinder x2 + y 2 = 4,
oriented upwards.
Pro
Math 2144 Homework 8: Due Friday March 23
Problem 1. Give the equation for the tangent plane to the surface parametrized by
r(u, v ) = u + v, 3u2 , u v
at the point (2, 3, 0).
Problem 2. Let r(u, v ) = x(u, v ), y (u, v ), z (u, v ) : D S be a smooth para