Problem Set 5
MAP 3161
due Wednesday, March 16, 2011
1.
x
y
= 2x 4y + 3xy
= x + y + x2
a) Show that the above system is almost linear.
b) Find all critical points.
c) Classify the critical points and indicate their stability.
2. A spring is suspended from
Solution to Problem Set #5
MAP 3161 - Spring 2011
1.
x
y
= 2x 4y + 3xy = F (x, y )
= x + y + x2 = G(x, y )
(a) Note that F and G are twice dierentiable for all real numbers since they are both
polynomials with integer exponents. Thus the system above is a
Problem Set 6
MAP 3161
due Monday, March 28, 2011
1. Find the rst three nonzero terms in the Taylor polynomial approximation of the solution
for the initial value problem below.
y + y 3 = sin x; y (0) = 0, y (0) = 0
Problems from Boyce and DiPrima:
5.2 #8
Problem Set 7
MAP 3161
due Monday, April 4, 2011
1. As a spring ages its springconstant decreases in value. One such model for a mass-spring
system with an aging spring without damping is
mx (t) + ket x(t) = 0,
where m is the mass, k and are positive cons
Problem Set 8
MAP 3161
due Friday, April 22, 2011
A synthesizer is an electronic musical instrument that can produce sounds by generating
signals of diering frequencies. They are usually comprised of a piano-style keyboard which,
when pressing a key, emit
Solution to Problem Set #1
MAP 3161 - Spring 2011
Problem numbers with a do not have answers in the back of the textbook. Here (aij )
means that the matrix A has the general element aij , while square brackets are used for
grouping only.
7.2
2. (See answe
MAP 3161: Math for Science and Engineering
CRN 11091 (4 credits)
Spring 2011
Instructor:
Oce:
Phone:
Email:
Oce Hours:
Text:
Class Location:
Meeting Times:
Dr. Daniel Kern, Department of Chemistry and Mathematics
AB7 224
(239) 590-1261
[email protected]
TR 1