Syllabus:
3450:436/536 Mathematical Models
Section 001, Spring 2013
Instructor:
J. Patrick Wilber
Oce:
Oce Hours:
Phone:
E-mail:
Website:
Arts and Sciences Bldg., Room 265
Mon. & Weds. 3:15-4:15, and by appt.
972-6994
jw50@uakron.edu
www.math.uakron.edu/p

Math Models, Spring 2013: HW 6
Note that some problems may not be graded.
1. On previous HW, we studied the motion of a bead constrained to slide along a straight
horizontal wire. We derived the equation of motion
x
m = k( x2 + h2 L0 )
x
bx.
x2 + h2
(1)

Math Models, Spring 2013: HW 5
Note that some problems may not be graded.
1. This problem is based on Strogatz p.84, # 3.5.4. Please see the gure on p.84 for the
basic geometry. A bead of mass m is constrained to slide along a straight horizontal wire.
Le

Math Models, Spring 2013: HW 4
Note that some problems may not be graded.
1. (a) Construct the bifurcation diagram for the scalar ODE x = rx + x3 . (b) This example
illustrates what is called a subcritical pitchfork bifurcation. Explain the dierence betwe

Math Models, Spring 2013: HW 2
Note that some problems may not be graded.
1. In class, we derived the IVP
(1)
dc
q
= (ci c) kc,
dt
V
c(0) = c0
to describe the concentration c in a chemical reactor. After rescaling c by ci and t by k 1 ,
we derived
d
c
(2)

Math Models, Spring 2013: HW 1
Note that some problems may not be graded.
1. In class we derived the IVP
(1)
d2 x
gR2
=
,
dt2
(x + R)2
x(0) = 0,
dx
(0) = V,
dt
for the projectile problem. We made the rescalings y = x/R and = t/RV 1 to get
(2)
d2 y
1
=
,
2

Math Models, Spring 2013: HW 3
Note that some problems may not be graded.
1. Do the following problems from Strogatz: pp.3643 # 2.2.6, 2.2.7, 2.2.8, 2.2.9, 2.3.2.
If you are taking the class at the 500 level, do the next problem.
2. Do the following probl