Math 102. Rumbos
Spring 2015
1
Solutions to Assignment #1
1. The diagram in Figure 1 shows a simplication of the chemostat model discussed
in Section 2.2 in the class lecture notes at http:/pages.pomona.edu/~ajr04747/.
The compartment in the diagram in Fi
Department of Mathematics
Pomona College
Course Outline for Mathematics 102
Differential Equations and Modeling
Spring 2015
Time
Place:
Instructor:
Office:
Phone/e-mail:
Courses Website:
Office Hours:
Text:
Prerequisites:
MWF 10:00 am - 10:50 am
SC Room 1
Math 102. Rumbos
Spring 2015
1
Solutions to Assignment #6
1. For the following linear system, give the equations for the solution curves and
sketch the phase portrait.
x = x + y;
y = x y.
(1)
Solution: The system in (1) is in the form of the system
dx
d
Math 102. Rumbos
Spring 2015
1
Solutions to Assignment#2
1. The second order dierential equation
d2 s
= ks bv + f (t),
(1)
dt2
models a springmass system consisting of an object of mass m, attached to a
spring with stiness constat k, subject to a friction
Math 102. Rumbos
Spring 2015
1
Solutions to Assignment #5
1. For the following linear system, give the equations for the solution curves and
sketch the phase portrait.
x = y;
(1)
y = x 2y.
Solution: Write the system in (1) in vector form
x
y
where
A=
x
,
Math 102. Rumbos
Spring 2015
1
Solutions to Assignment #4
Do the following problems
1. Explain why the following linear system of dierential equations cannot be put
in diagonal form.
dx
dt = 2x + y;
dy
= x + 4y.
dt
Solution: The linear system cannot be
Math 102. Rumbos
Spring 2015
1
Solutions to Assignment #3
Due on Monday, February 2, 2015
Read Chapter 3 on Solving Linear Systems in the class lecture notes at
http:/pages.pomona.edu/~ajr04747/
Read Section 2.2, on The Geometry of Systems, in Blanchard,
Math 102. Rumbos
Spring 2015
1
Review Problems for Exam 1
1. When people smoke, carbon monoxide is released into the air. Suppose that in
a room of volume 60 m3 , air containing 5% carbon monoxide is introduced at
a rate of 0.002 m3 /min. (This means that
Math 102. Rumbos
Spring 2015
Topics for Exam 1
1. Modeling via Dierential Equations
1.1 Conservation principles
1.2 Compartment models
2. Types of Dierential Equations
2.1 Order
2.2 Linear versus nonlinear
2.3 Systems
2.4 Autonomous systems
3. Solving Lin