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Math. 224. Review problems 1
David Gurarie
Name
Topics
1.
Modeling:
growthdecay (population et al), heatingcooling, free fall, mixing, chemi
cal reactions,
f
nancing, mechanics, geometry;
(a)
MultiD models
: interacting species (competitioncooperation), predatorprey,
oscillators
2.
Concepts:
initial value problem, general solution, uniqueness, equilibriua, phase line
3.
Methods, techniques:
(a)
Analytic
: separation, mulitpiers, change of variables, linear approximation
(b)
Qualitative
:s
lope
f
eld, phase line, equilibria (stability and bifurcations)
(c)
Numeric
:Eu
le
r
Sample problems
4.
Modeling.
Write di
f
erential equation models for the following systems. Classify
them as DE/DS, autonomous/nonautonomous,
f
rst or higher order, linear/nonlinear,
separable etc. Indicate solution methods for each one.
(a) The logistic growth model with the growth rate
α
=
.4, threshold capacity
N
=
20
, initial population of 30, and di
f
erent harvesting methods (
f
xed, variable,
proportional to
p
...)
(b) Oscillator (massspring) system of mass
m
, damping coe
ﬃ
cient
α
,sp
r
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This note was uploaded on 05/09/2008 for the course MATH 224 taught by Professor Hahn during the Spring '07 term at Case Western.
 Spring '07
 Hahn
 Geometry

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