MAT1332A  Calculus for the Life Sciences II  Fall 2009
Assignment 3
This assignment is worth a total of 50 points.
Due on Thursday, November 19, at the beginning of the lecture.
Sorry, no late assignments will be accepted.
Please write your answers neatly in complete and clear sentences.
Explain your reasoning. Providing only an answer is not acceptable.
Do staple your pages.
(1)
(a) [5 points]
Check that
z
(
t
) = 1+
√
1 + 2
t
is a solution of the autonomous
diﬀerential equation
dz
dt
=
1
z

1
with initial condition
z
(0) = 2.
(b) [7 points]
Estimate
z
(4) if
z
obeys the diﬀerential equation
dz
dt
=
1
z

1
with initial condition
z
(0) = 2. Use Euler’s method with Δ
t
= 1 for four
steps. Compare with the exact answer in (a).
(2)
Consider the equation
dx
dt
=
ax

x
3
for both positive and negative
values of
x
.
(a) [2 points]
Find the equilibria as functions of
a
for values of
a
between

1 and 1.
(b) [3 points]
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 Fall '09
 ARIANEMASUDA
 Calculus, Invertible matrix, Bifurcation theory

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