MATH 310
Fall 2011
Differential Equations
Homework Exercises, Set 10
Quiz
on Wednesday, 30 November 2011
Course Information is on
WebCT
.
The
quiz
will be based on the problems from Section 7.1 (converting between higherorder
equations and firstorder systems; nullclines and phase portraits) and Section 7.5 (linear constant
coefficient systems with real eigenvalues).
Textbook references are to:
Boyce and DiPrima
“
Elementary Differential Equations and Boundary Value Problems
” (9th edition).
Reading
:
•
Sections 7.1, (7.2, 7.3), 7.4, 7.5, 7.6
Problems to prepare for quiz (no need to hand in):
•
Section 7.1,
#
3, 6, 10, 12
Firstorder equations, method of elimination, phase portraits
For #10 & 12
, also plot fixed point(s) and nullclines in the phase diagrams,
and use them to determine the regions where
x
or
y
are increasing/decreasing;
hence sketch the phase portrait — see the lecture notes pp.7.8–7.11
.
(Fixed point: where
x
0
=
y
0
= 0
— intersection of
x
 and
y
nullclines;
x
nullcline: where
x
0
= 0
; trajectories cross this curve vertically;
y
nullcline: where
y
0
= 0
; trajectories cross this curve horizontally.)
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 Spring '11
 RWK
 Math, Differential Equations, Equations, #, phase portraits, Abel, Boyce, real eigenvalues

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