AMATH 402/502
MT Closed book, closed notes, no calculators.
Please write your NAME on an exam blue book (or blank paper for EDGE
students, as you wish) and place your answers inside. Please show all of your work,
and present your answers and calculations
AMATH 502
Mid term exam Winter 2014
You are allowed one double-sided 8 1/2 by 11 sheet of notes, but no other reference
materials. No electronics aids (calculators or otherwise) are permitted. You have 50
minutes to complete this exam. Dont forget to put
AMATH 402/502
Mid term exam Winter 2013
You are allowed one double-sided 8 1/2 by 11 sheet of notes, but no other reference
materials. No electronics aids (calculators or otherwise) are permitted. Please submit
your sheet of notes with your exam. You have
AMATH 402/502 Winter 2014
Homework 2
DUE at 3pm Friday Jan 31
1. For the following dynamical systems on a circle [0, 2], please nd and classify the
xed points, and sketch the phase portrait (vector eld) on the circle.
(a) = 1 + 2 cos()
(b) = sin3 ()
2. Fo
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Kilograms to Stones/ Pounds conversion table (up to 12st)
provided by www.metric-conversions.org
Kg
St. lbs
Kg
St. lbs
Kg
St. lbs
Kg
St. lbs
0.453kg
0st 1lb
19.50kg
3st 1lb
38.55kg
6st 1lb
57.60kg
9st 1lb
0.907kg
0st 2lb
19.95kg
3st 2lb
39.00kg
6st 2lb
58
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ARCH150 Appreciation of Architecture I
Assignment #2
The Large Theater of Pompeii
Flavian Amphitheater
Pompei, Italy
Built in 2nd Century BCE
Roman Republic Era
Rome, Italy
Built in 70-80 AD
Roman Imperial Era
Figure 01: Aerial view, th
AMATH 402/502 Winter 2014
Homework 1
DUE at 3pm Friday Jan 17
1. (a) For both of the following systems, sketch the phase portrait and graphs of the
solutions for each of these ve initial conditions: x(t = 0) cfw_2, 1, 0, 1, 2.
Also identify the stability
AMATH 402/502 Winter 2014
Homework 4
DUE at 3pm Friday, Feb 7
1. Consider a LRC circuit, which contains a capacitor, resistor, and inductor. Recall that
the voltage across a capacitor is V = Q/C where Q is the charge on the capacitor,
and C 0 is the capac
AMATH 402/502 Winter 2014
Homework 2
DUE at 3pm Friday Jan 24
1. For each of the following dynamical systems, please: i) sketch all of the qualitatively
dierent phase portraits (vector elds) that occur as the parameter r is varied. ii)
Identify the critic
Final
AMATH402
Winter 2006
Bernard Deconinck
1. (20 points) Consider the system
x = (x 1)(r(1 + x2 ) x),
where r is a real parameter.
Find all the values of r at which bifurcations occur.
What kinds of bifurcations are these?
Sketch the bifurcation dia