AMATH 402 - Winter 2018
Homework #1
Due on Friday, January 12, 2018
1. For each of the following systems, sketch the phase portrait and identify the stability
(or instability) of the equilibrium (fixe
AMATH 402 - Winter 2018
Homework #2
Due on Friday, January 19, 2018
1. (Strogatz 3.1.3, 3.2.3, 3.4.8) For each of the following dynamical systems, find the
bifurcation point rc and the fixed point xc
Exercises on Bifurcations
1. Purpose: To study saddle node bifurcations in a model. From [Str94], Example 8.1.1.
Exercise: The following system has been discussed by [Gri71] as a model for a genetic c
AMATH 402 - Winter 2018
Homework #6
Due on Friday, February 23, 2018
1. Consider the Duffing equation
x + x + x3 = 0
where > 0 is a small constant. This can be thought of as a model of an undamped
spr
AMATH 402 - Winter 2018
Homework #3
Due on Friday, January 26, 2018
1. (Strogatz 4.1.2 & 4.1.4) For the following dynamical systems on a circle, find and
classify the fixed points and sketch the phase
AAZlO Dry Friction, Wedges & Screws 1
This lab is an introduction to dry friction. wedges & screws. To do this, the reading material
can be found in the textbook chapter 8.18.4.
Problem 1 Theory of
1
one 220 Axial Loading
Lab Exercise
M
The purpose of this lab is to provide further practice analyzing 1D axial loading behavior, and to apply
the basic ideas in a simple experimental context.
1 Mate
CEE 220 Statics and Design Lab Exercise
The purpose of this lab is to improve statics skills on a real world problem and to explore some basic
design concepts.
Materials
0 This handout.
0 Real world s
AAZ] 0
Pressure & Moment of Inertia l
This lab is an introduction to pressure, moment of inertia and parallel axis theorem. To do
this, the reading material can be found in the textbook chapter 9.1-
AAZlO Dry Friction, Wedges & Screws 1
This lab is an introduction to dry friction. wedges & screws. To do this, the reading material
can be found in the textbook chapter 8.18.4.
Problem 1 Theory of
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AAZlO Dry Friction, Wedges & Screws 1
This lab is an introduction to dry friction. wedges & screws. To do this, the reading material
can be found in the textbook chapter 8.18.4.
Problem 1 Theory of
AMath 352 Winter 2018
Homework 2
Due Sunday Jan. 28th, 11:59pm, on Canvas
Problem 1
1
2
3
Let x = 2 , y = 3 , z = 4. Find R such that x + y is orthogonal to y.
3
4
5
Find R such x + y + z is o
AMath 352 Winter 2018
Homework 3
Due Sunday Feb. 4th, 11:59pm, on Canvas
Problem 1
Find the basis and dimension of the following linear spaces:
1. V = x R3 : x1 + 3x2 + 9x3 = 0
2. V = x R4 : x3 x4
AMath 352 Winter 2018
Homework 1
Due Friday Jan. 19th, 11:59pm, on Canvas
Problem 1
Determine (and justify) whether the following function is a norm:
x
x = 1 R2 , kxk = |x1 + x2 | + |x1 x2 | .
x2
So
AMath 352 Winter 2018
Homework 3
Due Sunday Feb. 4th, 11:59pm, on Canvas
Problem 1
Find the basis and dimension of the following linear spaces:
1. V = x R3 : x1 + 3x2 + 9x3 = 0
2. V = x R4 : x3 x4
AMath 352 Winter 2018
Homework 4
Due Sunday Feb. 18th, 11:59pm, on Canvas and Scorelator
This homework comprises two parts: one part must be returned on Canvas (Problems 1 to 4)
while the second part
Prof. Chris Bretherton
AMATH 567
Due: Wednesday, November 8, 2017
Homework Set 4
Problem 1. Find the partial fraction decomposition of the following, using the method discussed
in class based on the f
Prof. Chris Bretherton
AMATH 567
Due: Wednesday, December 6, 2017
Homework Set 8
Problem 1. Consider Laplaces equation = xx + yy = 0 in the domain D between the y-axis
(x = 0), where (0, y) = 0, and t
Prof. Chris Bretherton
AMATH 567
Due: Friday, October 20, 2017
Homework Set 2
Problem 1.
(a) Show that
Z
i/2
cosh(z)dz = i
0
where the integral can be taken along any path between the two endpoints. (
Prof. Chris Bretherton
AMATH 567
Due: Wednesday, November 15, 2017
Homework Set 5
Problem 1. Find the following integrals by casting them as the real or imaginary parts of complex
exponentials and clo
Prof. Chris Bretherton
AMATH 567
Due: Wednesday, November 29, 2017
Homework Set 7
Problem 1. Consider the wave equation from the last homework:
2 2
=0
t2
x2
( < x < , 0 < t < ),
subject to initial con
Prof. Chris Bretherton
AMATH 567
Due: Wednesday, November 22, 2017
Homework Set 6
Problem 1. Consider the wave equation:
2 2
=0
t2
x2
( < x < , 0 < t < ),
subject to initial conditions at time t = 0:
Prof. Chris Bretherton
AMATH 567
Due: Friday, October 27, 2017
Homework Set 3
Problem 1. For what region in the complex plane does the power series
1 + (z 1)2 /22 + (z 1)4 /24 + (z 1)6 /26 + .
converg