AMath 250
Assignment #3
Spring 2015
Solutions
PS1 #1
PS1 #2
Given:
d2 x
+ x + x3 = F0 sin t.
2
dt
Here, x is a displacement and t is a time, so
d2 x
L
m 2 = M 2 = M LT 2 .
dt
T
m
By the principle of dimensional homogeneity, the other three terms
must have
AMATH 250
ASSIGNMENT 2: Sketching Solutions
Winter 2014
Submit your work before noon on Tuesday, January 21st . Late assignments or those put
into the wrong drop slot will not be marked.
Include course name, assignment #, name, ID #, and tutorial section
AMath 250, W14
Assignment 2: Selected Solutions
Page 1 of 4
1.
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UNIVERSITY OF WATERLOO
FINAL EXAMINATION
SAMPLE EXAM # 1
Student Name (Print Legibly)
(family name)
(given name)
Signature
Student ID Number
COURSE NUMBER
AMATH 250
COURSE TITLE
Introduction to Dierential Equations
COURSE SECTION(s)
001
DATE OF EXAM
Today
AMath 250, Fall 2012
1.
This was done in the lecture.
2.
Assignment 8 solutions
Page 1
AMath 250, Fall 2012
3.
Assignment 8 solutions
Page 2
AMath 250, Fall 2012
Assignment 8 solutions
Page 3
4.
5.* Note that solutions to the challenge problem will not be
AMath 250
Assignment #2
Spring 2012
Due: Wednesday, May 23rd
A/ Problem Set 1 #6 (all), #11
(I also recommend trying #7 and #8; solutions will be posted.)
Note: Dont spend too much time struggling with #6viii; read the question, and
keep in mind that the
AMATH 250
ASSIGNMENT 3
Fall 2012
Submit your work before noon on Tuesday, October 2nd in the correct drop slot. Late
assignments will receive a grade of zero.
1. Use the method of undetermined coecients to nd the general solution for each DE
where applica
AMATH 250
ASSIGNMENT 4 (double)
Fall 2012
Submit your work before noon on Tuesday, October 16th in the correct drop slot across
from MC4066. Note that this is a double assignment due to Thanksgiving.
1. The DE
N
dN
=r 1
dt
K
N h,
where r, K and h are posi
AMATH 250
ASSIGNMENT 5: Pi Theorem, basic 2nd-order DEs
Winter 2015
Submit your work before noon on Tuesday, Tuesday, February 10th .
2
(PS2#21)
(PS2#24)
1. Consider a lake with average diameter D and kinematic viscosity (units: L ). Assume
T
that D is la
AMATH 250
ASSIGNMENT 1: Review, Separable & Linear DEs
Winter 2014
Submit your work before noon on Tuesday, January 14th in location TBA. Late assignments or those put into the wrong drop slot will not be marked.
Include course name, assignment #, name,
AMath 250, W15
250S0L
1.
Assignment 6 Solutions
Page 1 of 3
AMath 250, W15
2.
3.
Assignment 6 Solutions
Page 2 of 3
AMath 250, W15
Assignment 6 Solutions
Page 3 of 3
4.
5. * Note that the RHS of the DE should have been mg, as the external force is gravity
UNIVERSITY OF WATERLOO
SAMPLE MIDTERM EXAMINATION #2
Student Name (Print Legibly)
(family name)
(given name)
Signature
Student ID Number
COURSE NUMBER
AMATH 250
COURSE TITLE
Intro to Dierential Equations
COURSE SECTION(s)
001
DATE OF EXAM
Today!
TIME PERI
AMATH 250
ASSIGNMENT 6: 2nd-order DEs, Oscillator
Winter 2015
Submit your work before noon on Tuesday, March 3rd . Note that this is due just
after the midterm rather than just before, to give you exibility on when you
do the assignment. As always, budget
Introduction to Di erential Equations
Course Notes for AMath 250
J. Wainwright 1
Department of Applied Mathematics
University of Waterloo
March 9, 2010
1
c J. Wainwright, April 2003
Contents
1 First Order Dierential Equations
1.1 DEs and Mechanics . . . .
AMath 250, W15
Assignment 11 solutions
Page 1 of 5
250S0L
1. (a) See Course Notes or lecture.
(b) Note: The fundamental matrices in (i) and (ii) were found on the previous assignment; there is no need to show the work here again.
(i)
AMath 250, W15
(ii)
A
AMATH 250
ASSIGNMENT 11: More Vector DEs
Winter 2015
Not due in, but you are responsible for this material for the nal exam. Good luck on exams!
#13(a)(b)(i)(iv)
1. (a) Give a description of the variation of parameters method for solving an inhomogeneous
UNIVERSITY OF WATERLOO
MIDTERM EXAMINATION
SPRING TERM 2016
Student Name (Print Legibly) WNW RU]:
FAMILY (LAST) NAME GIVEN (FIRST) NAME
Signature
Student ID Number
COURSE NUMBER AMATH 250
COURSE TITLE Intro to Differential Equations
COURSE
AMath 250, F16
Assignment 4 selected solutions
Page 1 of 3
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and make
1. sure that JavaScript is enabled. You will likely need to download the file firs
AMath 250, F16
Assignment 3: Selected Solutions
Page 1 of 4
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and make
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AMATH 250
ASSIGNMENT 10: More Vector DEs
Winter 2015
Submit your work before noon on Tuesday, March 31st in the usual place.
PS5#9
1. Suppose a mechanical oscillator obeys the IVP
y + 4y + 5y = 0
y(0) = 0, y (0) = 1
(1)
(a) Write this as a rst-order vecto
[9]
[ll
AMath 250, F16 QUIZ 4 (version A) SOLUTIONS
ID#:
First Name:
25 min. Na calculators are allowed on quizzes or exams. Leave your answers in exact form,
such as 5 | W, 41/3 sin( 3 ), etc. Solutions must be clearly stated and fully justied.
1.
E
(a)
AMath 250
Assignment #9
Spring 2015
Due Tuesday, July 21st
Note: Assignments are to be submitted to the appropriate drop box opposite MC
4066, by 12:00pm.
1. Problem Set 5 #2b
2. Find the particular solution to each problem above, if the initial condition
AMath 250
Assignment #6
Winter 2017
Solutions
1.
a) The homogeneous solution is Yh = C1 cos + C2 sin . Therefore, for a particular
solution, we try
Y = A cos + B sin .
This gives
and
Y 0 = A cos
Y 00 =
A sin + B sin + B sin
2A sin
A cos + 2B cos
B sin
AMath 250
Assignment #5
Winter 2017
Due Wednesday, March 1
The assignment should be submitted through Crowdmark.
A/ Problem Set 3:
# 2
# 3ab
# 6
# 12
It would be a good idea to start with #1 as a warm-up.
B/
1. Solve the IVP y 00 + 2y 0 + 5y = 10, y (0) =
AMath 250
Assignment #6
Winter 2017
Due Wednesday, March 8th
Please submit your assignment through Crowdmark.
1. Consider the forced oscillator DE
mx00 + cx0 + kx = F0 cos !t.
As we discussed in class, this can be converted into the dimensionless form
Y 0
AMath 250
Assignment #7
Winter 2017
Due Wednesday, March 15th
Please submit your assignment through Crowdmark
A/ From the course notes
1. Problem Set 4 #1 (ii and vi)
2. Problem Set 4 #2 (you may use the table on page 209)
3. Problem Set 4 #7 (i)
4. Probl