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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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
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
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 #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 #1
Spring 2014
Due Tuesday, May 20th
Note: Assignments are to be submitted to the appropriate drop box opposite MC
4066, by 12:00pm.
A/
1. Problem Set 1 #1v, #2i, iv, #4i
Hint for #1: The constant of integration should not appear in t
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 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, 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
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,
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
ASSIGNMENT 2: Sketching, approximation, and the method of
undetermined coecients
Fall 2014
Submit your work by noon on Friday, September 26th in the dropbox. (Location posted
on LEARN).
Include course name, assignment number, name, and student
AMATH 250 ASSIGNMENT 5: Second order equations and oscillations Fall 2014
Submit your work by noon on Friday, October 31 in the dropbox. (Location posted on
LEARN).
Include course name, assignment number, name, and student ID on your submission.
Acknowl
AMATH 250
Fall 2014
ASSIGNMENT 6: Laplace Transforms
Submit your work by noon on Friday, November 14 in the dropbox. (Location posted
on LEARN).
Include course name, assignment number, name, and student ID on your submission.
Acknowledgements: be sure t
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
Objectives:
Contents:
Introduction to Dierential Equations
Winter 2015
The course introduces the basic methods for solving and analyzing ordinary
dierential equations and gives a variety of applications in the sciences and
in engineering.
Topic
AMATH 250
ASSIGNMENT 7: Homogeneous Linear Systems
Fall 2014
Submit your work by noon on Friday, November 21 in the dropbox. (Location posted
on LEARN).
Include course name, assignment number, name, and student ID on your submission.
Acknowledgements: b
AMATH 250
ASSIGNMENT 9: Inhomogeneous Linear Systems
Fall 2014
NOT FOR SUBMISSION.
1. (a) Find the general solution to the homogeneous system
x (t) =
1 2
x(t)
1 4
using any method you like.
(b) Write the solution to the DE in (a) in the form x(t) = (t)a w
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
Fall 2014
ASSIGNMENT 8: Homogeneous Linear Systems: Phase portraits
Submit your work by noon on Friday, November 28 in the dropbox. (Location posted
on LEARN).
Include course name, assignment number, name, and student ID on your submission.
Ac
AMATH 250
Fall 2014
ASSIGNMENT 8: Homogeneous Linear Systems: Phase portraits
Submit your work by noon on Friday, November 28 in the dropbox. (Location posted
on LEARN).
Include course name, assignment number, name, and student ID on your submission.
Ac