THE UNIVERSITY OF CALGARY
DEPARTMENT OF MATHEMATICS AND STATISTICS
FINAL EXAMINATION
AMAT 307
L01 thru L04
Fall 2011
Time: 3 hours
32 questions
Last Name
First name
Lecture Section
A Schulich calculator is permitted. NO notes or aids are allowed.
Enter yo
Department of Mathematics and Statistics
AMAT 307
Handout # 3
Second order linear dierential equations
1. Find the general solution of the following dierential equations
a)
b)
c)
d)
e)
f)
y
y
y
y
y
y
2y 3y = e4x
y = x2
+ 3y 4y = xex
4y + 3y = 20 cos 2x
Laplace Transforms
f (t) = L
1
[F(s]
1/s
1
t
F(s) = L [ f (t)]
n
n!/s
n at
n+1
n+1
t e
n!/(s a)
sin(at)
a/(s2 + a2)
cos(at)
s/(s2 + a2)
sinh(at)
a/(s2 a2)
cosh(at)
s/(s2 a2)
at
e f (t)
F(s a)
ua (t)
e
as
/s
ua(t) f (t a)
e
as
F(s)
f
(n)
(t)
n
n
s F(s) s
AMAT 307
Handout # 3 - Answers, Hints, Solutions
1. Find the general solution of the following dierential equations
a) y 2y 3y = e4x
Solution. Since r2 2r 3 = 0 r = 3, 1, then the general solution of the
homogeneous equation is yhom = C1 e3x + C2 ex . The
University of Calgary
Department of Mathematics & Statistics
MIDTERM - Fall semester, 2010
Monday October 25, 2010
Time: 13:00-13:55
Place: ICT 114
Calculators and tables are not allowed.
I.D. #
Name (First/Second)
Good luck!
Part A. Show your work.
1. (2
AMAT 307
01.
Midterm Examination
About the dierential equation
y y + y ey + 5y = t,
which of the following statement is correct?
(A) Linear, second order.
(B) Nonlinear, third order.
(C) Linear, third order.
(D) Nonlinear, second order.
(E) None of the ab
Department of Mathematics & Statistics
AMAT 311 MIDTERM - Monday October 25, 2010
Answers, Hints, Solutions
Part A. Show your work.
1. (20%) Find the general solution of the equation y 3y + 2y = 2x2 .
Solution. The characteristic equation r2 3r + 2 = 0 ha
UNIVERSITY OF CALGARY - FACULTY OF SCIENCE
Department of Mathematics and Statistics
FINAL EXAMINATION
Amat 307, L01 - L06, Fall 2005
Time 3 hours, NO AIDS, NO CALCULATORS
Surname
Given Names
Lec.
ID
Score/100
Examination Rules
1. Students late in arriving
THE UNIVERSITY OF CALGARY
DEPARTMENT OF MATHEMATICS AND STATISTICS
FINAL EXAMINATION
AMAT 307 L01 thru L04 Fall 2008
I.D. NUMBER
COURSE NUMBER
AMAT
307
Exam No.
87
LAST NAME
STUDENT NAME
1st Initial
Lecture No.
2nd Initial
Time: 3 hours, 40 questions.
STU
Daniel Le Lam
F2013AMAT307L03
Practice Final is due on Monday, December 09, 2013 at 01:17pm.
The number of attempts available for each question is noted beside the question. If you are having trouble guring out your error,
you should consult the textbook,
THE UNIVERSITY OF CALGARY
DEPARTMENT OF MATHEMATICS AND STATISTICS
FINAL EXAMINATION
VERSION # 1
AMAT 307
LEC 01-04
FALL 2012
TUESDAY, DECEMBER 11, 2012
3 HOURS
Last Name
First Name
Student I.D. Number
Section Number
This examination consists of 29 equall
THE UNIVERSITY OF CALGARY
DEPARTMENT OF MATHEMATICS AND STATISTICS
MIDTERM EXAMINATION
AMAT 307
Lec 01 - 04
FALL 2012
Friday, November 09, 2012
90 minutes
Last Name
First Name
Student I.D. Number
Section Number
This examination consists of 20 equally weig
THE UNIVERSITY OF CALGARY
DEPARTMENT OF MATHEMATICS AND STATISTICS
FINAL EXAMINATION
AMAT 307
L01 thru L04
Fall 2009
Time: 3 hours
30 questions
Last Name
First name
Lecture Section
A Schulich calculator is permitted. NO notes or aids are allowed.
Enter yo
Answers to midterm - 2013
1-D
2-E
3-A
4-C
5-D
6-E
7-C
8-B
9-A
10 - D
11 - A
12 - C
13 - B
14 - C
15 - B
16 - E
17 - D
18 - B
19 - A
20 - B
Comment: this year, # 9 is not in the framework of the course, though you can use it
by multiplying and checking tha
DEPARTMENT OF MATHEMATICS AND STATISTICS
COURSE OUTLINE
FALL 2014
1.
Course: AMAT 307 Differential Equations for Engineers
Lecture Day/Time
Room
Instructor
Office
Phone
Email
L04
MWF 14:00-14:50 ICT 122 Elena Braverman
MS 444 (403)-220-3956 [email protected]
Department of Mathematics and Statistics
AMAT 307
Handout # 5
Systems of linear dierential equations
1. Find the general solution of the following systems of dierential equations
2 1
3 4
X
1 3
3
1
a) X =
c) X =
X
d) X =
3 1 1
1 1 X
h) X = 1
4 1 4
X
j) X =
THE UNIVERSITY OF CALGARY
DEPARTMENT OF MATHEMATICS AND STATISTICS
FINAL EXAMINATION
VERSION # 1
AMAT 307
LEC 01-04
FALL 2012
TUESDAY, DECEMBER 11, 2012
3 HOURS
Last Name
First Name
Student I.D. Number
Section Number
This examination consists of 29 equall
Department of Mathematics and Statistics
AMAT 307 - Handout # 2
First Order Equations - Bernoulli, Exact Equations, Review
Homogeneous Second Order Equations
1. Find the general solution of the following dierential equations
a) y + y = xy 3
b) x2 y = y(x
AMAT 307
Handout # 5 - Answers, Hints, Solutions
Systems of linear dierential equations
1. Find the general solution of the following systems of dierential equations
2 1
3 4
X
1 3
3
1
X
a) X =
c) X =
1 5
1
1
X
3 2 1
f ) X = 3 4 3 X
2 4
0
1 2 1
1
1 X
g) X
Department of Mathematics and Statistics
AMAT 307
The Laplace Transform
1. Find the Laplace Transform of the following functions
a)
f (t) = 2 sin t cos t
b) f (t) = t3 et
t
d) f (t) = (t + 1) sin 2t
g)
e)
f (t) =
cos2 (u) du
c) f (t) = sin mt cos nt
f)
f
AMAT 307
Handout # 6 with Answers and Solutions
The Laplace Transform
1. Find the Laplace Transform of the following functions
a) f (t) = 2 sin t cos t
b) f (t) = t3 et
c) f (t) = sin mt cos nt
t
d) f (t) = (t + 1) sin 2t
g)
e)
f (t) =
cos2 (u) du
f)
f (t
Department of Mathematics and Statistics
AMAT 307
Handout # 2 - ANSWERS, HINTS, SOLUTIONS
1. Find the general solution of the following dierential equations
a) y + y = xy 3
b) x2 y = y(x + y)
c) y + x 3 y = 3y
Hints and answers. All these equations are Be
DEPART
TMENT OF MA
ATHEMATICS A
TICS
AND STATIST
COURSE OUTLINE
E
FALL 2014
F
1
1.
Course: AMAT 307 Differential Equa
A
ations for Engin
neers
Lecture Day/Time
Room
In
nstructor
Offic
ce
Phone
L01
L02
L03
L04
MS 332
MS 4
440
MS 5
530
MS 4
444
(403)22
20-8
COURSE OUTLINE
Fall 2014
a
SCHULICH
SGIimi—(‘zf tnpinuvrin}; . 1-.
Presentation and description of data, introduction to probability theory, Bayes' theorem,
discrete and continuous probability distributions, estimation, sampling distributions, te
@350)
U
SCHULICH g, I The University of Calgary
SLIka ul’ Engineer rig am
Schulich School of Engineering
ENGG 319 Probability & Statistics for Engineers (Fall 2013)
Final Examination
Wednesday, 18 December 2013, 12:00 - 15:00, Red Gym
Instructions:
0
QUIZ 2 ENGG 319 L01 Thursday 17 October 2013
1. (3%) The probability of manufacturing defective mechanical pencils is 1%.
What should be the quality inspection batch size so that there is 90%
probability that at least one defective mechanical pencil is fo
Mode: the most common outcome
A S, where " denotes "is a subset of
C D = "union" = the elements in C or D or both
A B = "intersection" = the elements in A and B. If A B= , then A and B are called "mutually
exclusive events"
D' = "complement" = the element
