Chapter 3
Systems of dierential equations
60
MAT 1332: Additional Course Notes
3.1
61
Systems of dierential equations - the linear case
Recall that a single linear dierential equation
d
x(t) = ax(t),
dt
x(0) = x0
has the solution x(t) = eat x0 . In partic
MAT 1332: Calculus for Life Sciences
A course based on the book
Modeling the dynamics of life
by F.R. Adler
Supplementary material
University of Ottawa
Frithjof Lutscher, Jing Li and Robert Smith?
January 9, 2014
Contents
1 Integration: tools techniques a
MAT 1332 3X, Spring/Summer 2014, Assignment 7
NOT TO BE HANDED IN; PREPARATION FOR FINAL EXAM
Instructor: Jerey Musgrave
Student Name
Student Number
By signing below, you declare that this work was your own and that you have not copied from
any other indi
MAT 1332 3X, Spring/Summer 2014, Assignment 7
NOT TO BE HANDED IN; PREPARATION FOR FINAL EXAM
Instructor: Jerey Musgrave
Student Name
Student Number
By signing below, you declare that this work was your own and that you have not copied from
any other indi
MAT 1332 3X, Spring/Summer 2014, Assignment 5
Due Thursday June 26th
Late assignments will not be accepted; nor will unstapled assignments.
Instructor: Jerey Musgrave
Student Name
Student Number
By signing below, you declare that this work was your own an
MAT 1332 3X, Spring/Summer 2014, Assignment 6 Solutions
Due Thursday July 3rd
Late assignments will not be accepted; nor will unstapled assignments.
Instructor: Jerey Musgrave
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Student Number
By signing below, you declare that this work was yo
MAT 1332 3X, Spring/Summer 2014, Assignment 4
Solutions
Instructor: Jerey Musgrave
Student Name
Student Number
By signing below, you declare that this work was your own and that you have not copied from
any other individual or other source.
Signature
Ques
MAT 1332 3X, Spring/Summer 2014, Assignment 6
Due Thursday July 3rd
Late assignments will not be accepted; nor will unstapled assignments.
Instructor: Jerey Musgrave
Student Name
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By signing below, you declare that this work was your own and
MAT 1332 3X, Spring/Summer 2014, Assignment 4
Due Thursday June 19th
Late assignments will not be accepted; nor will unstapled assignments.
Instructor: Jerey Musgrave
Student Name
Student Number
By signing below, you declare that this work was your own an
MAT 1332 3X, Spring/Summer 2014, Assignment 5
Due Thursday June 26th
Late assignments will not be accepted; nor will unstapled assignments.
Instructor: Jerey Musgrave
Student Name
Student Number
By signing below, you declare that this work was your own an
MAT 1332 3X, Spring/Summer 2014, Assignment 2
Due Tuesday May 27th
Late assignments will not be accepted; nor will unstapled assignments.
Instructor: Jerey Musgrave
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By signing below, you declare that this work was your own and
Version 1
Question 1.
[4 points] Calculate
2
a)
2
1
dy
29
y
/2
b)
/2
sin(x)
dx
1 + cos2 (x)
Solution. a) We have
y2
1
1
a
b
(a + b)y + 3(a b)
=
=
+
=
,
9
(y 3)(y + 3)
y3 y+3
(y 3)(y + 3)
with a + b = 0 and 3(a b) = 1, which implies a = 1/6 and b = 1/6.
2
MAT 1332, Winter 2015, Assignment 2
Due Wednesday February 4 in the math department dropboxes by 4:00pm.
Late assignments will not be accepted; nor will unstapled assignments.
Professors in the math department will not lend you a stapler; do not ask for o
MAT 1332, Summer 2014 Practise Midterm II
Instructor: Dr. Je Musgrave
NAME
I.D.#
Instructions: This exam consists of 7 long answer questions.
Duration: 80 minutes
NO CELL PHONES. NO BOOKS. NO NOTES.
2
1. (a) For which values of c is the matrixx
1 0 c
A= 2
MAT 1332, Winter 2015, Assignment 5
Due Wednesday March 25 in the dropboxes by 4:00pm.
Late assignments will not be accepted; nor will unstapled assignments.
Professors in the math department will not lend you a stapler; do not ask for one.
Instructor (ci
MAT 1332, Winter 2015, Assignment 3
Due Thursday February 12 by 9:00pm.
Late assignments will not be accepted; nor will unstapled assignments.
Professors in the math department will not lend you a stapler; do not ask for one.
Instructor (circle one): Robe
MAT 1332, Winter 2015, Assignment 1
Due Wednesday January 28 by 4:00pm.
Late assignments will not be accepted; nor will unstapled assignments.
Professors in the math department will not lend you a stapler; do not ask for one.
Instructor (circle one): Robe
MAT 1332, Winter 2015, Assignment 4
Due Wednesday March 11 in the math department dropboxes by 4:00pm.
Late assignments will not be accepted; nor will unstapled assignments.
Professors in the math department will not lend you a stapler; do not ask for one
University of Ottawa
Department of Mathematics and Statistics
MAT 1332
Summer 2014
Calculus for Life Sciences II
INSTRUCTOR:
EMAIL:
Dr. Je Musgrave
[email protected]
OFFICE:
585 King Edward, Room B07-B
PHONE:
613 562 5800 ext 2029
OFFICE HOURS: Tuesday
MAT 1332 Midterm I, June 10th, 2014
Solutions
Instructor: Dr. Je Musgrave
NAME
I.D.#
Instructions: This exam consists of 7 long answer questions on 9 pages. The marks for
each question are as listed with the question itself. The total value of the exam is
MAT 1332 Midterm II, July 10th, 2014
Instructor: Dr. Je Musgrave
NAME
I.D.#
Instructions: This exam consists of 7 long answer questions on 12 pages. The marks for
each question are as listed with the question itself. The total value of the exam is 30. You
MAT 1332, Summer 2014
Tentative schedule
Professor: Jeff Musgrave
Date
Topic/Section
PP: practice
problems
Section (old book)
Comments
Theme: Integration: tools techniques, applications
May 01
6.2 and 6.5
Review of
Integration
May 06
6.3 Riemann sums,
int
MAT 1332, Summer 2014 Practise Midterm II
Instructor: Dr. Je Musgrave
NAME
I.D.#
Instructions: This exam consists of 7 long answer questions.
Duration: 80 minutes
NO CELL PHONES. NO BOOKS. NO NOTES.
2
1. (a) For which values of c is the matrixx
1 0 c
A= 2
MAT 1332, Summer 2014 Practise Midterm I
Instructor: Dr. Je Musgrave
NAME
I.D.#
Instructions: This exam consists of 6 long answer questions.
Duration: 80 minutes
NO CELL PHONES. NO BOOKS. NO NOTES.
2
1. Calculate
2
(a)
2
1
dy
y2 9
2
(b)
2
sin(x)
dx.
1 + c
MAT 1332 3X, Spring/Summer 2014, Assignment 1
Due Tuesday May 20th
Late assignments will not be accepted; nor will unstapled assignments.
Instructor: Jerey Musgrave
Student Name
Student Number
By signing below, you declare that this work was your own and
MAT 1332 3X, Spring/Summer 2014, Assignment 3
Due Tuesday June 3rd
Late assignments will not be accepted; nor will unstapled assignments.
Instructor: Jerey Musgrave
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Student Number
By signing below, you declare that this work was your own and
Sample Midterm Examination
ADM 2340
Financial Accounting
Please note that this exam may not cover the same
chapters or materials that you are responsible for in
your current course!
Time: 2 hours
Student Name: _
Student #: _
Section:
Instructions:
1. Answ