Departmental website ��
http://www.mathstat.concordia.ca
Department of Mathematics & Statistics
Concordia University
MATH 203
Differential & Integral Calculus I
Summer 2014
Instructor*:
Office/Tel No.:
Office Hours:
*Students should get the above information from their instructor during class time. The instructor is the person to contact should there be
any questions about the course.
Course Examiners: Dr. H. Proppe, Dr. A. Atoyan.
Text:
Single Variable Calculus, by James Stewart, 7th Edition, Nelson Education.
Prerequisite:
Math 201 or an equivalent Functions course.
Tutorials:
Calculus requires a lot of practice. There is not enough class time to do all the examples
and problems needed to learn the material thoroughly. The Department has therefore
organized special
calculus Tutorials conducted once per week for every section of this
course to provide additional support to students outside the lecture room environment.
Tutorials are conducted by senior students who will help with solving problems on the
topics learned in class that week, with particular emphasis on the material that students
may have difficulties with in this course. Students are strongly encouraged to participate
and be active at these problem-solving sessions which represent an important new resource
to help you succeed in this course.
WeBWorK:
Every student will be given access to an online system called
WeBWorK. The system
provides you with many exercises and practice problems. Students will use this system to
do online assignments. Students also are strongly encouraged to use this resource to work
on the Practicum problem sets - problems similar to the assignment problems, and in areas
where they need extra assistance.
Math Help Centre:
In addition to Tutorial classes, a Math Help Centre staffed by graduate students has been
organized to help students in solving problems on every-day bases. A schedule of its
operation and its location will be posted in the Department.
Office Hours:
Your professor will announce her/his office hours during which she/he will be also
available to give a reasonable amount of help. Note, however, that if you missed a class it
is not reasonable to expect your professor to cover the missed material for you.
MATH 203 – Summer 2014
Page 2
Assignments:
Students are expected to submit assignments online using
WeBWorK. Late assignments
will not be accepted
. WeBWorK assignments contribute 10% to your final grade (see the
Grading Scheme below). Working regularly on the assignments is essential for success in
this course. Students are also strongly encouraged to do as many problems on their own as
their time permits from the list of recommended problems included in this outline as well
as the practice problems in WeBWorK mentioned above. A solutions manual for all odd-
numbered questions is packaged with the textbook.
Midterm Test:
There will be one midterm test in Week 4 which will contribute up to 25% to your final
grade (see the Grading Scheme below).
NOTE: It is the Department's policy that tests missed for any reason,
including illness,
cannot be made up. If you miss a test because of illness
(to be confirmed by a valid medical
note) the final exam can count for 90% of your final grade, and 10% will be contributed by
the assignments.
Final Exam:
The final examination will be three hours long.
NOTE: Students are responsible for finding out the date and time of the final exams once
the schedule is posted by the Examinations Office. Conflicts or problems with the
scheduling of the final exam must be reported directly to the Examinations Office,
not to
your instructor. It is the Department's policy and the Examinations Office's policy that
students are to be available until the end of the final exam period. Conflicts due to travel
plans will not be accommodated.
Grading Scheme:
The final grade will be based on the
higher of (a) or (b) below:
a) 10% for the WeBWorK, assignments
25% for the midterm test,
65% for the final exam.
b) 10% for the WeBWorK, assignments
10% for the midterm test,
80% for the final exam.
IMPORTANT:
PLEASE NOTE THAT THERE IS NO "100% FINAL EXAM" OPTION IN THIS COURSE.
The term work contributes at least 20% to the final grade. Therefore active participation in
classes and continuous work on the course material
during the semester is incremental for
the success in this course. Also, note that although class attendance is not mandatory, years
of experience has shown that students who do not attend classes and believe they can keep
up with the material on their own do poorly on the final examination.
Calculators:
Only calculators approved by the Department (with a sticker as proof of approval) are
permitted in the class test and final examination. The preferred calculators are the
Sharp
EL 531 and the
Casio FX 300MS, available at the Concordia Bookstore.
MATH 203 – Summer 2014
Page 3
CONTENTS
Note:
All of Chapter 1 is a review of material that was covered in prerequisite courses, and is
important for this course. The material that is skipped in this review will be introduced
briefly later in the course when needed. If you don��t know this preliminary material
thoroughly, it is particularly important that you learn it through assignment questions and
recommended problems. If you still feel you don��t know it well enough after the first class
or so (you should also try the quiz at the very end of this document) you may want to
consider dropping the course and taking MATH 201 instead.
Weeks/Lectures
Topics
Recommended Problems
1/1
1.1 Representations of functions
p.19: 3, 23, 29, 33, 49, 51
(Review of
1.2 A catalogue of functions
p.33
1, 9, 13, 15
functions)
1.3 New functions from old
p.42: 11, 23, 33, 35, 43
1/2
2.1 The tangent and velocity problems
p.86: 3, 5, 7
2.2 Limit of a function
p.96: 7, 11, 21, 33
2.3 Calculating limits
p.106: 11, 17, 27, 45, 63
2.6 Limits at infinity, horizontal asymptotes
p.140: 19, 21, 27, 29, 45
2/3
2.5 Continuity
p.127: 3, 21, 23, 41
2.7 Derivatives and rates of change
p.150: 7, 23, 31, 39
2.8 Derivative as a function; higher derivatives p.162: 21, 25, 37, 53
2/4
1.5 Exponential functions
p.57: 3, 11, 17, 21, 23
1.6 Inverse and logarithmic functions
p.69: 9, 11, 21, 37 41, 57
3/5
3.1 Derivatives of polynomials and exp.
p.181: 9, 17, 21, 29, 43, 47
3.2 Product and quotient rules
p.189: 3, 13, 19, 27
App. D Trigonometric functions (an overview) p.A32 3, 9, 13, 49, 65, 69
3/6
3.3 Derivatives of trigonometric functions
p.197: 3, 7, 11, 23, 25
3.4 Chain Rule
p.205: 13, 23, 31, 33, 35, 53
4
MIDTERM TEST
(based on the material of weeks 1-3)
4/7
3.5 Implicit differentiation
p.215: 9, 17, 27, 29, 39
3.6 Derivatives of logarithmic functions
p.223: 7, 19, 23, 43, 45
5/8
3.8 Exponential growth/decay
p.242 3, 9, 11, 17, 19
3.9 Related rates
p.248: 3, 5, 11, 13, 15, 23, 33
5/9
3.10 Linear approximations, differentials
p.255: 1, 5, 11, 13, 17, 19, 33, 37
4.1 Maximum/minimum values
p.280: 25, 31, 37, 43, 51, 61
6/10
4.2 Mean Value Theorem
p.288: 3, 9, 17, 19, 25
4.4 Indeterminate forms; L'Hôpital's Rule
p.307: 11, 17, 19, 41, 51
6/11
4.3 Shape of graphs
p.297: 9, 11, 15, 19, 21
4.5 Summary of curve sketching
p.317: 5, 13, 23, 29, 45
7/12
4.7 Optimization problems
p.331: 13, 15, 19, 23, 29, 33, 37
7
REVIEW
MATH 203 – Summer 2014
Page 4
Choosing Between Math 201 and Math 203
If the last math course you took was at the high school level (Quebec), and more than five years have
passed since, you should probably register for Math 200. If you are still unsure of your level, read on.
Math Courses at Concordia
Math 200
Basic Algebra
Math 206
Algebra/Functions
Math 201
Functions & Trigonometry
Math 209
Cal I/Commerce
Math 208
Algebra/Commerce
Math 202
Interm. Algebra/
Science
Math 203
Cal I /Science
Math 204
Linear Algebra
Math 205
Cal II /S
cience
B.A.; Social Science, Commerce, etc.
Non-Science Mathematics
B.Sc.; Engineering, Computer Science, etc. Science
Mathematics
A self-administered test to help you decide between Math 201 and Math 203 follows. Give yourself
about 30 minutes to complete the test. Be honest with yourself, since registering in the wrong course
may cost you money and result in a poor grade. Remember that all university-level courses usually
demand quite a bit of your time. Students in Math 203 will find they will not have time once the course
begins to review material that they are expected to know before they enter the course.
Scoring: 10 or less = Math 201; 11-14 = see an advisor; 15 or better = Math 203. Answers are on the last
page.
MATH 203 – Summer 2014
Page 5
MATH 203
Qualifying Test
1) What is the equation, in
slope--intercept form, of the line whose slope is 7 and whose
y-intercept
a)
y = 3x + 7
b)
y = 7x
3
c) y = 7
x + 21
d)
y = 7x 21
e)
2) What is the slope of any line
parallel to the line 5
x + 6
y= 30?
a) -
6
5
b) -
5
6
c) 0
d)
5
6
e)
6
5
3)
x + 5
y
x +
ky = 12 are perpendicular. What is the value of
k?
e) 10
4) Find the coordinates of the
midpoint M, and the
length L of the line segment joining the points (3
a)
M
7
2
,-
3
2
⎛
⎝
��
⎞
⎠
�� ,
L= 2 b)
M
7
2
,
3
2
⎛
⎝
��
⎞
⎠
�� ,
L= 3
c)
M
1
2
,-
1
2
⎛
⎝
��
⎞
⎠
�� ,
L= 2
d)
M -
1
2
,
1
2
⎛
⎝
��
⎞
⎠
�� ,
L = 2
e)
M
1
2
,-
1
2
⎛
⎝
��
⎞
⎠
�� ,
L= 3
5) What is the equation of the line having a slope of 0 and passing t
a)
x = 6
b)
x = 1
c)
y = 6
d)
y = 1
e)
y =
1
6
6) Factor: 2
x2 + 11
x + 15
a) (2
x+3)(
x+5)
b) (
x+3)(
x+5)
c) (2
x+15)(
x+1)
d) (2
x+5)(
x+3)
e) (2
x+1)(
x+15)
7) The expression
x2
kx +
R is a perfect square. Find the value of
R.
a) 25
b) 5
k2
c) 25
k2
d) 100
k2
e) 25
k2x2
8) Consider solving
x2 + 12
x + 5 = 0 by completing the square: x2 + 12
x
What is the number that goes in the blanks?
a) 144
b) 36
c) 16
MATH 203 – Summer 2014
Page 6
9) Solve 3
x2
x
a)
-10 �� 101
3
b)
-5 �� 37
6
c)
5 �� 37
6
d)
10 �� 101
9
e)
10 �� 101
3
10) The graph of the parabola
y =
x2 + 6
x + 13 is symmetric about a line. What is the equation of that line?
a)
x
b
) x = 0
c)
x = 3
d)
y = 0
e)
y = 3
11)
a) (
x + 4)2 + (
y 5)2 = 16
b) (
x 4)2 + (
y + 5)2 = 4
c) (
x + 4)2 + (
y 5)2 = 256
d) (
x 4)2 + (
y + 5)2 = 256
e) (
x + 4)2 + (
y
2 = 4
12) Determine which of the following triangles are right triangles if the sides�� lengths are:
I) 8, 15, 17 II) 4, 5, 6
III) 2, 2, 3
IV) 9, 12, 15
a) I only
b) II only
c) III only
d) I and IV only
e) I, II and IV
13) A triangle ABC has right angle B. Sides AB and BC have the lengths 3 and 4 respectively. Determine the
cosine of angle
A (cos
A).
a)
3
5
b)
3
4
c)
4
5
d)
4
3
e)
5
3
14) Which of the following ratios is the tangent of an angle?
a)
opposite
hypotenuse
b)
hypotenuse
adjacent
c)
adjacent
hypotenuse
d)
hypotenuse
opposite
e)
opposite
adjacent
15) What is the value of sin
2��
3
?
a)
1
2
b) -
1
2
c)
3
2
d)
- 3
2
e)
2
2
MATH 203 – Summer 2014
Page 7
16) What is the value of cot
3��
2
?
a) 0
b) 1
d)
2
2
e) does not exist
17) What is the value of log2 64?
a) 6
b) 8
c) 16
d) 128
e) 4096
18) Which of the following is equal to log
k A =
3
2
?
a)
k =
A
3
b)
k =
3
2
⎛
⎝
��
⎞
⎠
��
A
c)
3
2
=
A
k
d)
A =
3
2
k
e)
A =
k
3
19) Write as a single logarithm: log8 5-2log8 6
a) log 8
5
36
b) log 8
5
12
c) log 8 11
d) log 8 41
e) log 8 180
20) What is the result when log
AB
C
is expanded?
a) log
A +
1
2
(log
B
C)
b)
1
2
(log
A + log
B – log
C)
c) log
A + log
B – 2 log
C
d)
1
2
(log
A log
B – log
C)
e) log
A + log
B -
1
2
log
C
ANSWERS:
1. b); 2. b); 3. c); 4. a); 5. d); 6. d); 7. c); 8. b); 9. c); 10. a); 11. d); 12. d); 13. a); 14. e); 15. c); 16. a); 17. a); 18. e);
19. a); 20. e)
