MAT 192 – Enriched Calculus II
2015 Winter Semester
Course Outline
1. INSTRUCTOR AND CONTACT INFORMATION
SYLVAIN BÉRUBÉ1
Office
Johnson 114-A
Email
sberube@ubishops.ca
2. COURSE OVERVIEW
2.1
OFFICIAL DESCRIPTION
Content
Area. The definite integral. The Fundamental Theorem of Calculus. Techniques of integration.
Applications of integration, Differential Equations. Emphasis is on analytical understanding.
This course is for students who lack Collegial Mathematics NYB or the equivalent. This course is
required for all students in Mathematics, Physics and Computer Science. Students who have
received credit for an equivalent course taken elsewhere may not register for this course. Credit will
be given for only one of MAT 192b and MAT 199b.
Credits
3.00 Credits
Hours
Three hours per week of lectures
No laboratory work nor other scheduled class activity
Prerequisite
MAT 191a or a grade of at least 70% in MAT 198a or 80% in MAT 197ab.
2.2
CONTEXT OF THE COURSE IN THE ACADEMIC PROGRESS
MAT 198 – Calculus I (for Life Sciences) is a first-year course intended for students in programs like Mathematics,
Physics and Computer Science without collegial Mathematics NYB or equivalent.
2.3
OBJECTIVE OF THE COURSE
The course has two primary objectives: enable students to use differential Calculus concepts in applications problems
(related rates, curve sketching, optimization) and to develop students’ understanding of the basic concepts of integral
Calculus (the Fundamental Theorem of Calculus, solution and evaluation of definite, indefinite and improper integrals
and applications of same).
Secondary course objectives include the development of steady work habits, logic and problem solving skills, and an
appreciation for the role of calculus in the modern world.
1 I would like to express my gratitude to my colleagues who contributed to the development of this course, and
especially to Dr. David Smith and Dr. Brad Willms who taught this course over the last years.
MAT 192 – Enriched Calculus II
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2.4
SYLLABUS
Some sections may be partially covered or completely dropped: the time available will determine which applications will
be covered. The order of presentation may be altered.
Part 1: Integrals and Area
Appendix E The Sigma Notation
5.1 Areas and Distances
5.2 The Definite Integral
5.3 Fundamental Theorem of Calculus (including 4.9 Antiderivatives)
6.1 Areas between Curves
5.4 Indefinite Integrals and the Net Change Theorem
Part 3: Applications of Integration
6.2 and 6.3 Volumes
6.5 Average Value of a Function
8.1 Arc Length
9.1, 9.3 and 9.5 Differential Equations
Part 2: Techniques of Integration
5.5 The Substitution Rule
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.8 Improper Integrals
2.5
FEEDBACK ON THE COURSE
Students are invited to answer an informal feedback form about the course in the fifth week of the session, and a final
evaluation at the end of the session. They are also invited to share their concerns about the course during periods of
availability of the teacher or by email.
3. LOGISTICS INFORMATION
3.1
SCHEDULE
Day
Tuesday
Thursday
3.2
Time
10:00 a.m. ‒ 11:20 a.m.
10:00 a.m. ‒ 11:20 a.m.
Room
Nicolls Building, Room 211
Nicolls Building, Room 211
AVAILABILITY
Students are very welcome to meet me outside the classroom to discuss any questions. Office hours are to be
determined in the first week of the semester. For communications on Moodle or email, you may expect answer in less
than 24 hours most of the time, except during weekend. A final exam review groups will also be offered. For extra free
help, visit Bishop’s Math Help Centre in Johnson 4.
3.3
WEBSITE
The course uses the e-learning platform Moodle. You find on this site: the syllabus; the solutions to assignments,
midterm tests and final exam; a discussion forum, which is a good place to engage discussions about topics related to
mathematics in general and to our course interest in particular.
Website
https://moodle.ubishops.ca/course/view.php?id=3008
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3.4
INSTRUCTIONAL METHOD
Interactive
lectures
The lectures in class address the theoretical, practical and technical contents of the course. They
request your active participation, by asking or answering questions, solving problems, sharing your
ideas and reflexions.
Assignments,
quizzes and
additional
exercises
Mathematics is not a spectator sport! The only way to learn mathematics is by doing it, which is why
I am assigning so many problems. Assignments, quizzes and additional exercises help to
strengthen and deepen the understanding of concepts covered in class. Also, the students have to
see the assignments and the quizzes as a very important tool in preparation for the lectures, the
midterms and the final exam.
Interaction on
the course
website
The Moodle website facilitate the interaction between the members of the group outsite the class.
The implemented forums are a good place to engage discussions about topics related to
mathematics in general and to our course interest in particular.
Advice: Mathematics can seem difficult and abstract, but it is ultimately just logic. If you think things through calmly
and systematically, you should be able to understand a concept or a problem. You should try to break a problem down,
and try to solve it one step at a time. It is very rare that one can see a solution to a problem immediately. It is
completely normal to have to do some trial and error before solving one.
You will get a lot more out of the lectures if you read the relevant sections of the text first. Ideally, you should try to read
over it superficially before the lecture, and then go through all the details by hand afterwards.
Finally, if you have any questions, please never hesitate to contact me or to come to office hours. That is what I am
here for.
4. COURSE MATERIALS
Required text
James Stewart, Single variable, Calculus, Early transcendentals, Seventh Edition, Thomson,
Brooks/Cole, 2012. ISBN: 978-0-538-49867-8.
Suggested
online
references
Stewart's Tools For Enriching Calculus
http://www.stewartcalculus.com/tec/ (Some exercises hints + visuals / animations)
PatrickJMT
http://patrickjmt.com/#calculus
Mathematical
software
We might use the free and open source mathematical software Sage (sagemath.org) to help us
analyze or calculate numeric or symbolic data. If you want to do computational mathematics in the
cloud, I recommend using Sagemath Cloud (cloud.sagemath.org), which is free.
Other requisites To perform simple mathematical calculations, a calculator might be useful.
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5. ASSIGNMENTS AND EVALUATION
5.1
PRESENTATION OF THE ASSIGNMENTS AND EVALUATION
Evaluation
Date
Duration
Weighting
Assignments
Up to 6 assignments during the semester
At least one week
10%
Quizzes
Up to 6 quizzes during the semester
15 minutes
10%
Midterm Test 1
Thursday, February 12 (subject to change)
80 minutes
20%
Midterm Test 2
Thursday, March 19 (subject to change)
80 minutes
20%
Final Exam
Between April 12 and April 24
180 minutes
40%
A grade of at least 50% at the final exam will guarantee you to pass the course. When this applies, your final grade will
be the maximum between 50% and the mark obtained using the marking scheme described above.
5.2
DESCRIPTION OF THE ASSIGNMENTS AND EVALUATION
Assignments
The assignments cover new material presented in class. While completing these assignments,
collaboration between fellow classmates is not only accepted, but warmly encouraged, because
working with peer is often a great way to learn. Also, you may submit your work in team, with up
to 3 students per team. It may happen that only selected problems, chosen at random, will be
marked.
Quizzes
The quizzes consist of a couple of the assigned problems. The date of the quizzes will be
announced on Moodle and in class.
Midterm Tests &
Final Exam
The midterm tests and the final exams are closed book with calculators allowed. Their content
will be discussed in class.
It is more important that your reasoning be good and your explanations clear than that your final answer be correct. If
you get stuck on a problem, write out what you have, and explain why you are stuck. Such an answer will be worth
much more than a correct answer with unclear or incorrect reasoning.
5.3
POLICY ON ACADEMIC INTEGRITY
Bishop’s University is committed to excellence in scholarship. All members of the university community have a
responsibility to ensure that the highest standards of integrity in scholarly research are understood and practiced.
The university takes a serious view of any form of academic dishonesty, such as plagiarism; submission of work for
which credit has already been received; cheating; impersonating another student; falsification or fabrication of data;
acquisition of confidential materials, e.g. exam papers; misrepresentation of facts; altering transcripts or other official
documents.
5.4
LATE ASSIGNMENTS
Assignments have to be handed back at the given time. An extension may be given to students who give me a valid
written justification before the deadline. In any other cases, late assignments will not be accepted.
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