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Course Outline - Calculus 1 for Honours Mathematics
CALCULUS 1 FOR HONOURS MATHEMATICS FALL 2022
MATH 137
Published Sep 06, 2022
CLASS SCHEDULE
Section
Location
Time
Instructor(s)
Mondays, Wednesdays &
MATH 137 001 [LEC]
DC 1350
Fridays
12:30 p.m. - 1:20 p.m.
Mondays, Wednesdays &
MATH 137 002 [LEC]
MC 4059
MATH 137 003 [LEC]
UTD 105
Fridays
2:30 p.m. - 3:20 p.m.
Mondays, Wednesdays &
MC 4020
Fridays
11:30 a.m. - 12:20 p.m.
Mondays, Wednesdays &
MATH 137 005 [LEC]
MC 4059
MATH 137 006 [LEC]
MC 4021
MATH 137 007 [LEC]
MC 4061
MATH 137 009 [LEC]
MATH 137 011 [LEC]
Jordan Hamilton
j4hamilton@uwaterloo.ca
Jacob Campbell
Mondays, Wednesdays &
Christopher James Lang
Fridays
12:30 p.m. - 1:20 p.m.
Fridays
4:30 p.m. - 5:20 p.m.
Fridays
9:30 a.m. - 10:20 a.m.
Mondays, Wednesdays &
Fridays
1:30 p.m. - 2:20 p.m.
Mondays, Wednesdays &
MATH 137 010 [LEC]
edupont@uwaterloo.ca
j48campbell@uwaterloo.ca
Mondays, Wednesdays &
MC 4020
Eddie Dupont
Fridays
8:30 a.m. - 9:20 a.m.
Mondays, Wednesdays &
MATH 137 008 [LEC]
ipayne@uwaterloo.ca
Fridays
11:30 a.m. - 12:20 p.m.
Mondays, Wednesdays &
MATH 137 004 [LEC]
Ian Payne
STC 0050
Fridays
4:30 p.m. - 5:20 p.m.
MC 4021
Mondays, Wednesdays &
Fridays
10:30 a.m. - 11:20 a.m.
cjlang@uwaterloo.ca
Dongchang Li
d235li@uwaterloo.ca
Eric Bembenek
abembenek@uwaterloo.ca
Jordan Hamilton
j4hamilton@uwaterloo.ca
Mani Thamizhazhagan
athamizhazhagan@uwaterlo
o.ca
Jordan Hamilton
j4hamilton@uwaterloo.ca
This table is generated automatically
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Section
Course Outline - Calculus 1 for Honours Mathematics
Location
Time
Instructor(s)
Mondays, Wednesdays &
MATH 137 012 [LEC]
Fridays
8:30 a.m. - 9:20 a.m.
Ian Payne
ipayne@uwaterloo.ca
This table is generated automatically
INSTRUCTOR / TA INFORMATION
Office hours and their locations will be determined during class.
For administrative questions (e.g. enrollment changes, technical problems etc.) please email
math137@uwaterloo.ca. You should think of this email address as the place to ask non‐math questions
(including re-mark requests).
The Math Tutoring Centre (https://learn.uwaterloo.ca/d2l/le/content/825279/viewContent/4524396/View) will
be available to all students and the schedule will be posted on LEARN. Although help for completing practice
problems is available (from instructors, TA's, or colleagues in the course) keep in mind that you will be on your
own during the quizzes, midterm, and final exam: seeking help should be in the scope of clarifying the material
taught rather than in having the problems completed.
COURSE DESCRIPTION
Calendar Description for MATH 137
Absolute values and inequalities. Sequences and their limits. Introduction to series. Limits of functions and
continuity. The Intermediate Value theorem and approximate solutions to equations. Derivatives, linear
approximation, and Newton's method. The Mean Value theorem and error bounds. Applications of the Mean
Value theorem, Taylor polynomials and Taylor's theorem, Big-O notation. Suitable topics are illustrated using
computer software. [Offered: F,W,S; online: F,W,S]
Prereq: 4U Calculus and Vectors. Antireq: MATH 116, 117, 127, 147
What is calculus? In essence, it is the study of the infinite and the infinitesimal. The infinitely large and infinitely
small. We will study these ideas as they relate to sequences and functions. Then, we will use the tools we discover
to solve problems and expand our knowledge. The main focus of the course will be approximation, as we examine
how to approximate solutions to difficult (or even impossible) to solve problems. The course can be broken down
into four main parts. First, we will examine sequences and what it means for one to converge. Next, we will use our
knowledge of sequences to discuss functions, including limits and derivatives. This will allow us to develop a
powerful theorem, the Mean Value Theorem, and we will examine many applications of it. Finally, we will discuss a
method for approximating complicated functions with Taylor Polynomials.
LEARNING OUTCOMES
By the end of this course students should be able to:
Write clear and well-organized mathematical solutions and proofs.
Solve problems in Calculus through logical thinking and careful analysis.
Determine if an explicitly-defined sequence converges and prove it with the formal definition.
Determine if a recursively-defined sequence converges and prove it using mathematical induction.
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Course Outline - Calculus 1 for Honours Mathematics
Compute the limits of various functions using both the formal definition of the limit, arithmetic rules for
limits,and l'Hopital's Rule.
Determine if a function is continuous or not.
Compute derivatives of various functions.
Apply Newton's Method to approximate the zeros of a function.
Understand the Mean Value Theorem and its applications.
Sketch curves by first analyzing a given function and its derivatives.
Approximate functions using Taylor polynomials and determine an upper bound on the error in this
approximation with Taylor's Theorem.
TENTATIVE COURSE SCHEDULE
Week
Course Notes
Topics Covered
1: Sept 6 - 9
1.1
Absolute Values, Triangle Inequality
2: Sept 12 - 16
1.2
Sequences
3: Sept 19 - 23
1.3, 1.4, 2.1
Squeeze Theorem, MCT, Induction, Functions Quiz 2
4: Sept 26 - 30 *
2.2 - 2.6
Limits of functions of a real variable
Quiz 3
5: Oct 3 - 7
2.7, 2.8
Infinite Limits, Continuity
Quiz 4
RW: Oct 10 - 14
N/A
Reading Week
MT: Oct 17 - 21
2.9, 2.10, 3.1, 3.2
IVT, EVT, Instantaneous rate of change
Quiz 5
6: Oct 24 - 28 ** †
3.3, 3.4, 3.7 - 3.9
Derivatives, Differentiation Rules
Midterm
7: Oct 31 - Nov 4
3.5, 3.6, 3.10, 3.11
Tangent Lines, Newton's Method, IFT
Quiz 6
8: Nov 7 - 11
3.12, 3.13, 4.2.8, 4.1 - 4.2.1 Implicit Differentiation, Extrema, MVT
Quiz 7
9: Nov 14 - 18
4.2.2 - 4.2.4, 4.3
Applications of MVT, L'Hopital's Rule
Quiz 8
10: Nov 21 - 25 ‡
4.2.5 - 4.2.7, 2.11, 4.4
Curve Sketching
Quiz 9
FE: Nov 28 - Dec 2 5.1, 5.2
Taylor Polynomials, Taylor's Theorem
Quiz 10
Final class: Dec 5
Review/Catch-up
N/A
Event
Quiz 1
* September 27: Last day to drop without penalty (100% refund); drop with WD starts September 28
** October 25: Last day to drop with 50% refund
† The midterm is currently scheduled for Monday, October 24 from 7:00 pm - 8:50 pm
‡ November 22: last day to drop with WD; drop with WF starts November 23
TEXTS / MATERIALS
Title / Name
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Notes / Comments
Required
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Course Outline - Calculus 1 for Honours Mathematics
Title / Name
Notes / Comments
Required
Calculus 1 for Honours
Mathematics by B. and B. Forrest
Hard copies are available at the W
No
Store. The PDF version is freely
available here:
http://www.math.uwaterloo.ca/~ba
forres/UCM137/CourseNotes/Forre
st_M137CN.pdf
PIAZZA/EMAIL
Piazza ( https://piazza.com/uwaterloo.ca/fall2022/math137 ) is an elegant way to organize various
communications throughout the course. This includes certain announcements and questions that you may have.
You should think of Piazza as the place to ask questions about math. If you have a concern about the assignment,
the online videos or basically anything you think would help others then please post a public question on Piazza so
that everyone can see the answer. You can make yourself anonymous on a post‐by‐post basis if you feel the need.
Private questions are ok too just think about the nature of your question before deciding the visibility status. Note
that Piazza supports LaTeX syntax for Math. There’s also a built‐in formula editor that ultimately pastes the LaTeX
code. Click here (http://tug.ctan.org/info/undergradmath/undergradmath.pdf) for a good LaTeX primer.
For administrative questions (e.g. enrollment changes, technical problems etc.) please use
math137@uwaterloo.ca. You should think of this email address as the place to ask non‐math questions
(including remark requests).
STUDENT ASSESSMENT
Component
Value
Academic Integrity Module
1
LaTeX Assignment
2 (BONUS)
Quizzes
19
Midterm Exam
30
Final Exam
50
ACADEMIC INTEGRITY MODULE (1%)
There is a 1% module on Academic Integrity on LEARN. It is composed of 6 reading topics and 6 quizzes. You will
have 3 attempts for each quiz.
LATEX ASSIGNMENT (2% BONUS)
There is a two-part bonus assignment on the typesetting language, LaTeX. The first part is a Mobius quiz and the
second part is a written assignment.
The Mobius quiz MUST be accessed through the link in LEARN. You will have 3 attempts and 2 hours per attempt
to complete the quiz.
The written assignment requires you to complete a (very simple) assignment typeset in LaTeX. The assignment can
be accessed through LEARN and your completed PDF should be uploaded to Crowdmark. Most of the questions
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Course Outline - Calculus 1 for Honours Mathematics
are review or easily found in the course notes. Except the first question (which we will cover in Week 2), you should
have all the tools required to complete it from the start of term.
Each assessment is worth a bonus 1% and will be available the entire term with a final due date being the last day
of class: December 6th, 11:59 pm.
QUIZZES (19%)
Quizzes will be written during your tutorial timeslot on Wednesdays from 6:30 - 7:20 PM. You will have an
assigned seat each week and you MUST write your quiz in that assigned seat. You seat will be available a few
days before each quiz on Odyssey. Note that you should ignore your tutorial location on Quest and
follow the information on Odyssey!!
Quizzes will be closed book with no aids allowed and you will have 35 minutes to complete each quiz.
Missed quizzes will be given a mark of zero unless valid documentation is provided
(https://uwaterloo.ca/math/accommodations (https://uwaterloo.ca/math/accommodations) ).
To help you prepare for the quizzes, practice problem sets will be posted on Learn 1-2 weeks before the quiz. There
will be at least one very similar (or even identical) problem that is common to both the practice problem sets and
the quiz you will be writing!
Your two lowest quizzes will be dropped from your final mark.
MIDTERM (30%) AND FINAL EXAM (50%)
The midterm and the final exams will be written in person. The midterm is currently scheduled for October
24th, 7:00 pm - 8:50 pm. If you are unable to write the midterm (for example, you are sick) then valid
documentation (such as a University of Waterloo Verification of Illness form) should be submitted to the Math
Undergraduate Office (MC 4022, mathuo@uwaterloo.ca) and to your instructor, following the instructions here:
https://uwaterloo.ca/math/accommodations (https://uwaterloo.ca/math/accommodations) . In this case, the
weight of the midterm will shift to your final exam. That is, if you are exempted from the midterm, your final will
be worth 80%. There will be NO make-up midterm.
The final exam will be scheduled by the registrar's office. Details will be posted on LEARN. If you miss the final
exam, you must have a valid reason and provide appropriate supporting documentation to the Math
Undergraduate Office (https://uwaterloo.ca/math/accommodations
(https://uwaterloo.ca/math/accommodations) ). Absence from the final exam may result in a grade of INC or
DNW at the discretion of the instructional team. To be considered for an INC, you must have a passing grade on
the midterm test and an overall average of at least 50% on the quizzes. (See https://uwaterloo.ca/math/currentundergraduates/regulations-and-procedures/incomplete-procedure (https://uwaterloo.ca/math/currentundergraduates/regulations-and-procedures/incomplete-procedure) .)
ASSIGNMENT SCREENING
No assignment screening will be used in this course.
NOTICE OF RECORDING
Activities for this course involve recording, in partial fulfillment of the course learning outcomes. You will receive
notification of recording via at least one of the following mechanisms: within the Learning Management System
(LEARN), a message from your course instructor, course syllabus/website, or other means. Some technologies may
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also provide a recording indicator. Images, audio, text/chat messaging that have been recorded may be used
and/or made available by the University to students in Math 137 for the purpose of reviewing missed
lectures. Recordings will be managed according to the University records classification scheme, WatClass
(https://uwaterloo.ca/records-management/records-classification-and-retention-schedules) , and will be securely
destroyed when no longer needed by the University. Your personal information is protected in accordance with
the Freedom of Information and Protection of Privacy Act (https://www.ontario.ca/laws/statute/90f31) , as well
as University policies and guidelines (https://uwaterloo.ca/privacy/) and may be subject to disclosure where
required by law.
The University will use reasonable means to protect the security and confidentiality of the recorded information,
but cannot provide a guarantee of such due to factors beyond the University’s control, such as recordings being
forwarded, copied, intercepted, circulated, disclosed, or stored without the University’s knowledge or permission
or the introduction of malware into computer system which could potentially damage or disrupt the computer,
networks, and security settings. The University is not responsible for connectivity/technical difficulties or loss of
data associated with your hardware, software or Internet connection.
By engaging in course activities that involve recording, you are consenting to the use of your appearance, image,
text/chat messaging, and voice and/or likeness in the manner and under the conditions specified herein. (In the
case of a live stream event, if you choose not to have your image or audio recorded, you may disable the audio and
video functionality (https://uwaterloo.ca/student-it-services/) . Instructions to participate using a pseudonym
instead of your real name are included where the feature exists; however, you must disclose the pseudonym to your
instructor in advance in order to facilitate class participation.) If you choose not to be recorded, this notice serves
as confirmation of your understanding that recorded lectures can be reviewed later and supplementary videos and
readings are provided.
You are not permitted to disclose the link to/URL of an event or an event session recording or copies of recording
to anyone, for any reason. Recordings are available only to authorized individuals who have been directly provided
the above instructions/link for their use. Recordings for personal use, required to facilitate your learning and
preparation of personal course/lecture notes, should not be shared with others without the permission of the
instructor or event coordinator. Review the University’s guidelines for faculty, staff and students entering
relationships with external organizations offering access to course materials
(https://uwaterloo.ca/secretariat/faculty-staff-and-students-entering-relationships-external) for more
information on your obligations with respect to keeping copies of course materials. For more information about
accessibility, connect with AccessAbility Services (https://uwaterloo.ca/accessability-services/) .
ADMINISTRATIVE POLICY
ILLNESS AND ACCOMMODATIONS
Please read the info here (https://uwaterloo.ca/math/accommodations) about any possible exemptions and
documentation that may be required for an illness.
MENTAL HEALTH
Please don't hesitate to make use of the services below if you are feeling overwhelmed or have the slightest
inclination that you are in need
of some support.
On-campus Resources:
Campus Wellness https://uwaterloo.ca/campus-wellness/
Counselling Services: counselling.services@uwaterloo.ca/ 519-888-4567 ext 32655
MATES: one-to-one peer support program offered by Federation of Students (FEDS) and Counselling Services:
mates@uwaterloo.ca
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Health Services: located across the creek from the Student Life Centre, 519-888-4096.
Off-campus Resources:
Good2Talk (24/7): Free confidential help line for post-secondary students. Phone: 1-866-925-5454
Here 24/7: Mental Health and Crisis Service Team. Phone: 1-844-437-3247
OK2BME: set of support services for lesbian, gay, bisexual, transgender or questioning teens in Waterloo. Phone:
519-884-0000 extension 213
DIVERSITY
It is our intent that students from all diverse backgrounds and perspectives be well served by this course, and that
students’ learning needs
be addressed both in and out of class. We recognize the immense value of the diversity in identities, perspectives,
and contributions that
students bring, and the benefit it has on our educational environment. Your suggestions are encouraged and
appreciated. Please let us
know ways to improve the effectiveness of the course for you personally or for other students or student groups.
In particular:
We will gladly honour your request to address you by an alternate/preferred name or gender pronoun.
Please advise us of this preference early in the semester so we may make appropriate changes to our records.
We will try to honour your religious holidays and celebrations. Please inform of us these at the start of the
course.
We will follow AccessAbility Services guidelines and protocols on how to best support students with
different learning needs.
UNIVERSITY POLICY
Academic integrity: In order to maintain a culture of academic integrity, members of the University of Waterloo
community are expected to promote honesty, trust, fairness, respect and responsibility. [Check the Office of
Academic Integrity (https://uwaterloo.ca/academic-integrity/) for more information.]
Grievance: A student who believes that a decision affecting some aspect of their university life has been unfair or
unreasonable may have grounds for initiating a grievance. Read Policy 70, Student Petitions and Grievances,
Section 4 (https://uwaterloo.ca/secretariat/policies-procedures-guidelines/policy-70) . When in doubt, please be
certain to contact the department’s administrative assistant who will provide further assistance.
Discipline: A student is expected to know what constitutes academic integrity to avoid committing an academic
offence, and to take responsibility for their actions. [Check the Office of Academic Integrity
(https://uwaterloo.ca/academic-integrity/) for more information.] A student who is unsure whether an action
constitutes an offence, or who needs help in learning how to avoid offences (e.g., plagiarism, cheating) or about
“rules” for group work/collaboration should seek guidance from the course instructor, academic advisor, or the
undergraduate associate dean. For information on categories of offences and types of penalties, students should
refer to Policy 71, Student Discipline (https://uwaterloo.ca/secretariat/policies-procedures-guidelines/policy-71) .
For typical penalties, check Guidelines for the Assessment of Penalties
(https://uwaterloo.ca/secretariat/guidelines/guidelines-assessment-penalties) .
Appeals: A decision made or penalty imposed under Policy 70, Student Petitions and Grievances
(https://uwaterloo.ca/secretariat/policies-procedures-guidelines/policy-70) (other than a petition) or Policy 71,
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Student Discipline (https://uwaterloo.ca/secretariat/policies-procedures-guidelines/policy-71) may be appealed if
there is a ground. A student who believes they have a ground for an appeal should refer to Policy 72, Student
Appeals (https://uwaterloo.ca/secretariat/policies-procedures-guidelines/policy-72) .
Note for students with disabilities: AccessAbility Services (https://uwaterloo.ca/disability-services/) , located
in Needles Hall, Room 1401, collaborates with all academic departments to arrange appropriate accommodations
for students with disabilities without compromising the academic integrity of the curriculum. If you require
academic accommodations to lessen the impact of your disability, please register with AccessAbility Services at the
beginning of each academic term.
Turnitin.com: Text matching software (Turnitin®) may be used to screen assignments in this course. Turnitin®
is used to verify that all materials and sources in assignments are documented. Students' submissions are stored on
a U.S. server, therefore students must be given an alternative (e.g., scaffolded assignment or annotated
bibliography), if they are concerned about their privacy and/or security. Students will be given due notice, in the
first week of the term and/or at the time assignment details are provided, about arrangements and alternatives for
the use of Turnitin in this course.
It is the responsibility of the student to notify the instructor if they, in the first week of term or at the time
assignment details are provided, wish to submit alternate assignment.
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