MAT135Y5

Calculus

University of Toronto Mississauga

Trigonometric functions. Limits, continuity. Review of differential calculus; applications. Graphing, extreme values and optimization. Integration and fundamental theorem; applications. Sequences and series. Power Series. Introduction to differential equations.
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24HR Notes for MAT135Y5

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Nadya Askaripour

MAT135Y5 Syllabus for Nadya Askaripour — Winter 2019

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1
University of Toronto Mississauga
MAT135Y5Y Calculus: Fall 2018 Winter 2019
Course Description:
MAT135 is a first year Calculus course with some examples of applications to Physics, Chemistry and
other Sciences. Although this course will have a theoretic component, the emphasis will be on concepts,
techniques, and applications. Theorems will be stated clearly, but mostly without proof, and many
examples will be included in the lectures.
Learning Objectives:
On successful completion of MAT135, you should be able to solve problems related to differential and
integral calculus, which includes limits, derivatives, integrals, sequences and series, and related
applications. A list of topics can be found on the last two pages of the course outline. You should aim for
a level of understanding that allows you to:
(1) carry out computations with ease;
(2) use your conceptual understanding of the material to solve a range of problems, even ones
that are different from, or a variation of problems you've seen before; and,
(3) give an explanation of your solutions to someone who has not seen the material before (i.e.
you should aim to understand the material well enough to able to explain each step in a
calculation, but also the general idea behind the solution).
Instructors:
Section(s):
Name:
Contact:
Office Hours (Fall):
Office Hours
(Winter):
LEC0107
Dr. Maria Wesslén
(course
coordinator)
maria.wesslen@utoronto.ca
Office: DH3048
Phone: 905-828 5323
Tuesdays 3:10-4:30
Fridays 11:30-1
Tue 10-11:30
Fri 10:30-12
LEC0101
Nathan Carruth
n.carruth@mail.utoronto.ca
Office: DH3021
Mondays 2-3
Thursdays 3-4
TBA
LEC0102
Dr. Julie Desjardins
julie.desjardins@utoronto.ca
Office: DH3062
Tuesdays 12-1
Thursdays 3-4
TBA
LEC0103
Dr. Andie Burazin
a.burazin@utoronto.ca
Office: DH3052 in the Fall
DH3090 in Winter term
Tuesdays 10-11
Thursdays 1-2
TBA
LEC0104
Dr. Kasun
Fernando
kasun.akurugodage@utoronto.ca
Office: DH3097B
Tuesdays 3-4
Thursdays 2-3
TBA
LEC0105
Dr. Timothy Yusun
tj.yusun@utoronto.ca
Office: DH3058
Thursdays 10-12:30 and
1:30-3:30
TBA
LEC0106
Dr. Jeffrey Carlson
j.carlson@utoronto.ca
Office: DH3021
Tuesdays 4-5
TBA
LEC0108,
LEC0109
Dr. Nadya
Askaripour
nadya.askaripour@utoronto.ca
Office: DH3097A
Mon. 10-11, Wed. 10-12
Frid. 11:30- 12:30
TBA
LEC0110,
LEC0111
Dr. Parker Glynn-
Adey
parker.glynn.adey@utoronto.ca
Office: DH3031
http://pgadey.youcanbook.me
TBA
LEC0112,
LEC0113
Dr. Michael Cavers
michael.cavers@utoronto.ca
Office: DH3023
Tuesdays 3-4
TBA
2
Office Hours and the Math Help Centre:
Please do not hesitate to ask us for help. Both the instructors and TAs of MAT135 are available for extra
help outside of class time, during our scheduled office hours. You do not need an appointment to visit
office hours. Just show up, but come prepared with questions you have. For example, you can ask
questions about a particular concept or something from lectures or the textbook that you want to
clarify. Or you can bring a problem you have tried to work on but have questions about (in that case
please bring the work that you have done, even if it is not complete). See the course website for any
updates on office hour times.
The teaching assistants will have office hours in room DH2027 (the Math Help Centre). A schedule will
be posted on the door as well as on Quercus. You can go to any office hour, not only your own TAs.
Textbook:
Single Variable Calculus: Early Transcendentals, 8th Edition, by James Stewart. You are expected to
have access to the textbook throughout the course.
Option 1: The UTM bookstore sells a package which includes the textbook, solution manual, and a
complementary copy of “Calculus Test and Exam Prep: A Collection of Problems and Worked Solutions”.
The extra booklet is not required but you can use it for extra practice.
Option 2: If you prefer an online textbook, there are access codes to the eBook (which comes with
WebAssign). The one term access code gives you access from now until April 2019. If you retake the
course for any reason in another year, you would need to buy another code. The “multi term” access
code gives you access for as long as edition 8 is being used. You can buy the eBook here
https://uoftbookstore.com/textbooks/access_codes.asp? Or by going in to the UTM bookstore.
Important: Unlike in previous years, a WebAssign access code is NOT required to complete the course.
However, WebAssign has many nice help features which you may want to use when studying. If you buy
the eBook you will have access to these extra help features.
Course Website:
You can access the MAT135 course website through the University of Toronto Quercus at
https://q.utoronto.ca/. After logging in, the course should appear on your Dashboard. All important
course information will be posted on Quercus throughout the course. You should therefore log in
regularly to check for any updates. You will also be able to see your term marks on Quercus, once they
are available. Email announcements will be sent through Quercus - make sure you check your
utoronto.ca email regularly. If you want to use another email to receive announcements, you can add
it under "account" and "settings".
Calculators:
Calculators will NOT be allowed during Term Tests and the Final Examination. A non-programmable,
non-graphing calculator may be used while working on Assignments and Homework.
3
Assessments of Learning Objectives:
You will be assessed in several different ways, including written assignments, online work, group work,
term tests, and a final examination.
Final Exam: 35%
4 Tests: 43% (7% for your lowest test mark and 12% each for your remaining three test marks)
Written assignments: 5%
Online assignments: 6%
Tutorial activities: 8%
CRA (Calculus Readiness Assessment): 3%
More information about each of these is given below. Additional information will be given on Quercus
throughout the course.
Tutorials and Tutorial Activities:
Tutorials start the week of 10th September 2018. All students must enroll in a tutorial section. You
should attend only the tutorial that you are enrolled in. It is important to attend your tutorial every
week, starting the week of 10th September. Tutorials give you a chance to study with the help of the TA
and together with other students. Attending tutorials and actively participating in them will increase
your chances of doing well on tests and the exam.
In some weeks (see the schedule below), there will be some “Tutorial activity” which will count towards
your final grade. Details about this tutorial activity will be posted on Quercus ahead of time. Often, you
do not need to prepare for the tutorial activity, other than to read and go over the relevant topics (info
will be given on Quercus) before your tutorial.
A list of which TA is responsible for which tutorial can be found on Quercus under ‘Information and
documents; TA and instructor contact info’.
Final Exam:
There will be a 3 hour final exam during the exam period in April. (There will be no exam in December.)
The exam will be cumulative, i.e. it will include problems from both the fall and winter semester,
although perhaps more problems from the second half of the course.
Term Tests:
The 4 term tests are on the following dates:
Test 1 Oct. 26, 2018
Test 2 Nov. 30, 2018
Test 3 Feb. 8, 2019
Test 4 Mar. 22 2019
The term tests will be held on Fridays from 15:10 to 17:00. Details such as which sections are covered on
each term test and which room to go to will be provided later, on Quercus.
4
Missed Term Tests:
There will be no make-up term tests. If you miss a term test due to illness or other valid reason, you
should declare your absence on ACORN and you must provide written documentation such as for
example a doctor’s note written on the Official UTM Verification of Illness or Injury form (available on
Quercus under ‘Information and Documents’). Documentation must be dated within a day of the test.
The deadline to submit it is three days after the test. Forms will be submitted through Quercus and
information on how to do this is available under ‘Information and Documents’. If these requirements are
not met, your test mark will be recorded as zero. If valid documentation is provided, the weights will be
shifted as follows:
One missed test: The lowest of the three tests you write will be worth 11% and the other two 16% each
Two missed tests: The two tests you write will be worth 18% each and the final exam will be worth 42%.
Three missed tests: The test you wrote will be worth 20% and the final exam will be worth 58%.
We hope that no one will miss all four tests!
Calculus Readiness Assessment (CRA):
CRA is an online test that will be written between 21st and 23rd of September 2018 and will be worth
3% of your final mark. The test is based on high school material. The main purpose of this test is for you
to assess your own readiness for University Calculus, as well as to give you an opportunity to review
some essential prerequisite material. Please read the CRA information on Quercus as soon as possible.
It tells you how to get started.
Written Assignments:
There will be 5 written assignments for this course, but only your best 4 will count towards 5% of your
final grade. Assignments will be posted on Quercus and it is your responsibility to download/print them
in time to complete them by the due date (see schedule below). Assignments should be submitted
through Quercus by the deadline. To submit, you can scan or take a photo of your work (or write your
work electronically). Please make sure that images are clear and easy to read before you submit them.
Normally, students will be required to submit their course assignments to Turnitin.com for a review of
textual similarity and detection of possible plagiarism. In doing so, students will allow their assignments
to be included as source documents in the Turnitin.com reference database, where they will be used
solely for the purpose of detecting plagiarism. The terms that apply to the University's use of the
Turnitin.com service are described on the Turnitin.com web site.
Note: It is ok (and you are encouraged) to work together on material related to the course, including
discussing the written assignments. HOWEVER, you must write up your own solutions independently. It
is an academic offence to copy someone’s solution, or to let someone copy yours.
Students are expected to adhere to the Code of Behaviour on Academic Matters:
http://www.governingcouncil.lamp4.utoronto.ca/wp-content/uploads/2016/07/p0701-coboam-2015-
2016pol.pdf
Also read http://advice.writing.utoronto.ca/using-sources/how-not-to-plagiarize/
5
Online Assignments:
This course uses WebWork, which is a FREE online learning and assessment tool. It will be used for
online assignments, and you can access it through Quercus. There are 9 online assignments but only
your best 8 will count for 6% of your final grade. Online assignments will always be due on Sundays at
11:59pm. No extensions will be given and there will be no make-up assignments.
Help and RGASC:
If you are finding the course difficult there are many ways in which you can get help. Please ask
questions in lectures if something is unclear. Longer questions can be asked in tutorials or during office
hours (both the instructors and teaching assistants have office hours). Tutorials are also a great
opportunity to work through examples on topics of your choice and ask questions about them. Working
in study-groups outside class where you can compare solutions and tackle problems together might also
be helpful. The Robert Gillespie Academic Skills Centre (RGASC) provides support and a variety of
resources to help students develop their numeracy and scientific literacy skills. The location of the
centre is in The New North Building, Room 3251 (3rd floor). Math drop-in sessions give students an
opportunity to get more general assistance with the skills they need to succeed in their math courses at
UTM. These appointments are generally short and offered on a first come, first served basis. (More
information: https://www.utm.utoronto.ca/asc/appointments-undergraduate). As well, Facilitated
Study Groups (FSGs) are a great way to help you improve your study skills and meet other students in
your courses. Check out the FSGs offered for various courses and other math and science courses get
advice on study methods from students who have taken the course, and done well. (More information:
https://www.utm.utoronto.ca/asc/facilitated-study-groups-fsgs) . You can also visit the Academic Skills
Centre for study tips and other help. Remember that all of these options are there to help you, so please
take advantage of them if you need it. Most important of all is to keep up with the homework and to not
fall behind. Ask for help early rather than the week of a test! Mathematics is not something you learn
overnight, and falling behind is one of the most common causes of not doing well in the course.
More information regarding academic resources can be found here:
http://www.utm.utoronto.ca/dean/academic-resources
Good luck and welcome to the course!
6
MAT135 Tentative Course Outline
The Sections correspond to Single Variable Calculus: Early Transc., 8th Edition, by James Stewart.
Week/Date
Sections to be covered
Additional Information
1
6 Sept.
to
9 Sept.
1.1 - Functions
PLEASE REVIEW of the following topics independently:
Appendix A - Numbers, inequalities, absolute values
Appendix B - Coordinate geometry and lines
Lectures begin Thursday 6 September
No tutorials this week.
2
10 Sept.
to
16 Sept.
1.2 - Essential functions
1.3 - New functions from old functions
1.4 - Exponential functions
1.5 - Inverse functions and logarithms
Tutorials start on Tuesday 11 September
Tutorial activity 1
3
17 Sept.
to
23 Sept.
Exponentials and logarithms continued
Appendix D - Trigonometry
1.5 cont. (Inverse trigonometric functions)
Sept. 19: Last day to change tutorials.
CRA online test 21-23 September
4
24 Sept.
to
30 Sept.
2.2 - Limits
2.3 - Limit laws
2.5 - Continuity
Tutorial activity 2
Assignment 1 (online) is due 30
September at 11:59pm
5
1 Oct.
to
7 Oct.
2.6 - Limits at infinity; horizontal asymptotes
2.7 - Derivative as a rate of change
2.8 - Derivative as a function
Assignment 2 (written) is due 7 October
at 11:59pm
Fall Reading Week (8-14 October)
6
15 Oct.
to
21 Oct.
3.1 - Derivatives of polynomials and exp.
3.2 - Product and quotient rules
Assignment 3 (online) is due 21 October
at 11:59pm
Tutorial activity 3
7
22 Oct.
to
28 Oct.
3.3 - Derivatives of trigonometric functions
3.4 - Chain rule
Review if time
26 Oct. - Term Test 1
8
29 Oct.
to
4 Nov.
3.5 - Implicit differentiation
3.6 - Derivatives of logarithmic functions
Assignment 4 (written) is due 4
November at 11:59pm
9
5 Nov.
to
11 Nov.
3.8 - Exponential growth and decay
3.9 - Related rates
Assignment 5 (online) is due 11
November at 11:59pm
Tutorial activity 4
10
12 Nov.
to
18 Nov.
4.1 - Max and min values
4.3 - Derivatives and graphs
4.5 - Curve sketching
Assignment 6 (written) is due 18
November at 11:59pm.
11
19 Nov.
to
25 Nov.
4.4 - l’Hopital’s rule
4.2 - The mean value theorem
Assignment 7 (online) is due 25
November at 11:59pm
Tutorial activity 5
12
26 Nov.
to
2 Dec.
4.7 - Optimization problems
Review if time
30 Nov. - Term Test 2
13
3 Dec.
to
5 Dec.
4.9 - Antiderivatives
Appendix E - Sigma notation
A short week. Last day of lectures is
Wednesday 5 December
No tutorials this week
7
Week/Date
Sections to be covered
Additional Information
1
7 Jan.
to
13 Jan.
5.2 - The definite integral
5.3 - The fundamental theorem of calculus
Lectures and tutorials resume
Assignment 8 (online) is due 13
January at 11:59pm
2
14 Jan.
to
20 Jan.
5.4 - Indefinite integrals
5.5 - The substitution rule
Tutorial activity 6
3
21 Jan.
to
27 Jan.
6.1 - Areas
6.2 - Volumes
Assignment 9 (written) is due 27
January at 11:59pm
4
28 Jan.
to
3 Feb.
6.5 - Average values
7.1 - Integration by parts
Tutorial activity 7
5
4 Feb.
to
10 Feb.
7.2 - Trigonometric integrals
7.3 - Trigonometric substitution
8 Feb. - Term Test 3
6
11 Feb.
to
17 Feb.
7.4 - Partial fractions
7.5 - Strategy for integration
Assignment 10 (online) is due 17
February at 11:59pm
Winter Reading Week (18-24 February)
7
25 Feb.
to
3 Mar.
7.8 - Improper integrals
9.3 - Separable equations
Assignment 11 (online) is due 3
March at 11:59pm
Tutorial activity 8
8
4 Mar.
to
10 Mar.
9.5 - Linear equations
11.1 - Sequences
Assignment 12 (written) is due 10
March at 11:59pm
9
11 Mar.
to
17 Mar.
11.2 - Series
11.3 - The integral test
Assignment 13 (online) is due 17
March at 11:59pm
Tutorial activity 9
10
18 Mar.
to
24 Mar.
11.4 - The comparison tests
11.5 - Alternating series
22 Mar. - Term Test 4
11
25 Mar.
to
31 Mar.
11.6 - Absolute Convergence and ratio and root tests
11.7 - Strategy for testing series
11.8 - Power series
Tutorial activity 10
12
1 Apr.
to
7 Apr.
11.9 - Representations of functions as power series
11.10 - Taylor and Maclaurin series
Catch-up/Review
Assignment 14 (online) is due 7 April
at 11:59pm
8
Suggested Homework Problems Fall Semester:
For each topic covered in this course, you are expected to do homework questions. You are NOT
required to hand in your solutions, but it is important that you do all of the questions to prepare for
term tests and the final examination. This is a list of the minimum number of problems you should work
on. To properly prepare for tests and the final exam you may also want to work on the rest of the
problems from the Complete Problem List (posted on Quercus under Course Materials), especially if you
are finding a certain topic or a type of question difficult. You may want to start with the Suggested
Homework List below, and later work on more problems from the Complete Problem List.
Problems refer to: Single Variable Calculus: Early Transcendentals, 8th Edition, by James Stewart.
Section:
Suggested Homework Problems:
Diagnostic Test: Algebra (p. xxvi)
Appendix A - Inequalities and Absolute Values
Appendix B - Coordinate Geometry and Lines
Appendix D - Trigonometry
1-10
9, 11, 23, 29, 37, 39, 49, 51, 53, 55, 59
1, 7, 17, 21, 27, 29, 33, 35, 37, 53*
9, 17, 29, 31, 61, 63, 65, 69, 71, 73, 79
1.1 - Functions
1.2 - Essential Functions
1.3 - New functions from old functions
1.4 - Exponential functions
1.5 - Inverse functions
Chapter 1 Review (p. 68-70)
7, 9, 31, 33, 35, 37, 43, 45, 49, 53, 61, 69, 73, 75
3, 5, 15, 19
3, 5, 7, 13, 17, 23, 29, 33, 41, 53, 57, 63*
1, 3, 13, 15, 17, 19, 37*
1, 5, 11, 15, 19, 21, 23, 37, 41, 51, 53, 57, 63, 67, 71
Concept Check: 3, 8, 13; T/F: 1, 5, 7, 11, 14 (F); Ex: 17, 23
2.2 - Limits
2.3 - Limit laws
2.5 - Continuity
2.6 - Limits at Infinity
2.7 - Derivative as a rate of change
2.8 - Derivative as a function
Chapter 2 Review (p. 165-168)
1, 3, 5, 7, 17, 31, 33, 35, 37, 39, 41, 43
11, 15, 17, 21-31 (odd), 37, 39, 41, 43*, 51, 59*, 65*
3, 5, 7, 17, 19, 21, 23, 35, 41, 45, 47, 51, 55, 69, 71
3, 9, 19, 21, 23, 27, 31, 33, 35, 39, 49, 55, 57, 65a, 67
5, 7, 11, 13, 17, 21, 25, 35, 37
3, 25, 27, 29, 41, 47, 51
T/F: 1, 7, 13
3.1 - Derivatives of polynomials and exp.
3.2 - Product and quotient rules
3.3 - Derivatives of trig. functions
3.4 - Chain rule
3.5 - Implicit differentiation
3.6 - Derivatives of logarithmic functions
3.8 - Exponential growth and decay
3.9 - Related rates
Chapter 3 Review (p. 266-269)
3-31 (odd), 33, 49, 51, 55, 61, 63, 77, 83
3-27 (odd), 33, 45, 49, 53
1, 5, 13, 15, 21, 31, 33, 39-49
9-17 (odd), 27, 31-45 (odd), 49, 53, 59, 63, 65
5, 9, 13, 17, 25, 29, 35, 49, 51, 57
2, 7, 11, 17, 19, 25, 33, 41, 43, 45, 49, 55*
3, 9, 11, 13, 15, 17
3, 5, 15, 19, 23-29 (odd), 33, 43, 45
Concept Check: 2a-n; T/F: 2(F), 6(F), 9, 11; Ex: 93, 107*
4.1 - Max and min values
4.2 - The mean value theorem
4.3 - Derivatives and graphs
4.4 - l’Hopital’s rule
4.5 - Curve sketching
4.7 - Optimization problems
4.9 - Antiderivatives
Chapter 4 Review (p. 358-362)
5, 9, 13, 31, 39, 43, 49, 53, 57
3, 11, 17, 19, 21, 25
1, 7, 11, 17, 29, 33, 43, 49, 57, 89*
15-27 (odd), 33, 43, 47-65 (odd), 75*, 79, 87*
9, 15, 21, 25, 29, 35, 41, 51, 61, 63, 65
3, 5, 7, 11, 15, 21, 25, 27, 31, 35, 37, 43, 49, 51, 73
3, 5, 9, 15, 29, 33, 39, 47, 59, 61
Concept Check: 8, 9
Appendix E - Sigma notation
3, 9, 15, 19, 29, 31, 33, 43
*These problems often require you to think a little harder; either they are ‘think outside the box’
problems or they are more difficult than other problems.

Parker Glynn-Adey

MAT135Y5 Syllabus for Parker Glynn-Adey — Winter 2019

Download
1
University of Toronto Mississauga
MAT135Y5Y Calculus: Fall 2018 Winter 2019
Course Description:
MAT135 is a first year Calculus course with some examples of applications to Physics, Chemistry and
other Sciences. Although this course will have a theoretic component, the emphasis will be on concepts,
techniques, and applications. Theorems will be stated clearly, but mostly without proof, and many
examples will be included in the lectures.
Learning Objectives:
On successful completion of MAT135, you should be able to solve problems related to differential and
integral calculus, which includes limits, derivatives, integrals, sequences and series, and related
applications. A list of topics can be found on the last two pages of the course outline. You should aim for
a level of understanding that allows you to:
(1) carry out computations with ease;
(2) use your conceptual understanding of the material to solve a range of problems, even ones
that are different from, or a variation of problems you've seen before; and,
(3) give an explanation of your solutions to someone who has not seen the material before (i.e.
you should aim to understand the material well enough to able to explain each step in a
calculation, but also the general idea behind the solution).
Instructors:
Section(s):
Name:
Contact:
Office Hours (Fall):
Office Hours
(Winter):
LEC0107
Dr. Maria Wesslén
(course
coordinator)
maria.wesslen@utoronto.ca
Office: DH3048
Phone: 905-828 5323
Tuesdays 3:10-4:30
Fridays 11:30-1
Tue 10-11:30
Fri 10:30-12
LEC0101
Nathan Carruth
n.carruth@mail.utoronto.ca
Office: DH3021
Mondays 2-3
Thursdays 3-4
TBA
LEC0102
Dr. Julie Desjardins
julie.desjardins@utoronto.ca
Office: DH3062
Tuesdays 12-1
Thursdays 3-4
TBA
LEC0103
Dr. Andie Burazin
a.burazin@utoronto.ca
Office: DH3052 in the Fall
DH3090 in Winter term
Tuesdays 10-11
Thursdays 1-2
TBA
LEC0104
Dr. Kasun
Fernando
kasun.akurugodage@utoronto.ca
Office: DH3097B
Tuesdays 3-4
Thursdays 2-3
TBA
LEC0105
Dr. Timothy Yusun
tj.yusun@utoronto.ca
Office: DH3058
Thursdays 10-12:30 and
1:30-3:30
TBA
LEC0106
Dr. Jeffrey Carlson
j.carlson@utoronto.ca
Office: DH3021
Tuesdays 4-5
TBA
LEC0108,
LEC0109
Dr. Nadya
Askaripour
nadya.askaripour@utoronto.ca
Office: DH3097A
Mon. 10-11, Wed. 10-12
Frid. 11:30- 12:30
TBA
LEC0110,
LEC0111
Dr. Parker Glynn-
Adey
parker.glynn.adey@utoronto.ca
Office: DH3031
http://pgadey.youcanbook.me
TBA
LEC0112,
LEC0113
Dr. Michael Cavers
michael.cavers@utoronto.ca
Office: DH3023
Tuesdays 3-4
TBA
2
Office Hours and the Math Help Centre:
Please do not hesitate to ask us for help. Both the instructors and TAs of MAT135 are available for extra
help outside of class time, during our scheduled office hours. You do not need an appointment to visit
office hours. Just show up, but come prepared with questions you have. For example, you can ask
questions about a particular concept or something from lectures or the textbook that you want to
clarify. Or you can bring a problem you have tried to work on but have questions about (in that case
please bring the work that you have done, even if it is not complete). See the course website for any
updates on office hour times.
The teaching assistants will have office hours in room DH2027 (the Math Help Centre). A schedule will
be posted on the door as well as on Quercus. You can go to any office hour, not only your own TAs.
Textbook:
Single Variable Calculus: Early Transcendentals, 8th Edition, by James Stewart. You are expected to
have access to the textbook throughout the course.
Option 1: The UTM bookstore sells a package which includes the textbook, solution manual, and a
complementary copy of “Calculus Test and Exam Prep: A Collection of Problems and Worked Solutions”.
The extra booklet is not required but you can use it for extra practice.
Option 2: If you prefer an online textbook, there are access codes to the eBook (which comes with
WebAssign). The one term access code gives you access from now until April 2019. If you retake the
course for any reason in another year, you would need to buy another code. The “multi term” access
code gives you access for as long as edition 8 is being used. You can buy the eBook here
https://uoftbookstore.com/textbooks/access_codes.asp? Or by going in to the UTM bookstore.
Important: Unlike in previous years, a WebAssign access code is NOT required to complete the course.
However, WebAssign has many nice help features which you may want to use when studying. If you buy
the eBook you will have access to these extra help features.
Course Website:
You can access the MAT135 course website through the University of Toronto Quercus at
https://q.utoronto.ca/. After logging in, the course should appear on your Dashboard. All important
course information will be posted on Quercus throughout the course. You should therefore log in
regularly to check for any updates. You will also be able to see your term marks on Quercus, once they
are available. Email announcements will be sent through Quercus - make sure you check your
utoronto.ca email regularly. If you want to use another email to receive announcements, you can add
it under "account" and "settings".
Calculators:
Calculators will NOT be allowed during Term Tests and the Final Examination. A non-programmable,
non-graphing calculator may be used while working on Assignments and Homework.
3
Assessments of Learning Objectives:
You will be assessed in several different ways, including written assignments, online work, group work,
term tests, and a final examination.
Final Exam: 35%
4 Tests: 43% (7% for your lowest test mark and 12% each for your remaining three test marks)
Written assignments: 5%
Online assignments: 6%
Tutorial activities: 8%
CRA (Calculus Readiness Assessment): 3%
More information about each of these is given below. Additional information will be given on Quercus
throughout the course.
Tutorials and Tutorial Activities:
Tutorials start the week of 10th September 2018. All students must enroll in a tutorial section. You
should attend only the tutorial that you are enrolled in. It is important to attend your tutorial every
week, starting the week of 10th September. Tutorials give you a chance to study with the help of the TA
and together with other students. Attending tutorials and actively participating in them will increase
your chances of doing well on tests and the exam.
In some weeks (see the schedule below), there will be some “Tutorial activity” which will count towards
your final grade. Details about this tutorial activity will be posted on Quercus ahead of time. Often, you
do not need to prepare for the tutorial activity, other than to read and go over the relevant topics (info
will be given on Quercus) before your tutorial.
A list of which TA is responsible for which tutorial can be found on Quercus under ‘Information and
documents; TA and instructor contact info’.
Final Exam:
There will be a 3 hour final exam during the exam period in April. (There will be no exam in December.)
The exam will be cumulative, i.e. it will include problems from both the fall and winter semester,
although perhaps more problems from the second half of the course.
Term Tests:
The 4 term tests are on the following dates:
Test 1 Oct. 26, 2018
Test 2 Nov. 30, 2018
Test 3 Feb. 8, 2019
Test 4 Mar. 22 2019
The term tests will be held on Fridays from 15:10 to 17:00. Details such as which sections are covered on
each term test and which room to go to will be provided later, on Quercus.
4
Missed Term Tests:
There will be no make-up term tests. If you miss a term test due to illness or other valid reason, you
should declare your absence on ACORN and you must provide written documentation such as for
example a doctor’s note written on the Official UTM Verification of Illness or Injury form (available on
Quercus under ‘Information and Documents’). Documentation must be dated within a day of the test.
The deadline to submit it is three days after the test. Forms will be submitted through Quercus and
information on how to do this is available under ‘Information and Documents’. If these requirements are
not met, your test mark will be recorded as zero. If valid documentation is provided, the weights will be
shifted as follows:
One missed test: The lowest of the three tests you write will be worth 11% and the other two 16% each
Two missed tests: The two tests you write will be worth 18% each and the final exam will be worth 42%.
Three missed tests: The test you wrote will be worth 20% and the final exam will be worth 58%.
We hope that no one will miss all four tests!
Calculus Readiness Assessment (CRA):
CRA is an online test that will be written between 21st and 23rd of September 2018 and will be worth
3% of your final mark. The test is based on high school material. The main purpose of this test is for you
to assess your own readiness for University Calculus, as well as to give you an opportunity to review
some essential prerequisite material. Please read the CRA information on Quercus as soon as possible.
It tells you how to get started.
Written Assignments:
There will be 5 written assignments for this course, but only your best 4 will count towards 5% of your
final grade. Assignments will be posted on Quercus and it is your responsibility to download/print them
in time to complete them by the due date (see schedule below). Assignments should be submitted
through Quercus by the deadline. To submit, you can scan or take a photo of your work (or write your
work electronically). Please make sure that images are clear and easy to read before you submit them.
Normally, students will be required to submit their course assignments to Turnitin.com for a review of
textual similarity and detection of possible plagiarism. In doing so, students will allow their assignments
to be included as source documents in the Turnitin.com reference database, where they will be used
solely for the purpose of detecting plagiarism. The terms that apply to the University's use of the
Turnitin.com service are described on the Turnitin.com web site.
Note: It is ok (and you are encouraged) to work together on material related to the course, including
discussing the written assignments. HOWEVER, you must write up your own solutions independently. It
is an academic offence to copy someone’s solution, or to let someone copy yours.
Students are expected to adhere to the Code of Behaviour on Academic Matters:
http://www.governingcouncil.lamp4.utoronto.ca/wp-content/uploads/2016/07/p0701-coboam-2015-
2016pol.pdf
Also read http://advice.writing.utoronto.ca/using-sources/how-not-to-plagiarize/
5
Online Assignments:
This course uses WebWork, which is a FREE online learning and assessment tool. It will be used for
online assignments, and you can access it through Quercus. There are 9 online assignments but only
your best 8 will count for 6% of your final grade. Online assignments will always be due on Sundays at
11:59pm. No extensions will be given and there will be no make-up assignments.
Help and RGASC:
If you are finding the course difficult there are many ways in which you can get help. Please ask
questions in lectures if something is unclear. Longer questions can be asked in tutorials or during office
hours (both the instructors and teaching assistants have office hours). Tutorials are also a great
opportunity to work through examples on topics of your choice and ask questions about them. Working
in study-groups outside class where you can compare solutions and tackle problems together might also
be helpful. The Robert Gillespie Academic Skills Centre (RGASC) provides support and a variety of
resources to help students develop their numeracy and scientific literacy skills. The location of the
centre is in The New North Building, Room 3251 (3rd floor). Math drop-in sessions give students an
opportunity to get more general assistance with the skills they need to succeed in their math courses at
UTM. These appointments are generally short and offered on a first come, first served basis. (More
information: https://www.utm.utoronto.ca/asc/appointments-undergraduate). As well, Facilitated
Study Groups (FSGs) are a great way to help you improve your study skills and meet other students in
your courses. Check out the FSGs offered for various courses and other math and science courses get
advice on study methods from students who have taken the course, and done well. (More information:
https://www.utm.utoronto.ca/asc/facilitated-study-groups-fsgs) . You can also visit the Academic Skills
Centre for study tips and other help. Remember that all of these options are there to help you, so please
take advantage of them if you need it. Most important of all is to keep up with the homework and to not
fall behind. Ask for help early rather than the week of a test! Mathematics is not something you learn
overnight, and falling behind is one of the most common causes of not doing well in the course.
More information regarding academic resources can be found here:
http://www.utm.utoronto.ca/dean/academic-resources
Good luck and welcome to the course!
6
MAT135 Tentative Course Outline
The Sections correspond to Single Variable Calculus: Early Transc., 8th Edition, by James Stewart.
Week/Date
Sections to be covered
Additional Information
1
6 Sept.
to
9 Sept.
1.1 - Functions
PLEASE REVIEW of the following topics independently:
Appendix A - Numbers, inequalities, absolute values
Appendix B - Coordinate geometry and lines
Lectures begin Thursday 6 September
No tutorials this week.
2
10 Sept.
to
16 Sept.
1.2 - Essential functions
1.3 - New functions from old functions
1.4 - Exponential functions
1.5 - Inverse functions and logarithms
Tutorials start on Tuesday 11 September
Tutorial activity 1
3
17 Sept.
to
23 Sept.
Exponentials and logarithms continued
Appendix D - Trigonometry
1.5 cont. (Inverse trigonometric functions)
Sept. 19: Last day to change tutorials.
CRA online test 21-23 September
4
24 Sept.
to
30 Sept.
2.2 - Limits
2.3 - Limit laws
2.5 - Continuity
Tutorial activity 2
Assignment 1 (online) is due 30
September at 11:59pm
5
1 Oct.
to
7 Oct.
2.6 - Limits at infinity; horizontal asymptotes
2.7 - Derivative as a rate of change
2.8 - Derivative as a function
Assignment 2 (written) is due 7 October
at 11:59pm
Fall Reading Week (8-14 October)
6
15 Oct.
to
21 Oct.
3.1 - Derivatives of polynomials and exp.
3.2 - Product and quotient rules
Assignment 3 (online) is due 21 October
at 11:59pm
Tutorial activity 3
7
22 Oct.
to
28 Oct.
3.3 - Derivatives of trigonometric functions
3.4 - Chain rule
Review if time
26 Oct. - Term Test 1
8
29 Oct.
to
4 Nov.
3.5 - Implicit differentiation
3.6 - Derivatives of logarithmic functions
Assignment 4 (written) is due 4
November at 11:59pm
9
5 Nov.
to
11 Nov.
3.8 - Exponential growth and decay
3.9 - Related rates
Assignment 5 (online) is due 11
November at 11:59pm
Tutorial activity 4
10
12 Nov.
to
18 Nov.
4.1 - Max and min values
4.3 - Derivatives and graphs
4.5 - Curve sketching
Assignment 6 (written) is due 18
November at 11:59pm.
11
19 Nov.
to
25 Nov.
4.4 - l’Hopital’s rule
4.2 - The mean value theorem
Assignment 7 (online) is due 25
November at 11:59pm
Tutorial activity 5
12
26 Nov.
to
2 Dec.
4.7 - Optimization problems
Review if time
30 Nov. - Term Test 2
13
3 Dec.
to
5 Dec.
4.9 - Antiderivatives
Appendix E - Sigma notation
A short week. Last day of lectures is
Wednesday 5 December
No tutorials this week
7
Week/Date
Sections to be covered
Additional Information
1
7 Jan.
to
13 Jan.
5.2 - The definite integral
5.3 - The fundamental theorem of calculus
Lectures and tutorials resume
Assignment 8 (online) is due 13
January at 11:59pm
2
14 Jan.
to
20 Jan.
5.4 - Indefinite integrals
5.5 - The substitution rule
Tutorial activity 6
3
21 Jan.
to
27 Jan.
6.1 - Areas
6.2 - Volumes
Assignment 9 (written) is due 27
January at 11:59pm
4
28 Jan.
to
3 Feb.
6.5 - Average values
7.1 - Integration by parts
Tutorial activity 7
5
4 Feb.
to
10 Feb.
7.2 - Trigonometric integrals
7.3 - Trigonometric substitution
8 Feb. - Term Test 3
6
11 Feb.
to
17 Feb.
7.4 - Partial fractions
7.5 - Strategy for integration
Assignment 10 (online) is due 17
February at 11:59pm
Winter Reading Week (18-24 February)
7
25 Feb.
to
3 Mar.
7.8 - Improper integrals
9.3 - Separable equations
Assignment 11 (online) is due 3
March at 11:59pm
Tutorial activity 8
8
4 Mar.
to
10 Mar.
9.5 - Linear equations
11.1 - Sequences
Assignment 12 (written) is due 10
March at 11:59pm
9
11 Mar.
to
17 Mar.
11.2 - Series
11.3 - The integral test
Assignment 13 (online) is due 17
March at 11:59pm
Tutorial activity 9
10
18 Mar.
to
24 Mar.
11.4 - The comparison tests
11.5 - Alternating series
22 Mar. - Term Test 4
11
25 Mar.
to
31 Mar.
11.6 - Absolute Convergence and ratio and root tests
11.7 - Strategy for testing series
11.8 - Power series
Tutorial activity 10
12
1 Apr.
to
7 Apr.
11.9 - Representations of functions as power series
11.10 - Taylor and Maclaurin series
Catch-up/Review
Assignment 14 (online) is due 7 April
at 11:59pm
8
Suggested Homework Problems Fall Semester:
For each topic covered in this course, you are expected to do homework questions. You are NOT
required to hand in your solutions, but it is important that you do all of the questions to prepare for
term tests and the final examination. This is a list of the minimum number of problems you should work
on. To properly prepare for tests and the final exam you may also want to work on the rest of the
problems from the Complete Problem List (posted on Quercus under Course Materials), especially if you
are finding a certain topic or a type of question difficult. You may want to start with the Suggested
Homework List below, and later work on more problems from the Complete Problem List.
Problems refer to: Single Variable Calculus: Early Transcendentals, 8th Edition, by James Stewart.
Section:
Suggested Homework Problems:
Diagnostic Test: Algebra (p. xxvi)
Appendix A - Inequalities and Absolute Values
Appendix B - Coordinate Geometry and Lines
Appendix D - Trigonometry
1-10
9, 11, 23, 29, 37, 39, 49, 51, 53, 55, 59
1, 7, 17, 21, 27, 29, 33, 35, 37, 53*
9, 17, 29, 31, 61, 63, 65, 69, 71, 73, 79
1.1 - Functions
1.2 - Essential Functions
1.3 - New functions from old functions
1.4 - Exponential functions
1.5 - Inverse functions
Chapter 1 Review (p. 68-70)
7, 9, 31, 33, 35, 37, 43, 45, 49, 53, 61, 69, 73, 75
3, 5, 15, 19
3, 5, 7, 13, 17, 23, 29, 33, 41, 53, 57, 63*
1, 3, 13, 15, 17, 19, 37*
1, 5, 11, 15, 19, 21, 23, 37, 41, 51, 53, 57, 63, 67, 71
Concept Check: 3, 8, 13; T/F: 1, 5, 7, 11, 14 (F); Ex: 17, 23
2.2 - Limits
2.3 - Limit laws
2.5 - Continuity
2.6 - Limits at Infinity
2.7 - Derivative as a rate of change
2.8 - Derivative as a function
Chapter 2 Review (p. 165-168)
1, 3, 5, 7, 17, 31, 33, 35, 37, 39, 41, 43
11, 15, 17, 21-31 (odd), 37, 39, 41, 43*, 51, 59*, 65*
3, 5, 7, 17, 19, 21, 23, 35, 41, 45, 47, 51, 55, 69, 71
3, 9, 19, 21, 23, 27, 31, 33, 35, 39, 49, 55, 57, 65a, 67
5, 7, 11, 13, 17, 21, 25, 35, 37
3, 25, 27, 29, 41, 47, 51
T/F: 1, 7, 13
3.1 - Derivatives of polynomials and exp.
3.2 - Product and quotient rules
3.3 - Derivatives of trig. functions
3.4 - Chain rule
3.5 - Implicit differentiation
3.6 - Derivatives of logarithmic functions
3.8 - Exponential growth and decay
3.9 - Related rates
Chapter 3 Review (p. 266-269)
3-31 (odd), 33, 49, 51, 55, 61, 63, 77, 83
3-27 (odd), 33, 45, 49, 53
1, 5, 13, 15, 21, 31, 33, 39-49
9-17 (odd), 27, 31-45 (odd), 49, 53, 59, 63, 65
5, 9, 13, 17, 25, 29, 35, 49, 51, 57
2, 7, 11, 17, 19, 25, 33, 41, 43, 45, 49, 55*
3, 9, 11, 13, 15, 17
3, 5, 15, 19, 23-29 (odd), 33, 43, 45
Concept Check: 2a-n; T/F: 2(F), 6(F), 9, 11; Ex: 93, 107*
4.1 - Max and min values
4.2 - The mean value theorem
4.3 - Derivatives and graphs
4.4 - l’Hopital’s rule
4.5 - Curve sketching
4.7 - Optimization problems
4.9 - Antiderivatives
Chapter 4 Review (p. 358-362)
5, 9, 13, 31, 39, 43, 49, 53, 57
3, 11, 17, 19, 21, 25
1, 7, 11, 17, 29, 33, 43, 49, 57, 89*
15-27 (odd), 33, 43, 47-65 (odd), 75*, 79, 87*
9, 15, 21, 25, 29, 35, 41, 51, 61, 63, 65
3, 5, 7, 11, 15, 21, 25, 27, 31, 35, 37, 43, 49, 51, 73
3, 5, 9, 15, 29, 33, 39, 47, 59, 61
Concept Check: 8, 9
Appendix E - Sigma notation
3, 9, 15, 19, 29, 31, 33, 43
*These problems often require you to think a little harder; either they are ‘think outside the box’
problems or they are more difficult than other problems.

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