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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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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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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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