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Area between curves, techniques of integration. Applications of integration to planar areas and lengths, volumes and masses. First order ordinary differential equations: separable, linear, direction fields, Euler's method, applications. Infinite series, power series, Taylor expansions with remainder terms. Polar coordinates. Rectangular, spherical and cylindrical coordinates in 3-dimensional space. Parametric curves in the plane and space: graphing, arc length, curvature; normal binormal, tangent plane in 3-dimensional space. Volumes and surface areas of rotation. Prerequisite: MATH 100. Notes: (1) This course may not be taken for credit if credit has already been obtained in either MATH 115, 118 or SCI 100. (2) Students in all sections of this course will write a common final examination. (3) Restricted to Engineering students. Non-Engineering students who take this course will receive *3.0.

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University of Alberta

Department of Mathematical & Statistical Sciences

MATH 101-WINTER 2019

CALCULUS II

Textbook: Calculus (early Transcendentals), by James Stewart, eighth edition.

Recommended: Student Solutions Manual.

Access to a hard copy and/or an electronic copy of the textbook is strongly recommended. The two typical

options are:

(1) Purchase one of the hard copy bundles as offered at the University Bookstore, which comes with solution

manual(s) and an access code to Enhanced WebAssign (the online homework system used in this course);

(2) Purchase stand-alone access code to Enhanced WebAssign (this access code includes access to an

electronic version of the textbook).

NOTE: Students intending to purchase a used textbook plus stand-alone access code to Enhanced

WebAssign may end up spending more than with option 1. You may not purchase any WebAssign stand-

alone access code but you have to be registered with WebAssign to the restricted access account.

Prerequisite: MATH 100.

Course Description: Area between curves, techniques of integration. Applications of integration to

planar areas and lengths, volumes and masses. First order ordinary differential equations (separable, linear)

direction fields, Euler’s method, and applications. Infinite series, power series, Taylor expansions with

remainder terms. Polar coordinates. Rectangular, spherical and cylindrical coordinates in 3-dimensional

space. Parametric curves in the plane and space: graphing, arc length, curvature; normal binormal, tangent

plane in 3-dimensional space. Volumes and surface areas of rotation.

Course Objectives and Expected Learning Outcomes:

Students should be able to:

§ Calculate integrals by using techniques of integration like integration by parts and substitutions.

§ Calculate standard trigonometric integrals and integrals of rational functions.

§ Conclude if an improper integral is convergent or divergent and evaluate

improper convergent integrals.

§ Apply the integral calculus to find the area between curves, the volume and the area of a solid of

revolution, and the length of a curve.

§ Solve separable and linear differential equations.

§ Calculate the sum of some elementary numerical series, apply the Integral, Comparison, Ratio,

Root and Alternating Series Tests to decide if a series is convergent or divergent.

§ Find the interval of convergence for power series and expand functions as power series by using

properties of series and also Taylor and Maclaurin series.

§ Estimate the sum of a numerical series and find the error of the estimation.

§ Approximate functions by Taylor polynomials and find the error of approximation.

§ Solve problems on plane and space parametric curves (sketch of the curve, tangents, curvature).

§ Understand and work with polar coordinates and polar curves (graph, tangents, length and area).

§ Work with cylindrical and spherical coordinates, recognize and graph standard quadrics.

Syllabus: Text Sections: 6.1-6.3, 7.1-7.5, 7.8, 8.1-8.2, 9.1, 9.3, 9.5, 10.1-10.4, 11.2-11.11, 12.5, 12.6,

13.1-13.3, 15.8 & 15.9 (Spherical and cylindrical coordinates only).

Course Objectives: In the first part of the course the students will learn basic techniques of integration

and applications of integrals in calculating lengths, areas and volumes. Some simple differential equations

(separable and linear) will be introduced in this course. The study of numerical series, power series, Taylor

series and their applications will be a major component of the second part of the course. Some basic

knowledge of parametric curves, polar curves, three-dimensional geometry and space curves, will be done

in the third part of the course.

Grading Scheme:

Final Exam

50%

Midterm Exam

30%

Lab Work

10%

Written Assignments

5%

On Line Homework

5%

The cut-off marks used to map final scores to letter grades are not set in advance. Normally, a final score of

about 50% would guarantee a passing grade (at least D) and a final score of about 90% would guarantee an

excellent grade (A or A+).

Grades are unofficial until approved by the Department and/or Faculty offering the course.

Exam Dates, Times:

Common Midterm Exam:

10:00-11:30, Saturday March 2, 2019(Location TBA)

Common Final Exam:

Posted on BearTracks

Deferred Exam:

9:00, Saturday, May 4, 2019, CAB 357

For the Deferred Final, you must be outside the room at 8:30 a.m. to register.

NOTE: Students must verify on the BearTracks when the Final Exam Schedule is posted.

Missed Midterm: Note that there is no deferred midterm. If you miss it due to incapacitating illness, severe

domestic affliction or other compelling reasons you can apply for an excused absence. To apply for an

excused absence, you must inform the instructor within two working days following the scheduled date of the

exam, or as soon as you are able, having regard to the circumstances underlying the absence. In all cases,

instructors may request adequate documentation to substantiate the reason for the absence at their

discretion.

If your absence to your midterm is excused, the weight of the midterm will be transferred to the final

exam; i.e., the weight of your final exam will be 80%.

An excused absence is a privilege and not a right; there is no guarantee that an absence will be excused.

Misrepresentation of Facts to gain an excused absence is a serious breach of the Code of Student

Behaviour.

Missed Final Exam: A student who cannot write the final examination due to incapacitating illness, severe

domestic affliction or other compelling reasons can apply for a deferred final examination. Students who

failed at the start of term to request exam accommodations for religious beliefs are expected to follow the

normal deferred final examination process. Such an application must be made to the student’s Faculty

office within two working days of the missed examination and must be supported by a Statutory Declaration

or other appropriate documentation (Calendar section 23.5.6). Deferred examinations are a privilege and

not a right; there is no guarantee that a deferred examination will be granted. Misrepresentation of Facts to

gain a deferred examination is a serious breach of the Code of Student Behaviour.

Reexamination: A student who writes the final examination and fails the course may apply for a

reexamination. These exams are governed by University (Calendar section 23.5.5) Misrepresentation of

facts to gain a reexamination is a serious breach of the Code of Student Behaviour.

Exam Requirements: Your student photo I.D. is required at exams to verify your identity. Students will not

be allowed to begin an examination after it has been in progress for 30 minutes. Students must remain in the

exam room until at least 30 minutes has elapsed.

Excused Absence Where the Cause is Religious Belief: For an excused absence where the cause is

religious belief, you must contact me within two weeks of the start of classes to request accommodation for

the term (including the final exam). I may request adequate documentation to substantiate your request.

Calculators, Cell Phones: Calculators (or other electronic device) or student prepared data sheet are

not allowed in midterm or final exams. You will not be asked to perform any extensive calculations on

exams. Cell phones are to be turned off during lectures, labs and seminars. Cell phones are not to be

brought to exams.

Recording: Audio or video recording, digital or otherwise, of lectures, labs, seminars or any other

teaching environment by students is allowed only with the prior written consent of the instructor or as a part

of an approved accommodation plan. Student or instructor content, digital or otherwise, created and/or used

within the context of the course is to be used solely for personal study, and is not to be used or distributed

for any other purpose without prior written consent from the content author(s).

Written Homework: There will be 4 homework written assignments, which will be posted on the

course web page. Each of these assignments contains questions for which you should provide detailed

written solutions. The assignments will be submitted and graded via crowdmark. Please note: late

assignments will not be graded.

Online Homework: There will be a set of 11 weekly on line assignments (the best ten will be

counted) submitted online through WebAssign (http://webassign.net/ ). Each on line assignment should be

completed on the due date, by 11:00 pm.

Online homework is a required component of the course. Completing the online homework helps students

self-assess their progress in the course and prepare for exams. Students have the following two options to

complete the online homework (registration instructions for both options are posted on eClass):

1. Students who have an access code to Enhanced WebAssign (through purchase of one of the hard copy

textbook bundles available in the bookstore or through purchase of the stand-alone version of Enhanced

WebAssign) can complete the online homework from any computer at any location at any time of the day,

and take advantage of the full Enhanced WebAssign suite of resources (including an electronic version of

the textbook, tutorials, and self-assessment tools).

2. Students who wish to opt out of the fee-for-service online homework system will be able to complete the

assignments without cost on the public computers available in Cameron Library. With this no-cost

alternative, students will be able to complete the assignments only; they will not have access to resources

such as the electronic textbook, tutorials, or self-assessment tools. Please note that the computers in

Cameron Library are available on a “first-come-first-served” basis; students should plan ahead to ensure

timely completion of assignments.

On-Line Homework Disclaimer: On-line homework is a component of this course and is provided by a

third-party company. Please be aware that this company will be storing assessment information that may be

associated with you. If you have any concerns about this, please contact the instructor of the course.

Labs: There is a weekly 50-minute lab period, and there will be a 20-minute quiz in each laboratory class.

In order to help you prepare for the quiz, a list of problems will be posted on the class web page. You are

strongly encouraged to do as many of these problems as possible before going to the lab. The lab instructor

will assist you during the first 30 minutes of the lab with any difficulties you may have encountered with

these problems. I cannot over emphasize the importance of your knowing how to do the problems before

going to the lab. There will not be enough time for the lab instructor to provide assistance with all of the

problems during the lab. The lowest graded quiz will not be counted.

The labs start on Monday, January 14.

Academic Integrity: The University of Alberta is committed to the highest standards of academic

integrity and honesty. Students are expected to be familiar with these standards regarding academic

honesty and to uphold the policies of the University in this respect.

Students are particularly urged to familiarize themselves with the provisions of the Code of Student

Behaviour (online at http://governance.ualberta.ca/) and avoid any behaviour, which could potentially result

in suspicions of cheating, plagiarism, misrepresentation of facts and/or participation in an offence.

Academic dishonesty is a serious offence and can result in suspension or expulsion from the University.

All forms of dishonesty are unacceptable at the University. Any offense will be reported to the Senior

Associate Dean of Science who will determine the disciplinary action to be taken. Cheating, plagiarism and

misrepresentation of facts are serious offenses. Anyone who engages in these practices will receive at

minimum a grade of zero for the exam or paper in question and no opportunity will be given to replace the

grade or redistribute the weights. As well, in the Faculty of Science the sanction for cheating on any

examination will include a disciplinary failing grade (no exceptions) and senior students should expect a

period of suspension or expulsion from the University of Alberta.

Accessibility Resources (AR): Eligible students have both rights and responsibilities with regard to

accessibility-related accommodations. Consequently, scheduling exam accommodations in accordance with

SAS deadlines and procedures is essential. Please note adherence to procedures and deadlines is required

for U of A to provide accommodations. Contact AR (https://www.ualberta.ca/current-students/accessibility-

resources for further information.

Academic Support Centre: Students who require additional help in developing strategies for better

time management, study skills or examination skills should contact the Academic Support Centre (2-300

Students’ Union Building).

Decima Robinson Support Centre: Students in any 100 or 200-level math stats course can drop

in to CAB 528 for course help from graduate student TA's. Drop-in help for

math runs MTWRF 9:00am to 3:00pm. The times for statistics drop-in help are still to be determined. Drop

in help is at no cost to students.

Access Outreach: Access Outreach is a support centre that has math tutors, writing tutors, and social

workers. If you require a tutor for your math background or could use support for your general well-being

please contact Access Outreach. All services provided by Access Outreach are of no cost to students. The

general email for Access outreach is: doshelp@ualberta.ca More information including the schedule for

math/general help is available at: https://www.ualberta.ca/current-students/access-outreach

Disclaimer: Any typographical errors in this Course Outline are subject to change and will be announced

in class.

MATHEMATICS 101- CALCULUS II-WINTER 2019

LECTURES AND ASSIGNMENTS SCHEDULE

The schedule below is a guide of what we intend to cover day by day. Also, the homework due dates are

indicated. Please, read the relevant sections before coming to each class.

NO

LECTURE

DATE

SECTION

On Line

Assign Due

Date

Written

Assign

Due Date

1

M, Jan 7

6.1 Area between Curves

Saturday

Jan 19

Friday

January

25

2

W, Jan 9

6.2 Volumes

3

F, Jan 11

6.3 Volume by Cylindrical Shells

4

M, Jan 14

7.1 Integration by Parts

Saturday

Jan 26

5

W, Jan 16

7.1 & 7.2 Integration by Parts; Trigonometric Integrals

6

F, Jan 18

7.2 Trigonometric Integrals

7

M, Jan 21

7.3 Trigonometric Substitution

Saturday

Feb 2

8

W, Jan 23

7.4 Integration of Rational Functions

9

F, Jan 25

7.4 & 7.5 Integration of Rational Functions; Strategy for Integration

10

M, Jan 28

7.8 Improper Integrals

Saturday

Feb 9

Friday

February

15

11

W, Jan 30

7.8 Improper Integrals

12

F, Feb 1

9.1-9.3 Modeling with Differential Equations; Separable Equations

13

M, Feb 4

9.5 Linear Equations

Saturday

Feb 16

14

W, Feb 6

11.2 Series

15

F, Feb 8

11.3 The Integral Test and Estimation of Sums

16

M, Feb 11

11.4 The Comparison Tests

Wednesday

Feb 27

17

W, Feb 13

11.5 Alternating Series

18

F, Feb 15

11.6 Absolute Convergence; Ratio and Root Tests

19

M, Feb 25

11.7 Strategy for Testing Series

Saturday

March 9

Friday

March 15

20

W, Feb 27

11.8 Power Series

21

F, March 1

11.9 Representations of Functions as Power Series

22

M, March 4

11.10 Taylor and Maclaurin Series

Saturday

March 16

23

W, March 6

11.10 Taylor and Maclaurin Series

24

F, March 8

11.11 Applications of Taylor Polynomials

25

M, March 11

10.1 & 10.2 Parametric Curves (not arc length, surface area)

Saturday

March 23

26

W, March 13

10.3 Polar Coordinates

27

F, March 15

10.4 Areas in Polar Coordinates (not arc length)

28

M, March 18

12.5 Equations of Lines and Planes

Saturday

March 30

Friday

April 5

29

W, March 20

12.6 Cylinders and Quadric Surfaces

30

F, March 22

12.6 Cylinders and Quadric Surfaces

31

M, March 25

15.7 &15.8 Cylindrical and Spherical Coordinates

Wednesday

April 10

32

W, March 27

13.1 Vector Functions and Space Curves

33

F, March 29

13.2 Derivatives and Integrals of Vector Functions

34

M, April 1

8.1, 10.2, 10.4, 13.3 Arc Length

35

W, April 3

8.1, 10.2, 10.4, 13.3 Arc Length

36

F, April 5

8.2 Area of a Surface of Revolution, 10.2 Surface Area

37

M, April 8

13.3 Curvature, the Normal and Binormal Vectors

38

W, April 10

13.3 Curvature, the Normal and Binormal Vector

CONSOLIDATED MIDTERM EXAMINATION: Saturday March 2, 2019, 9:00-10:30.

The midterm exam covers the sections in the lectures 1-19

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