Calculus II

University of Alberta

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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MATH101 Syllabus for Wiersma,Matthew — Spring 2019

University of Alberta
Department of Mathematical & Statistical Sciences
MATH 101-WINTER 2019
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
Midterm Exam
Lab Work
Written Assignments
On Line Homework
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
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
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 ( ). 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 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 (
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: More information including the schedule for
math/general help is available at:
Disclaimer: Any typographical errors in this Course Outline are subject to change and will be announced
in class.
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.
On Line
Assign Due
Due Date
M, Jan 7
6.1 Area between Curves
Jan 19
W, Jan 9
6.2 Volumes
F, Jan 11
6.3 Volume by Cylindrical Shells
M, Jan 14
7.1 Integration by Parts
Jan 26
W, Jan 16
7.1 & 7.2 Integration by Parts; Trigonometric Integrals
F, Jan 18
7.2 Trigonometric Integrals
M, Jan 21
7.3 Trigonometric Substitution
Feb 2
W, Jan 23
7.4 Integration of Rational Functions
F, Jan 25
7.4 & 7.5 Integration of Rational Functions; Strategy for Integration
M, Jan 28
7.8 Improper Integrals
Feb 9
W, Jan 30
7.8 Improper Integrals
F, Feb 1
9.1-9.3 Modeling with Differential Equations; Separable Equations
M, Feb 4
9.5 Linear Equations
Feb 16
W, Feb 6
11.2 Series
F, Feb 8
11.3 The Integral Test and Estimation of Sums
M, Feb 11
11.4 The Comparison Tests
Feb 27
W, Feb 13
11.5 Alternating Series
F, Feb 15
11.6 Absolute Convergence; Ratio and Root Tests
M, Feb 25
11.7 Strategy for Testing Series
March 9
March 15
W, Feb 27
11.8 Power Series
F, March 1
11.9 Representations of Functions as Power Series
M, March 4
11.10 Taylor and Maclaurin Series
March 16
W, March 6
11.10 Taylor and Maclaurin Series
F, March 8
11.11 Applications of Taylor Polynomials
M, March 11
10.1 & 10.2 Parametric Curves (not arc length, surface area)
March 23
W, March 13
10.3 Polar Coordinates
F, March 15
10.4 Areas in Polar Coordinates (not arc length)
M, March 18
12.5 Equations of Lines and Planes
March 30
April 5
W, March 20
12.6 Cylinders and Quadric Surfaces
F, March 22
12.6 Cylinders and Quadric Surfaces
M, March 25
15.7 &15.8 Cylindrical and Spherical Coordinates
April 10
W, March 27
13.1 Vector Functions and Space Curves
F, March 29
13.2 Derivatives and Integrals of Vector Functions
M, April 1
8.1, 10.2, 10.4, 13.3 Arc Length
W, April 3
8.1, 10.2, 10.4, 13.3 Arc Length
F, April 5
8.2 Area of a Surface of Revolution, 10.2 Surface Area
M, April 8
13.3 Curvature, the Normal and Binormal Vectors
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

Dragos Hrimiuc

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