Math 1220-003
Calculus II
Summer 2016
General Course Information:
Course: Calculus II, Math 1220-003.
Instructor: Keyvan Yaghmayi.
Office: JWB 107.
Phone: 801-581-8345.
Email: yaghmayi@math.utah.edu.
Class location: WEB 2250.
Class time: Mondays - Thursdays 8:00am - 9:30am. Class meets: 06/13/2016 to 08/03/2016.
Office Hours: Mondays, Tuesdays, and Thursdays after the class 9:30am-10:30am or by appointment.
Course website: I will use the Canvas: https://gate.acs.utah.edu/. You can get there easily
from the main University of Utah website www.utah.edu. To log in, you use the same student ID
and password that you use for Campus Information System.
Textbook: Calculus, with Differential Equations, by Varberg, Purcell, and Rigdon, 9th edition published by Pearson. ISBN-10: 0132306336 — ISBN-13: 978-0132306331. Before buying the textbook, please read ”Calculus Textbook Information” file on Canvas or visit http:
//www.math.utah.edu/schedule/bookInfo/.
Prerequisites: ”C” or better in (MATH 1210 OR MATH 1250 OR MATH 1270 OR MATH 1311
OR MATH 1310) OR AP Calculus AB score of at least 4 OR AP Calculus BC score of at least 3.
Important dates: the last day to add/drop/audit is Friday, June 17th. The last day to withdraw is Wednesday, July 6. For more information see http://registrar.utah.edu/handbook/
miscellaneous.php or talk with people in the Office of the Registrar.
Final exam: Friday, August 5 at 7:30am in our classroom.
This Course:
Course Description: Geometric applications of the integral, logarithmic, and exponential functions, techniques of integration, conic sections, improper integrals, numerical approximation techniques, infinite series and power series expansions, differential equations (continued).
Expected Learning Outcomes: Upon successful completion of this course, a student should
be able to:
• Compute derivatives and integrals for exponential, logarithmic, hyperbolic functions, and
inverse trigonometric functions.
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• Integrate integrable functions using integration by parts, u-substitution, trigonometric substitutions, rationalizing substitutions, partial fraction decomposition, and trigonometric identities. This includes knowing which techniques to apply to a given integral.
• Use L’Hopital’s Rule to calculate indeterminate-type limits and also know what limits are
the non-indeterminate forms and how to compute those limits.
• Compute improper integrals.
• Understand the difference between an infinite sequence and infinite series and determine if a
sequence converges or diverges.
• Determine whether or not an infinite series of numbers converges or diverges using a variety
of tests.
• Understand what it means for a Power Series to converge or diverge and be able to find the
Taylor Series for a given function.
• Differentiate and integrate functions in polar coordinates.
Here is the course outline: (We will follow it but subject to circumstances there might be little
changes.)
Week
Week 1
Day
Monday 6/13
Tuesday 6/14
Wednesday 6/15
Thursday 6/16
Monday 6/20
Week 2
Week 3
Week 4
Week 5
Week 6
Tuesday 6/21
Wednesday 6/22
Thursday 6/23
Monday 6/27
Tuesday 6/28
Wednesday 6/29
Thursday 6/30
Monday 7/4
Tuesday 7/5
Wednesday 7/6
Thursday 7/7
Monday 7/11
Tuesday 7/12
Wednesday 7/13
Thursday 7/14
Monday 7/18
Tuesday 7/19
Wednesday 7/20
Thursday 7/21
Summary of Plan
Recall from Algebra: Inverse Function; 6.1-6.4 Logarithm
and Exponential Functions and Their Derivatives; 6.8 Inverse Trig Functions and Their Derivatives
6.9 The Hyperbolic Functions and Their Inverses; 6.5 Exponential Growth and Decay
6.6 Linear Differential Equations; 6.7 Approximations for
Differential Equations
7.1 Basic Integration Rules; 7.2 Integration by Parts; Quick
Review for Exam 1
Midterm 1 from 6.1-6.9 & 7.1-7.2
7.3 Some Trigonometric Integrals; 7.4 Rationalizing Substitutions; 7.5 The Method of Partial Fractions; 7.6 Strategies
for Integration
8.1 Indeterminate Forms of Type 0/0; 8.2 Other Indeterminate Forms
Independence Day Holiday
8.3 Improper Integrals: Infinite Limits of Integration;
8.4 Improper Integrals: Infinite Integrands;
Quick Review for Exam 2
Midterm 2 from 7.3-7.6 & 8.1-8.4
9.1 Infinite Sequences; 9.2 Infinite Series;
9.3 Positive Series: The Integral Test; 9.4 Positive Series:
Other Tests; 9.5 Alternating Series, Absolute Convergence,
and Conditional Convergence
9.6 Power Series; 9.7 Operations on Power Series;
9.8 Taylor and Maclaurin Series;
9.9 The Taylor Approximation to a Function
Midterm 3 from 9.1-9.9
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Week 7
Week 8
Monday 7/25
Tuesday 7/26
Wednesday 7/27
Thursday 7/28
Monday 8/1
Tuesday 8/2
Wednesday 8/3
Friday 8/5
Pioneer Day Holiday (Observed)
10.5 The Polar Coordinate System
10.6 Graphs of Polar Equations
10.7 Calculus in Polar Coordinates
Review for the Final Exam
Final Exam (Comprehensive)
Homework:
You will be assigned some homework problems from the book. Homework problems and due dates
are posted on Canvas (please see the file ”Homework” on Canvas). I encourage you to discuss your
homework problems with one another, ask help from instructors in the tutoring center, or stop by
at office hours. Be sure that the final copy you hand in is written entirely with your words as you
understand the solution. If you spend enough time on the homework to gain understanding, then
the exams would be easy for you! Late assignments will not be accepted and if you will be absent
the day that an assignment is due you must turn it in to me before the class in which it is due.
Homework problems will be graded and returned to you.
Tests:
There will be three midterms along with a comprehensive final exam. All of them are in the scheduled classroom (WEB 2250) and at the class time.
Midterm one: on Thursday, June 23 (from Chapter 6 & 7.1-7.2)
Midterm two: on Thursday, July 7 (from 7.3-7.6 & 8.1-8.4)
Midterm two: on Thursday, July 21 (from Chapter 9)
Final exam: on Friday, August 5 (comprehensive)
It is essential that you show all your work. Credit will not be given without the proper work
and partial credit will be awarded if you show correct steps even if you do not obtain the final
correct number!
Grading:
The grades will be calculated as follows:
Homework 15%
Midterm one 15%
Midterm two 15%
Midterm three 15%
Final Exam 40%
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At the end of the semester, I will arrange the overall scores from the highest to the lowest and
the grades would be like:
A, A- : for the top 20%-25% of the class
B+ , B, B- : for the next 30%-35% of the class
C+ , C, C- : for the next 25%-30% of the class
D, E, W: for the rest of the class
Some Policies:
• Unless specifically noted, no calculators will be allowed during tests or quizzes. It is recommended that you complete your homework without calculators and then check your answers
by calculators (or any other preferred technology).
• Cheating will not be tolerated at any time during this course. Any student found cheating
will receive a zero for the assignment or test on which the cheating occurred.
• A Formula Card, that is in the back of the book, will be provided with the exams. Since
some of you don’t have it in your texts, I have posted the Formula Card on Canvas (you can
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find this in the ”files”). For instance, you do not need to memorize Dx sin−1 x = √
1 − x2
R
−1
because it is in the formula card. However, you should be able to find sin x dx (we will
learn how to do this by integration by parts). You are NOT allowed to bring any other kinds
of notes or formula to the exams.
• Please staple your homework! Otherwise, I am not responsible for lost papers.
• If you have any questions, ideas, or suggestion, please feel free to contact me. I promise to
do everything in my power to help.
• If there is something that I want to inform you, I will reach you by your email. That
is usually your default UMail address (uNID@utah.edu) that you have in the CIS. If you
are using other emails more frequently than your UMail, then you can set your UMail to
forward to your preferred email address. Also the fastest way to reach me is my email:
yaghmayi@math.utah.edu.
Tutoring and Extra Help:
• Tutoring Lab: The math tutoring center is available free of charge to all university students. It is located in room 155 of the T. Benny Rushing Mathematics Center (adjacent
to the LCB and JWB). The tutoring center is open Monday-Thursday 8:00am-8:00pm, and
Friday 8:00am-4:00pm. Please take advantage of the tutoring center as needed throughout
the semester. They are also offering group tutoring sessions. If you’re interested, inquire at
http://www.math.utah.edu/ugrad/tutoring.html
• ASUU Tutoring Center: University Tutoring Services, 330 SSB. They offer inexpensive
tutoring, please see their website: http://tutoringcenter.utah.edu
• The Math Department: They here has put together a complete set of lecture videos
for several classes, including Math1210, 1220 and 2210. You can find them here: http:
//www.math.utah.edu/lectures/
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• Khan Academy: is a non-profit, free, educational organization for anyone, anywhere. They
have some amazing videos in the Youtube. Check them out: https://www.khanacademy.
org/
Summer Warning: this class is pretty intense, meaning over a shortened schedule of 7 weeks,
rather than 15 (and we will miss two classes due to Holidays). We still have to cover all the same
material. That being said, we have to perform accordingly. I recommend you to spend 2-3 hours
per day (or 5-6 hours every other day) outside of class time to succeed in the class.
Student Responsibilities: All students are expected to maintain professional behavior in
the classroom setting, according to the Student Code, spelled out in the Student Handbook. You
have specific rights in the classroom as detailed in Article III of the Code. The Code also specifies proscribed conduct (Article XI) that involves cheating on tests, collusion, fraud, theft, etc.
Students should read the Code carefully and know you are responsible for the content. According to Faculty Rules and Regulations, it is the faculty responsibility to enforce responsible classroom behaviors, beginning with verbal warnings and progressing to dismissal from class and a
failing grade. Students have the right to appeal such action to the Student Behavior Committee.
http://regulations.utah.edu/academics/6-400.php
A.D.A. Statement: The University of Utah seeks to provide equal access to its programs,
services and activities for people with disabilities. If you will need accommodations in the class,
reasonable prior notice needs to be given to the Center for Disability Services (CDS), 162 Olpin
Union Building, 581-5020 (V/TDD). CDS will work with you and me to make arrangements for
accommodations. All information in this course can be made available in alternative format with
prior notification to CDS.
Disclaimer: All information on this syllabus is subject to change. Students will be notified of
any changes on this syllabus, course policies or course outline if they arise throughout the semester.
Good Luck!
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