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INSTRUCTOR: Professor Arkady
Berenstein, Fenton 306, PHONE: 346-5624, E-MAIL: arkadiy@uoregon.edu
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CLASSES: 102 Peterson: MUWF, 14:00--14:50 p.m.
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OFFICE HOURS: W 15:00--16:30 (or by appointment, please use
email).
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TEXT: OpenSTAX
Calculus Volume II. Available for free at http://openstax.org/details/books/calculus-volume-2, Chapters 5, 6.
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PREREQUISITES: Knowledge of Calculus 1 (Math 251) and Calculus 2
(Math 252) is assumed. You must have a good understanding of differentiation
and integration. I suggest reviewing all the differentiation rules and all the
techniques of integration.
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COURSE CONTENT: This course will cover chapter 5 (sequences and
series) and chapter 6 (power series and their applications) that may take more
than half a term. It is the most important topic in the course, and the hardest
topic in calculus.
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LEARNING
OUTCOMES: The course aims to equip students with a variety of
tools for analyzing sequences and series. These tools include the ε-N
definition of limit to show that sequences do not converge, as well as standard
series convergence tests. Students will learn to estimate sums using the
integral test, the alternating series test, and the comparison test where
possible. They will also gain the ability to calculate radii of convergence for
power series, find Taylor series, and represent common transcendental functions
as power series. Using Taylor’s remainder theorem, students will be able
to approximate values of transcendental functions to given levels of accuracy.
Furthermore, the course will cover giving power series solutions to appropriate
differential equations and recognizing solutions when they are common
transcendental functions.
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ATTENDANCE: Please remember that if you miss a class it is your
responsibility to find out what happened in that class.
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COURSE WEB PAGE: The homework and other class material is also
available at the web page http://pages.uoregon.edu/arkadiy/253new.html
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GRADING: Total 100%. Will be based on:
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HOMEWORK (20%): Homework will be collected on
Fridays. The first homework is due on Friday April 12. Late homework
will not be accepted. I will choose a subset of the assigned problems to be
graded. The lowest homework score will be dropped. You may collaborate with
other class members on your homework, although you must each write up your
solutions independently and in your own words. To avoid falling behind, you
should do the reading and homework as the material is presented in class,
rather than leaving it all until the last minute. We will usually reserve
Wednesdays for homework problem discussions.
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QUIZZES (15%) There will be short quizzes on Mondays, weeks 3, 7,
10. They will be based on the material covered in the previous week's homework.
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MIDTERM 1 (20%) on Monday April 29
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MIDTERM 2 (20%) on Monday May 20.
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FINAL (25%) on Monday June 10, 14:45-16:45.
· REMARK:
I expect you to be able to carry out calculations by hand so as to gain a solid
understanding of what these calculations entail. You may use calculators, Mathlab, Maple, etc. on your homework problems. You will
not be allowed to use them on your quizzes or exams. You may have a card 3x5
inches with any formulas you wish during the quizzes and exams.
Tentative Schedule
|
Week 1/Apr 1-5 |
section 5.1: Sequences,
5.2: Series |
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Week 2/Apr 8-12 |
sections 5.2: Series, 5.3:
Divergence and Integral Tests |
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Week 3/Apr 15-19 |
Quiz 1, sections 5.3, 5.4: Comparison
Test, 5.5: Alternating series |
|
Week 4/Apr 22-26** |
sections 5.5: Alternating series, 5.6: Ratio and Root Tests; Review |
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Week 5/Apr
29-May 3** |
Midterm 1, sections 6.1: Power series, 6.2: Properties of power series |
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Week 6/May 6-10 |
sections 6.2, 6.3: Taylor
and Maclaurin series |
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Week 7/May 13-17 |
Quiz 2, section 6.3: More on Taylor series; Review |
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Week 8/May 20-24 |
Midterm 2, section 6.4: Applications of Taylor series |
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Week 9/May 27*-31 |
section 6.4: Power series solutions to differential equations |
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Week 10/Jun 3-7 |
Quiz 3, Final Review |
*No
class on May 27 - Memorial Day holiday
**I will not be around on Tuesday--Wednesday of Week 4 and Monday--Tuesday
of Week 5. The classes will be covered via zoom or by other professors.
Important dates (See Schedule of Courses or Academic
Calendar):
Mar 31: Last day to drop a class without a
"W;"
Apr 8: Last day to add a
class;
May 19: Last day to drop a class with a "W", change grade options
(Graded or P/N).