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Course number: Math 253,
CRN 33738.
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Course title: Calculus 3.
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Time and place: MTuWF 8:00--8:50 am, 102 University.
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Instructor: N. Christopher
Phillips.
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Office: 105 University.
The office is on the main level at the east end of the building,
opposite the stairs.
Please knock.
I can't leave my door open, because if I do I get too many people
asking to borrow my telephone or pencil sharpener, or
where to find the math department office
or nonexistent rooms (such as 350 University).
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Office hours: MTu 9:00--9:50 am,
W 10:00--10:50 am,
or by
appointment.
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Email.
The subject line of your message must start with
"M253", followed by your last name,
then first initial.
When emailing me, please use plain text
(7 bit ASCII)
only.
That is, only the characters found on a standard English
language keyboard; no curved quotation marks, curved apostrophes,
accented letters, Greek letters, etc.
In particular:
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No html encoded (web page format, or "styled") messages.
See "Configuring
Mail Clients to Send Plain ASCII Text"
for how to turn off html.
(The University of Oregon webmail program is apparently capable
of sending plain text email.)
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See
writing
mathematics in plain text email.
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No binary files or attachments (except by prior arrangement).
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No Microsoft Word files.
I do not accept these under any circumstances,
since I don't have software that reads them.
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No mime encoding or other encoding of ordinary text messages.
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Textbook:
OpenSTAX Calculus Volume II.
An
electronic
edition of this text is available for free.
The course covers most of Chapters 5 and 6,
plus some additional material
on using power series to solve differential equations.
Some of this is in OpenSTAX Calculus Volume II,
and some in Chapter 12.8 of Marsden and Weinstein's book
Calculus II; a free electronic version is available
here.
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Instructions for written
homework (pdf).
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External help.
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Extra credit will be given for identifying errors and misprints
in any course materials,
with more extra credit for mathematical errors.
(You must say what the correct version is supposed to be,
and only the first two people to catch an error can get extra credit.)
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Students with documented learning disabilities who wish to
use the
Accessible Education Center
to
take
tests under specifically arranged conditions
should let me know as soon as possible,
certainly by Wednesday of the third week of classes.
Such students must also
be sure to meet the Accessible Education Center's
separate deadlines for requests;
these are likely to be a week or more in advance of the exam date
(much more for final exams),
and I can't do anything to help a student who misses its deadline.
(I have tried in the past.)
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Learning objectives
A pdf file with considerably more detail will be posted soon.
There are two primary goals of the course:
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Learn to approximate functions with Taylor polynomials,
and learn to use Taylor's theorem to estimate the error.
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Learn the differences between convergent and divergent infinite series,
learn various methods for distinguishing the two,
and learn how this material applies to Taylor series.
In somewhat greater detail (and including some things going beyond
the list above),
students successfully completing this course will be able to:
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Find limits of sequences,
and show that sequences do or do not converge without
knowing the limit.
In particular, use the epsilon and N definition of the limit
To show that a series does not converge.
(For a top grade, also use the epsilon and N definition of the limit
To show that a series does converge.)
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Relate convergence of an infinite series
to convergence of its sequence of partial sums.
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Use convergence tests to prove that
an infinite series does or does not converge.
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Estimate sums of infinite series using the integral test,
alternating series test, and comparison test
(where applicable).
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Calculate radii of convergence of power series,
and calculate the Taylor series
representing common transcendental functions.
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Use Taylor's Remainder Theorem to approximate transcendental functions
to given levels of accuracy.
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Use Taylor's remainder theorem to approximate values of
transcendental functions to given levels of accuracy.
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Give power series solutions to appropriate differential equations.
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Correctly use terminology and notation of the course,
and terminology and notation of the parts of previous courses
that are used in this course.
Correct use of terms and symbols is taken as evidence
of understanding of their meaning.
In addition, it is like using correct grammar and spelling
in an essay or term paper.
Here is an incomplete list of examples:
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Correct use of parentheses.
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Correct use of "="
(in particular, "=" isn't used for approximations).
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Correct placement of "lim".
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Recognizing that expressions
like infinity/infinity,
0 / 0,
0 times infinity,
etc.
are not numbers and therefore may not appear in equations.
Information on common notation errors in
Math 251 is here.
Weekly homework problems,
as well as problems on the midterms and final exam,
will provide students with opportunities to demonstrate the level
of their abilities on the learning outcomes above.
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Syllabus
The following is an
approximate
schedule.
Adjustments may be made as we go through the quarter.
After motivational material, we will start with Taylor polynomials
and some formal manipulations with Taylor series.
Then we will look at limits of sequences and sums of series more
carefully, then return to Taylor series, and then
series solutions to differential equations.
More detailed schedule (subject to change if necessary).
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Week 1 (3 April--7 April):
Section 6.3: Taylor polynomials as approximations.
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Week 2 (10 April--14 April):
Section 5.1: Sequences.
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Week 3 (17 April--21 April):
Second version of Midterm Zero.
Section 5.2, start Section 5.3:
Series, divergence and integral tests.
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Week 4 (24 April--28 April):
Finish Section 5.3; Section 5.4:
Divergence and integral tests, comparison tests.
Midterm 1.
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Week 5 (1 May--5 May):
Sections 5.5 and 5.6: Alternating series; ratio and root tests.
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Week 6 (8 May--12 May):
Sections 6.1 and 6.2: Power series.
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Week 7 (15 May--19 May):
Section 6.3: Taylor and Maclaurin series.
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Week 8 (22 May--26 May):
Section 6.4: Applications of Taylor series.
Midterm 2.
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Week 9 (29 May--2 June):
Section 6.4: Power series solutions to differential equations.
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Week 10 (5 June--9 June):
Catch up and review.
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Exams
Exam and review session schedule
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Midterm 0: Monday 10 April; repeatable Tuesday 18 April
(postponed from Monday 17 April).
Special instructions for Midterm 0.
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Midterm 1 review session: Wednesday 26 April 5:00--7:00 pm
(changed by class agreement in class of Friday 21 April
from 8:00--10:00 pm),
room to be announced.
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Midterm 1: Friday 28 April, in class.
If
everybody in the class agrees
and I can get the room,
I am willing to start Midterm 1 at 7:00 am or 7:30 am.
Details later.
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Midterm 2 review session: Monday 22 May 8:00--10:00 pm
(subject to change),
room to be announced.
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Midterm 2: Wednesday 24 May (subject to change), in class.
If
everybody in the class agrees
and I can get the room,
I am willing to start Midterm 2 at 7:00 am or 7:30 am.
Details later.
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Final exam review session: To be announced.
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Final Exam: 10:15 am--12:15 pm Friday 16 June 2023,
102 University (our usual classroom).
(The final exam schedule is
here.)
No early final exams, according to University rules.
If you have another final exam scheduled at the same time
as our final exam,
you need to give me the details
(course number and instructor)
by Monday of the 7th week of classes.
Exam policies
for Midterm 0
It will be review; only 25 minutes long.
For those who know the material of the prerequisites,
it should be an easy way to start the quarter with a high grade.
See the
sample (together with other
information)
(assigned as homework in the first week of classes),
and read its instructions.
Note in particular
that calculators and note cards are not allowed, that
there is no partial credit, and that it is graded on an absolute scale.
Complaints about the grading of any exam must be submitted in
writing by the beginning of the first class period after the class in
which that exam is returned.
Items (4)
(answers must be simplified)
and (6) (use correct notation)
of the
general
instructions for written homework
also apply to Midterm 0.
Exam policies
for all exams except Midterm 0
All exams are cumulative, although they will
usually emphasize the most recent material.
All exams
will cover material through the most recently turned in homework.
No calculators or other electronic devices will
be permitted on any exam.
In particular, no electronic dictionaries will
be permitted on any exam.
Exams will permit a 3 by 5 file card, written on both sides,
readable without a magnifying glass.
At least 80% of the points on each of Midterms 1 and 2,
and the final exam,
will be based on homework problems, on problems on separate
supplementary lists (including sample exams),
and on problems from all versions of Midterm 0.
Note that numbers may be changed in these problems.
Similarly variable names, function names, and names of people etc. in
word problems may be changed.
Thus, f(x) = 2x^3 could become any of
f(x) = -4 x^3, f(x) = 2x^{-4}, g(x) = 2x^3, or f(t) = 2t^3.
Such changes might turn a local maximum into a local minimum
or result in other such reversals.
Complaints about the grading of any exam must be submitted in
writing by the beginning of the first class period after the class in
which that exam is returned.
Except where obviously inapplicable
(such as in the parts about working with other people,
or where explicitly contradicted by exam instructions),
the
general
instructions for written homework
also apply to exams.
Miscellaneous
Back to top of page.
Homework
Homework will be written.
(No WeBWorK.
It can't grade your explanation of
why an infinite series does or doesn't converge.)
Assignments will be turned in to me at the beginning of the
class period in which they are due.
Links to them are in the
list of publicly available documents
associated with this course.
Most of them will probably be graded by a homework grader.
Here,
you will unfortunately see the disadvantage
of not using WeBWorK:
many problems will not actually get graded.
Read the separate
Instructions for written
homework (pdf);
here is a brief summary of the most important points:
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Staple pages together.
Don't fold or tear corners or fold in half.
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If you cooperate with someone else, that person's name
must appear below yours.
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Simplify all answers.
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Show your work.
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Use correct notation.
(In particular, use enough parentheses.)
It is assumed that you know that the notation described as
being wrong here is in fact wrong.
Here is a list of links for homework assignments.
They won't work until the relevant assignment is posted;
the links
I will also award extra credit points to the first two people
who catch any particular error or misprint in the book
or in any of the handouts,
in particular, in solutions to
midterms, homework, etc.
The largest amount of extra credit is given for catching
mathematical mistakes.
You must point out exactly where the mistake is,
and how it should be fixed,
and if it is on something on the website you must
point it out to me (perhaps by email) before I find and fix it myself.
There will also be extra credit for getting perfect scores on both
administrations of Midterm zero.
Extra credit will count toward the grade only for those who
consistently do the homework reasonably,
and only for those whose grade in the course would be at least a
B- without it.
Here is a list of publicly available documents
associated with this course.
The material is arranged in approximate chronological order: most
recent items at the bottom.
Links to written homework solutions,
exams, and exam solutions will not work until after
the corresponding written homework has been turned in
or the corresponding exam has been given, and
the links to sample exams and their solutions will not work until
these items have been prepared.