Math 253 (Phillips)
This is the home page for N. C. Phillips' section of
Math 253 at the University of Oregon, Spring quarter 2023
(CRN 33738).
This page, especially its links,
has not yet been properly checked!
Also, much is still missing.
Quick links:
Contents:
Read this first
First read the
important information about this course.
Contents:
Back to top of page.
Summary of updates (most recent first)

21 June 2023:

15 June 2023:

The
worksheet
used at the review session, and its
solutions,
have now been posted.
There is one correction to the solution to the last problem:
"The exponent 4 is less than 1"
has been corrected to
"The exponent 4 / 5 is less than 1".
There are probably also further errors.

Graded Homework 8 was returned at the review session.
If you didn't get it, please come to my new office to get it.
That is 320 Fenton Hall; the label on the
door says "Shabnam Akhtari".
I expect to be there approximately 9:50 am11:50 am
and 1:15 pm1:55 pm today (Thursday), and maybe for
some time after 2:00 pm.

14 June 2023:

Solutions
to the sample final exam problems have been posted.
Make sure you look at the solutions to Problems 1 and 2,
so that you understand what you are asked for.
At least one of these will appear on the final exam.

The final exam will have the same rules as the midterms.
In particular, the note card allowed is the same size.

Reminder: Bring your student ID to the final exam.

The grader has promised to have Homework 8 returned by the
time of the review session.

13 June 2023:

Recall: the final exam is Friday 16 June, 10:15 am12:15 pm,
102 University (our usual classroom).
Scheduling and university rules prevent an early start or retakes;
sorry.

Bring your student ID to the final exam.

The review session will be 79 pm Wednesday 14 June,
102 University (our usual classroom).
Information is on the
finals
week web page.

Finals week office hour: 13 pm, 105 University, or by
appointment.
If I am not there, look for me in the "Hilbert Space",
107 University, the room I have often used during the quarter.

Two further problems have been added at the end of the
sample
final exam problem list.
If you don't see a Problem 17 at the end, please reload the page.

Homework
9 solutions have been posted.

Worksheets and their solutions through the end of the quarter are posted.
See links on the
Week 10
page.

11 June 2023:

Some
sample
final exam problems
have been posted.
The problems on this list are not intended to
be representative of all the kinds of problems
which will appear on the final exam.
Rather, they are "extra" sample problems.
(The worksheet version will better represent the weights
of the different parts of the course.)

Full
Homework 8 solutions have been posted.

The review session will be 79 pm Wednesday 14 June.
I have requested a room reservation.

2 June 2023:

Homework
9 has been posted.
It is due in class Friday 9 June.
Problems 18 (all of the same type), 9, and 15 can all be done
with the material seen so far.
Problems 18 depend on recognizing the power series for standard
elementary functions.
For example (not one of the problems on the assignment), if you are
given the series 1 + 2 + 2^2 / 2! + 2^3 / 3! + ...,
you can recognize that its sum is e^2.

29 May 2023:

A retake of Midterm 2
will be given Friday 2 June.
As usual, if everyone agrees, there will be an early start.
See the permission form,
due in class Tuesday 30 May, or on
Canvas by 5:00 pm
Tuesday 30 May.

Corrected solutions to Midterm 2 have been posted.
See the links on the Midterm 2 page.

Worksheets and their solutions through Friday 26 May are posted.
See links on the
Week 8
page.

The
Week 9
page
has been posted.

26 May 2023:

Homework 8
(full version) has been posted.
It is due in class Wednesday 31 May.
Four more problems have been added, for a total of 15,
and two minor misprints in the previously posted version
have been corrected.

25 May 2023:

An
incomplete version of Homework 8 has been posted.
A few more problems will be added by Friday morning.
It is due in class Wednesday 31 May.

Corrected and improved Midterm 2 solutions will be posted soon.

23 May 2023 (second update):

A short
information file
for Midterm 2 has beeen posted.
It is about what you can take as known on the midterm
without justification.

23 May 2023:

By class agreement, Midterm 2 will start at 7:30 am.

Homework
7 solutions have been posted.

The worksheet used at the review session,
and its solutions, have been posted.
See links on the
Midterm 2
page.

There was no worksheet in class Tuesday 23 May.
22 May 2023:

The Week 8
and
Midterm 2
web pages now exist.

Worksheets and their solutions through today are posted.
(Note the correction in the solutions for today.)
See links on the
Week 8
page.

Canvas
should now be fully up to date,
except for extra credit scores.
The Midterm 1 and Midterm 1 retake scores now "don't count
towards the final grade"; only the best of the two scores counts.

22 May 2023:

Solutions
to the sample problems for Midterm 2 have been posted.
Little proofreading has been done!

20 May 2023:

19 May 2023:

An expanded version of the
sample
problems for Midterm 2
has been posted, with four new problems at the end.
If you don't see 20 problems, reload the page in your browser.

Worksheets and their solutions through today are posted.
See links on the
Week 7
page.

The review session will be Monday 5:107:00 pm in
210 University Hall.

18 May 2023:

17 May 2023:

Homework 7
has been posted.
It is due Tuesday of Week 8 (23 May).
It is worth only 80 points, but it looks shorter than it really is.

Midterm 2 will be on Wednesday of Week 8 (24 May).
It will cover material through using remainder estmates
for Taylor series, in Section 6.3 of the book.

Official Midterm 2 sample problem will be posted soon.
They will include all but Problem 5 on
Midterm 2
from Spring 2018.
(The solutions are already posted,
but don't look at them until you have attempted the problems.)

The Week 8 web page doesn't exist yet, but will soon be posted.
I want to get Homework 7 out right away.

15 May 2023:

Worksheets and their solutions through Monday 15 May are posted.
See links on the
Week 6
page
and the
Week 7
page.
In the worksheet solutions for Friday 12 May, extraneous parentheses
have been removed from the limits in the solution to Problem 1.

On
Homework 6,
in Problems 10 and 11, "radius of comparison"
has been corrected to "radius of convergence"
in multiple locations.
(Reload the page if necessary to see the corrected version.)

In the
Midterm 1
solutions,
in Problem 3, I have corrected 3^3 and 3^5 to 2^3
and 2^5, both in the last line and in the last expression in the
middle equation.
(Reload the page if necessary to see the corrected version.)

10 May 2023 (second update):
Homework
6 has been posted.
It is due Wednesday 17 May.

10 May 2023:

Worksheets and their solutions through today are posted.
See links on the
Week 6
page.
Note the correction to the solution to to Problem 1 on
the worksheet: the limit gotten from the Root Test is 3/2,
not 2/3, and the series therefore diverges.

Solutions
to Homework 5
are posted.

9 May 2023:

Worksheets and their solutions through today are posted.
See links on the
Week 6
page.

The Midterm 1 retake and its solutions have been posted.
See links on the
Midterm 1
page.

6 May 2023:

The Midterm 1 retake will start at 7:30 am
(Monday 8 May).
Note: Problems 1 and 2 on Homework 4 are on material for Midterm 1.

Homework
4 solutions have been posted.

Worksheets and their solutions through Friday 5 May are posted.
See links on the
Week 5
page.

4 May 2023:

Homework 5
has been posted.
It is due Wednesday 10 May.

3 May 2023:

Worksheets and their solutions through Wednesday 3 May are posted.
See links on the
Week 5
page.

The real Midterm 1 and its solutions have been posted.
See links on the
Midterm 1
page.

There will be a retake Midterm 1 on Monday 8 May, in class.
See information on the
Week 6
page.
The permission form for a 7:30 am start
is due due Thursday 4 May at 5:00 pm,
in person, by email (no Microsoft Word files accepted), or on
Canvas.

29 April 2023:
The
Week 5
page
is up.
It has a link to Homework 4, which is due Friday 5 May.

26 April 2023, second update:
The worksheet used at the review session, and its solutions,
have been posted.
See links on the
Midterm 1
page.

26 April 2023:

Since everyone who turned in a form agreed,
Midterm 1 will start Friday at 7:30 am.

Worksheets and solutions are current through today.
See links on the
Week 4
page.

Homework 3 solutions have been posted.
Again, see the link on the
Week 4
page.

Solutions to the sample problems for Midterm 1 have been posted.
See links on the
Midterm 1
page.

24 April 2023:

Midterm 1
information
has been posted.
This includes sample problems,
review session information, and a copy of
the permission form for an early start.

Today's worksheet and its solutions have been posted.

21 April 2023:

Solutions to Homework 2, today's worksheet, and its solutions,
have been posted.
They are linked on the
Week 3
page.

The time of the Midterm 1 review session has been
changed to Wednesday 26 April 5:007:00 pm
(from Wednesday 26 April 8:0010:00 pm).
Location still not known.

If everyone agrees (permission form not yet posted),
Midterm 1 will start at 7:30 am (not 7:00 am).

20 April 2023:

Homework 3
has been posted.

Midterm Zero version 2 and its solutions have been posted.
They are linked
here.

Worksheets and solutions have been posted through Wednesday 19 April.
The new ones are linked
here.

Midterms 1 and 2, and the final exam, from Spring 2018
(the last time I taught this course) have been posted.
They are linked
here.

14 April 2023:

Solutions
to Homework 1
have been posted.
They are also linked on the
Week
2 page.

Solutions
to the second set of extra problems for Midterm Zerohave been posted.
They are also linked on the
Midterm 0 page.

Friday's worksheet and its solutions have been posted.
See links on the
Week
2 page.
Two egregious misprints in the hint on Problem 3 have been corrected:
in two places, the version handed out in class had 17^x
where it should have been x^{17}.
An additional misprint in the solution to Problem 5 has been corrected.

13 April 2023:

The
solutions to
the first set of extra sample Midterm Zero problems (pdf);
were corrected at about 12:30 pm 13 April 2023:
misprints in the solutions to Problems 22 and 50 have been fixed.
Reload the page from your browser to be sure you have the current
version.
(Somebody got extra credit for catching the error in the solution
to Problem 50.)

Worksheet and its solutions for Wednesday are now posted on the
Week
2 page.

11 April 2023:

10 April 2023:

Midterm 0 version 1 and its solutions, and Monday's worksheet and
solutions, have all been posted, and are linked on the
Week
2 page.

9 April 2023:

Solutions to the sample Midterm 0,
Friday's worksheet, and solutions to Friday's worksheet,
are now all linked on the
Week 1 page.

Solutions to the first set of extra Midterm 0 practice problems
are linked on the
Midterm 0 page.

6 April 2023 (more):

6 April 2023:
Homeswork 1,
due in class Wednesday 12 April (pdf).

5 April 2023:
Back to top of page.
Basic course information
This section contains administrative information.
See below for information on
learning objectives,
the syllabus,
exams,
homework,
grading,
academic conduct,
course documents,
and important dates.

Course number: Math 253,
CRN 33738.

Course title: Calculus 3.

Time and place: MTuWF 8:008:50 am, 102 University.

Instructor: N. Christopher
Phillips.

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).

Office hours: MTu 9:009:50 am,
W 10:0010:50 am,
or by
appointment.

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:

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.)

See
writing
mathematics in plain text email.

No binary files or attachments (except by prior arrangement).

No Microsoft Word files.
I do not accept these under any circumstances,
since I don't have software that reads them.

No mime encoding or other encoding of ordinary text messages.

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.

Instructions for written
homework (pdf).

External help.

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.)

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.)
Back to top of page.
Learning objectives
A pdf file with considerably more detail will be posted soon.
There are two primary goals of the course:

Learn to approximate functions with Taylor polynomials,
and learn to use Taylor's theorem to estimate the error.

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:

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.)

Relate convergence of an infinite series
to convergence of its sequence of partial sums.

Use convergence tests to prove that
an infinite series does or does not converge.

Estimate sums of infinite series using the integral test,
alternating series test, and comparison test
(where applicable).

Calculate radii of convergence of power series,
and calculate the Taylor series
representing common transcendental functions.

Use Taylor's Remainder Theorem to approximate transcendental functions
to given levels of accuracy.

Use Taylor's remainder theorem to approximate values of
transcendental functions to given levels of accuracy.

Give power series solutions to appropriate differential equations.

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:

Correct use of parentheses.

Correct use of "="
(in particular, "=" isn't used for approximations).

Correct placement of "lim".

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.
Back to top of page.
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).

Week 1 (3 April7 April):
Section 6.3: Taylor polynomials as approximations.

Week 2 (10 April14 April):
Section 5.1: Sequences.

Week 3 (17 April21 April):
Second version of Midterm Zero.
Section 5.2, start Section 5.3:
Series, divergence and integral tests.

Week 4 (24 April28 April):
Finish Section 5.3; Section 5.4:
Divergence and integral tests, comparison tests.
Midterm 1.

Week 5 (1 May5 May):
Sections 5.5 and 5.6: Alternating series; ratio and root tests.

Week 6 (8 May12 May):
Sections 6.1 and 6.2: Power series.

Week 7 (15 May19 May):
Section 6.3: Taylor and Maclaurin series.

Week 8 (22 May26 May):
Section 6.4: Applications of Taylor series.
Midterm 2.

Week 9 (29 May2 June):
Section 6.4: Power series solutions to differential equations.

Week 10 (5 June9 June):
Catch up and review.
Back to top of page.
Exams
Exam and review session schedule

Midterm 0: Monday 10 April; repeatable Tuesday 18 April
(postponed from Monday 17 April).
Special instructions for Midterm 0.

Midterm 1 review session: Wednesday 26 April 5:007:00 pm
(changed by class agreement in class of Friday 21 April
from 8:0010:00 pm),
room to be announced.

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.

Midterm 2 review session: Monday 22 May 8:0010:00 pm
(subject to change),
room to be announced.

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.

Final exam review session: To be announced.

Final Exam: 10:15 am12:15 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:

Staple pages together.
Don't fold or tear corners or fold in half.

If you cooperate with someone else, that person's name
must appear below yours.

Simplify all answers.

Show your work.

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 here will only be posted when
they are working.

Week 1 homework
and solutions.

Week 2 homework
and solutions.

Week 3 homework
and solutions.

Week 4 homework
and solutions.

Week 5 homework
and solutions.

Week 6 homework
and solutions.

Week 7 homework
and solutions.

Week 8 homework
and solutions.

Week 9 homework
and solutions.

Week 10 homework
and solutions.

Finals week omework
and solutions.
Advantages of WeBWorK (unfortunately lost for this class):

All your work gets graded.

Grading is done quickly.

Multiple attempts may be allowed.
Disadvantages of WeBWorK:

No partial credit.

Only the final answer is graded.
(But many graders do this anyway.)

WeBWorK is picky about format
(but this is something you will have to get used to anyway).
Back to top of page.
Grading
Letter grades will be assigned according to the Math Department's
Undergraduate
Grading Standards.
Grading percentages
Grading percentages:

The three midterms will each be about 17% of the grade.

The final exam will be about 34% of the grade.

Written homework will be about 15% of the grade.
Course grade limited by final exam grade
The course grade will not be more than one letter grade
above the final exam grade.
Extra credit
There will probably be extra credit problems
on the midterms and final exam.
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.
Back to top of page.
Academic conduct
The code of student conduct and
community standards is
here.
In this course, it is
appropriate to help each other on homework as long as the work you are
submitting is your own and you understand it,
and you give the names of any people you cooperated with.
It is not appropriate to submit as your own work
homework solutions gotten from, or modifications of homework solutions
gotten from, homework solution websites, other class members,
your aunt the physicist, the sentient fungi of the planet Yuggxth,
or any similar source.
It is not appropriate
to help each other on exams, to look at other students' exams, or to
bring any unauthorized material to exams, including calculators
and cell phones.
(Exams will permit a 3 by 5 file card,
written on both sides,
readable without a magnifying glass.)
Back to top of page.
Publicly available documents
associated with this course
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.
Most files will be pdf.
Previous
course information:
selected items from the last time I taught this course.
(Exams and solutions to them.)
Notation errors seen in the class
and in prerequisite classes.
(Read this and don't make these mistakes!
You are responsible for knowing the contents of the
documents linked here.)
Sample and real
Midterms Zero and their solutions.
General
instructions for written homework.
Week 1 worksheets, homework,
and solutions.
(The sample Midterm Zero and the questionnaire are here.)
Week 2 worksheets, homework,
and solutions.
(The official Homework 1 is here, since it is due Wednesday of
Week 2.)
Week 3 worksheets, homework,
and solutions.
Week 4 worksheets, homework,
and solutions.
Week 5 worksheets, homework,
and solutions.
Back to top of page.
Important dates, according to the
Academic
Calendar at the registrar's office
(not guaranteed!)

Su 2 April:
Last day to process a complete drop (100% refund, no W recorded).

Sa 8 April:
Last day to drop this course (100% refund, no W recorded).

Sa 8 April:
Last day to process a complete drop (90% refund, no W recorded).

Su 9 April:
Last day to process a complete drop (90% refund, W recorded).

Su 9 April:
Last day to process a complete drop (75% refund, no W recorded;
after this date, W's are recorded).

M 10 April:
Last day to add this course.

Su 16 April:
Last day to withdraw from this course (75% refund, W recorded).

Su 23 April:
Last day to withdraw from this course (50% refund, W recorded).

Su 23 April:
Last day to withdraw from this course (50% refund, W recorded).

Su 23 April:
Last day to process a complete drop (50% refund, W's recorded).

Su 30 April:
Last day to process a complete drop (25% refund, W's recorded).

Su 21 May:
Last day to withdraw from this course (0% refund, W recorded).

Su 21 May:
Last day to change grading option for this course.

M 29 May:
No classes.
(Memorial Day.)

Su 11 June:
Last day to process a complete drop (no refund, W's recorded).
Back to top of page.
This page maintained by
N. Christopher Phillips,
email.
Please email plain text
(7 bit ASCII)
only
(no web page coded files, Microsoft Word documents, binary
characters, etc.; see above for more).
Last significant change: 2 April 2023.