Math 224, Calculus and Analytic Geometry II

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**Lectures:** MTWΘF 1-1:50pm in PM 112
**Office Hours:** MWF2-2:50pm, TΘ12-12:50pm, or by appointment

**Instructor:** Jonathan
Poritz
**Office:** PM 248
**E-mail:**
jonathan.poritz@gmail.com

**Phone:** 549-2044 (office — any time); 357-MATH
(personal; please use sparingly)

**Text:** *Calculus for scientists and engineers* by Briggs,
Cochran, and Gillett.

**Prerequisite:** A grade of **C** in Math 126, or the equivalent.

**Corequisite:** Chem 321 and 322 and EE 201. If you are planning to
go on to Math 325, you should take Math 224 and Math 207 concurrently.

**Postrequisites:** This course is a prerequisite for EN 231 and 571,
Math 307, 320, 325, 330, 337, 345, 445, and 480, and Phys 323.

**Course Content/Objective:** The Catalog says that this course
covers

This amounts to a continuation of the methods and applications of one-variable calculus, including games with inverse functions, more techniques and applications of integration, sequences and series, and some parametric equations and polar coordinates.Differentiation and integration of trigonometric, logarithmic, and other transcendental functions. Infinite sequences and series, parametric representation of curves, and selected applications.

**Attendance, work load:** Regular attendance in class is a key to
success — don't skip class, don't be late. But more than merely
attending, you are also expected to be *engaged* with the material in
the class. In order for this to be possible, it is necessary to be current
with required outside activities such as reading textbook sections and doing
homework problems: you are expected to spend 2-3 hours per hour of class on
this outside work. This is not an exaggeration (or a joke!), but if you put
in the time and generally approach the class with some seriousness you will
get quite a bit out of it (certainly including the grade you need).

If you absolutely have to miss a class, please inform me in advance (as late as a few minutes before class by phone or e-mail would be fine) and I will video the class and post the video on the 'net. You can then watch the class you missed in the comfort of you home and (hopefully) not fall behind. Classes I have videoed will have the icon next to that day's entry on the schedule/homework page to remind you of the available video.

**Calculators:** Students are required to have and to become (somewhat)
familiar with the basic functioning of a graphing calculator such as the
*Texas Instruments TI-8x*. Your calculators will be permitted
(suggested) for (large parts of) all of our exams — while *symbolic*
calculators (like the *TI-89*) will be **forbidden**.

The Mathematics Department does have a *TI-84 Plus* calculator rental
program, with rental of a limited number of calculators available on a first
come, first serve basis for a non-refundable fee of $20 per semester
payable at the Bursar's window in the Administration Building. For more
information, contact Prof. Tammy Watkins in the Math Learning Center (PM 132).

**Homework:** Mathematics at this level is a kind of practical
(although purely mental) **skill**, not unlike a musical or sports
skill — and, like for those other skills, one must **practice**
to build the skill. In short, *doing problems is the only way truly to
master this material* (in fact, the only way *to pass*). To this
end, there will be **daily**, fairly extensive homework set. Similarly,
we will spend a good part of our time in class discussing problems. In fact, I
am happy to work with you during class time on the homework set due on the
following day (or even due that very day).

Here are some specifics:

- Homework is due each day either in class or under my office door,
**no later than 3pm**. - Homework is assigned by day but graded by problem. Each problem will
typically be worth
**3 points**, meaning:- problem entirely missing (or wrong problem done!)
- some work present, but also several errors and/or important missing parts;
- most of the correct content is present, but there is at least one key idea or step which is missing, and/or there is a significant flaw in exposition (a variable used without definition, that kind of thing);
- all content is present, all notation is defined, all steps are explained and justified.

- Note that none of us is actually at all interested in the specific
*answers*to these problems: homework is about learning*how to do these kinds of problems*; everyone knows that quote about giving someone a fish versus teaching them how to fish. In short, "Showing your work" is not something extra that you can add to a homework assignment —**it is the homework assignment**. - If we have agreed that homework is a form of communication between
student and instructor about what
*thought process*the student is following, then some things are important to make that communication as clear as it can be. For example:- Always define
**all**variables, clearly and completely and with units (if relevant). - Always justify
**all**steps of every calculation you do. - Always label all axes of graphs and parts of diagrams.

- Always define
- Homework assignments appear on the homework web page on a regular basis. Please get used to going to that page frequently — at least every class day and certainly before starting your work on a homework set.
- Please try to be neat (how can I give you credit for your work if I
cannot follow it?). In particular, don't skimp on paper. If you can,
cut off ragged edges and use staples to attach multiple pages (rather
than that terrible thing where you sort of chew on the corner of the
pages). But I care much more about the
**content**than the**form**of your work, so don't worry if you just have bad handwriting or something (I certainly do!). - Make sure to label each assignment you hand in with your name and date, the course number, and number of the homework assignment (from the HW page).
- Late homework will count, but at a reduced value — generally,
the score will be reduced by 20% for each day late, unless you use
a
*Homework Late Pass*[see below].**Exception:**Late homework will count as**zero**, even even if you try to use a*Homework Late Pass*, if handed in after the next major test (the next hour exam during the semester, and the final for the end of the course).**Exception to the exception:**revisions of graded homework [see below] can always be handed in at the next class meeting after the graded work was returned, even if that is after the midterm ending a unit of the class.

- After you complete
**HW0**, you will receive a sheet of 10which may be used to hand in homework late but without penalty, subject to the restrictions mentioned above. It is your responsibility to keep track of these passes — don't loose them, they are valuable! Any unused passes may be turned in at the end of the term for general course extra credit.*Homework Late Passes* - Your seventeen (yes, 17) lowest scores (on individual homework problems) will be dropped.
- I am trying to reduce the carbon footprint of my classes. So I ask
that you reuse paper whenever possible, by taking any pages you can
find that are blank on one side (handouts from other classes, drafts of
your work for this or other classes,
*etc.*), putting a big "X" over the previously used side, and doing your HW for this class on the blank side. To encourage this, I will keep track of how many such reused pages you hand in and they will be worthextra credit at the end of the term.*Green Points*

**Big Ideas [BIs]:** Along with every homework set, you must turn in a
written explanation of the *Big Idea* of the last class. This should
be at least a clear and complete sentence, although sometimes several (or a
paragraph, or an equation with explanatory sentences) will be more
appropriate. The goal here is to get some practice with good exposition of
mathematical facts and with mathematics as a body of general results and
ideas, not merely a collection of worked examples. Some specifics:

- The
*BIs*will be graded out of**2 points**, according to the following scheme:- missing;
- present but very skimpy or wrong in some important respect; or
- present, completely, and (essentially) entirely correct.

- Please hand in your
*BI*each day attached to the regular*HW*, but a clear indication of which is which. - Late
*BIs*will be handled the same way as late*HWs*; if you use a homework pass to hand in a late*HW*without penalty, it will also apply to a*BI*if you choose to attach one. - You should think of the
*BIs*as a complete outline of and study guide for the course which you will be assembling bit by bit through the whole term. So each*BI*should be written in such a way that it will be clear and complete to you even weeks (months? years?) later. - The most common issues students have with
*BIs*are:- Submitting a
*BI*which is more the**name**of some content than**the content itself**. For example,

*Today we studied the Pythagorean Theorem.*

*If a triangle has sides of lengths $a$, $b$, and $c$, and a right angle between the sides with lengths $a$ and $b$, then $a^2+b^2=c^2$.*

*BI*(in the right class). *BIs*must be**general results, not merely examples**. So*Today we did $x^2-9=(x-3)(x+3)$.*

*Today we did things like $x^2-9=(x-3)(x+3)$.*

*Quadratics of the form $x^2-a^2$, where $a$ is any real (or complex) constant, can always be factored as $x^2-a^2=(x-a)(x+a)$.*

*BI*.- All parts of a
*BI*must be explained in a complete and precise way, including all variables. For example,*In a right triangle, $a^2+b^2=c^2$.*

*BI*. A better version of this is the one given just above (beginning with*"If a triangle has sides of lengths..."*).

- Submitting a

**Quizzes:** Most Fridays, during weeks in which there is no hour
exam, there will be a short (10-15 minute) quiz at the end of class. These
will be closed book, but calculators will (usually) be allowed. Your lowest
quiz score will be dropped.

**Exams:** We will have three in-class hour exams, on dates and
covering material to be announced. Our **(comprehensive!) final exam** is
scheduled for **Wednesday** and **Thursday**, **December 10th** and
**11th, from 1-3:20am in our usual classroom**.

**Revision of work on HWs, BIs, quizzes, and tests:** A great learning
opportunity is often missed by students who get back a piece of work graded
by their instructor and simply shrug their shoulders and move on —
often depositing their graded work in a trash can without even looking at it!
In fact, painful though it may be, looking over the mistakes on those
returned papers is often the best way to figure out exactly where *you*
tend to make mistakes. If you correct that work, taking the time to make
sure you really understand completely what was missing or incorrect, you will
often truly master the technique in question, and never again make any
similar mistake.

In order to encourage students to go through this learning experience, I will
allow students to hand in revised solutions to all homeworks, BIs, quizzes, and
midterms. There will be an expectation of slightly higher quality of
exposition (more clear and complete explanations, all details shown, all
theorems or results that you use carefully cited, *etc.*), but you will
be able to earn a percentage of the points you originally lost, so long as you
hand in the revised work at the very next class meeting. The percentage you
can earn back is given in the "revision %" column of the
table.

**Grades:** On quiz or exam days, attendance is required — if you
miss a quiz or exam, you will get a **zero** as score; you will be able to
replace that zero only if you are regularly attending class and have informed
me, **in advance**, of your valid reason for missing that day.

In each grading category, the lowest *n* scores of that type will be
dropped, where *n* is the value in the "# dropped" column. The total
remaining points will be multiplied by a normalizing factor so as to make the
maximum possible be 100. Then the different categories will be combined,
each weighted by the "course %" from the following table, to compute your
total course points out of 100. Your letter grade will then be computed in a
manner not more strict than the traditional "90-100% is an **A**, 80-90%
a **B**, *etc.*" method. *[Note that the math department does not
give "+"s or "-"s.]*

pts each | # of such | # dropped | revision % | course % | |
---|---|---|---|---|---|

Quizzes: | 10 | ≈10 | 1 | 33.3% | 14% |

Homework: | 3/prob | ≈55 sets ≈175 probs |
17 probs | 75% | 14% |

Big Ideas: | 2 | ≈55 (≈1 per HW set) |
3 | 50% | 4% |

Midterms: | >100 | 3 | 0 | 33.3% | 42% |

Final Exam: | >200 | 1 | 0 | 0% | 26% |

**Contact outside class:** Over the years I have been teaching, I have
noticed that the students who come to see me outside class are very often the
ones who do well in my classes. Now correlation is not causation, but why not
put yourself in the right statistical group and drop in sometime? I am always
in my office, PM 248, during official office hours. If you want to talk to me
privately and/or cannot make those times, please mention it to me in class or
by e-mail, and we can find another time. Please feel free to contact me for
help also by e-mail at
`jonathan.poritz@gmail.com`, to
which I will try to respond quite quickly (usually within the day, often
much more quickly); be aware, however, that it is hard to do complex
mathematics by e-mail, so if the issue you raise in an e-mail is too hard
for me to answer in that form, it may well be better if we meet before the
next class, or even talk on the telephone (in which case, include in your
e-mail a number where I can reach you).

**A request about e-mail:** E-mail is a great way to keep in touch
with me, but since I tell all my students that, I get *a lot* of e-mail.
So to help me stay organized, please **put your full name and the course name
or number in the subject line of all messages to me**. Also, if you are
writing me for help on a particular problem, please do not assume I have my
book, it is often not available to me when I am answering e-mail; therefore,
you should give me enough information about the problem so that I can
actually help you solve it (*i.e.,* "How do you do problem number
*n* on page *p*" is often not a question I will be able to answer).

**Academic integrity:** Mathematics is more effectively and easily
learned — and more fun — when you work in groups.
However, all work you turn in must be your own, and any form of cheating
is grounds for an immediate **F** in the course for all involved parties.
Please do not use a cell phone during class. You may not use a cell phone or
share a calculator with another student during a test.

** Nota bene:** Most rules on due dates, admissibility of make-up
work, etc., will be interpreted with great flexibility for students who are
otherwise in good standing (

**Students with disabilities:** The University abides by the **Americans
with Disabilities Act and Section 504 of the Rehabilitation Act of 1973**,
which stipulate that no student shall be denied the benefits of education
"solely by reason of a handicap." If you have a documented disability that
may impact your work in this class for which you may require accommodations,
please see the Disability Resource Coordinator as soon as possible to arrange
accommodations. In order to receive accommodations, you must be registered
with and provide documentation of your disability to: the Disability Resource
Office, which is located in the Library and Academic Resources Center, Suite
169.