**Course:** Math 231/Math 249, Honors
Calculus II, Section D1H/P1H

**Time:** MWF 11:00--11:50am

**Location:** 145 Atlgeld Hall

**Instructor:** Prof. Leininger

**Phone:** 265-6763

**Email:** clein (at) math.uiuc.edu

**Office:** 265 Altgeld Hall

**Office hours (my office):** Wednesday 4:00--5:00, Thursday 10--11:50
and by appointment.

**Text:** Smith and Minton, *Calculus: Early Transcendental functions 3e*, McGraw-Hill.

**About the honors course:** Although the syllabus for this class is the same as the usual Math 231, we will
be delving deeper into certain aspects of the material. I will be pushing many of you to your limitations in the
hopes that you will gain a better understanding of calculus. If you are not willing to put in the extra effort
required to succeed, I strongly urge you to switch to one of the regular sections of Math 231. On the other hand,
you will not be punished for enrolling in the honors section, and I will be reasonable when it comes to grading
more difficult problems.

**Grades:** Grades for Math 231 will be based on homework [10%] three exams [20% each] and a final exam [30%].
The grade for the one credit hour Math 249 will be assigned based on your completion of the ``honors problems''. These are four problems assigned throughout the semester that will require deeper understanding of the material and techniques than the regular homework.

I will curve an exam score if absolutely necessary (e.g. the problems were legitimately too difficult or the exam
was too long). The final grades will be assigned on the usual scale: 90--100 A, 80--90 B, 70--80 C, 60--70 D,
below 60 Failing.

**Homework:** Assignments will be made on Monday and will be collected the following Monday.
I'll only be grading (some of) the even problems, though you are assigned and should turn in all
problems. I expect assignments handed in to be written neatly. Poorly written homework will be returned,
ungraded.

Collaboration is allowed... In fact, I encourage it! However, I also expect that you attempt (with real effort)
each problem on your own before discussing it in a group. Moreover, *each individual must turn in their own assignment*.

**Missed exams/homework:** A missed exam will count as ZERO, except under the most extreme circumstances
(e.g. death in the family or serious illness/injury *requiring* medical attention). Make-up exams for the three midterms will not be given, and a make-up
for the final will occur only under extreme circumstances as noted above. In the rare situation that there is
actual cause to miss an exam (my discretion), I expect prior notification of the absence if it is humanly
possible. In the case of a midterm, the lower of the other two exam scores will be used to replace the missing
score. Homework will not be accepted late under any circumstances.

**Attendance:** I will not take attendance, but I'll know who is coming to class and who is not. This will
be relevant in making grade decisions for borderline cases.

Tentative schedule.

**First Midterm:** February 8 -- covering Sections 6.1--6.4, 6.6.

**Second Midterm:** March 12 -- covering Sections 8.1--8.5

**Third Midterm:** April 18 -- covering Sections 8.6--8.8, 9.1--9.3

**Final Exam:** May 3, 8:00am to 11:00am -- covering everything to
here, plus 9.4--9.6, 7.1

**Assignments:**

**Problem set 1.** Due 1/22 (in my mailbox by 2:00pm): § 6.1 -- 7, 10, 13, 19, 33; §
6.2 -- 1, 2, 7, 8, 23, 24, 31, 32, 39, 59, Exploratory 2; § 6.3 --
1, 2, 7-10, 31.

**Honors problem 1** here.
There was a little typo, and perhaps a little more explanation is in order:

I meant to say that the integral ∫ cos^{m}(x) sin^{n}(x)dx can be solved for any integers m ≥ 0 and n ≥ 0 using the techniques of § 6.3 (not § 6.2 as was written in the problem sheet). Your job is to explain how to compute this integral for any integers m and n *using any techniques you want.*

**Problem set 2.** Due 1/28: § 6.3 -- 17-19, 22-29. § 6.4 --
1-14.

**Problem set 3.** Due 2/4: § 6.4 -- 15-20, 23, 24. § 6.6 -- 11-16, 19-22, 31, 32, 40, 41, 45-48.

**Problem set 4.** Never due: § 7.1 -- 9, 11, 17, 19, 23, 25.

**Review for Midterm 1.** Chapter 6 Review Exercises,
page 561-562 --
1-50, 61-68.

There are a lot of problems here, but great practice for
the exam. These are not to turn in.

**Problem set 5.** Due 2/18: § 8.1 --
13,14,19-22,27-30,35,36,39,40,49.

**Problem set 6.** Due 2/25: § 8.2 -- 5-8, 11, 12, 17, 18, 37, 44, 54. § 8.3 -- 3-6, 9, 10, 19, 20, 23-26.

**Problem set 7.** Due 3/3: § 8.3 -- 11-14, 29-32, 42-44. § 8.4 -- 5, 6, 9, 10, 17, 18, 43.

**Problem set 8.** Due 3/7!!: § 8.4 -- 44. § 8.5 -- 9, 10, 16, 17, 28, 29, 32, 33, 36, 38.

**Honors Problem 2.** Due 3/31 (new due date!). Here it is.

**Review for Midterm 2.** Chapter 8 Review Exercies, page 710-711 -- 1-22, 25-48. These are not to turn in, but are to use for practice.

Be sure you know what it means for a *sequence* to converge---know what it means intuitively, what the definition is, and how the definition fits the intuition.

Also make sure you know what it means for a *series* to converge---know the definition and how it works. Keep in mind the difference between sequences and series and their convergence. Review all your tests for convergence of series and make sure you know what the hypotheses are for these tests so you know when they do and do not apply.

**Problem set 9.** Due 3/31; § 8.6 -- 1, 2, 9, 10, 15 -- 22, 27, 28 (for these last 10 problems, find the radius of convergence only; that is, you do not need to test the endpoints).

**Office hours this week:(3/23--3/28)** Wednesday and Thursday's office hours will be cancelled. Instead, I will be available Monday 4:00--5:00 (note this is monday, not tuesday as in my email) and Wednesday 9:00--11:00. We will also hold a discussion/review session regarding honors problem 2, Tuesday 8:00--9:00pm in 143 Altgeld hall.

**Office hours this week:(3/31--4/4)** Wednesday and Thursday's office hours will again be cancelled. I will be available Tuesday afternoon 3:00--4:00 and Wednesday morning 9:00--11:00.

**Friday 4/4** This friday's class will also be cancelled. We will have another problem session discussion/review in a few weeks for the next honors problem (to be posted soon) to make up for this.

**Hint for Challenge part (i)** Express the sequence as the exponential
of the sequence of partial sums of a certain series, then show that the
series converges.

**Problem set 10.** Due **WEDNESDAY** 4/9 (notice the change!);
§ 8.6 -- 33, 34. § 8.7 -- 1-6, 11, 12, 22, 23, 29, 30.

**Honors Problem 3** Due 4/23. Here it is.

**Problem set 11.** Due 4/14; § 8.8 -- 2, 3, 4, 14, 15, 33, 34. § 9.1 -- 25-30, 32, 36.

**Review for Midterm 3** Not due; Chapter 8 Review, pages 711-712 -- 53-76; § 9.1 -- 1-10, 31--40. § 9.2 1--6, 9--14, 21--28.

**Discussion for Honor's Problem 3** Tuesday evening, 4/22,
8:00PM in 143 Altgeld.

**Problem set 12.** Due 5/1 by 9:00am in my mailbox.**NOTE THE CHANGE!** here Regarding problem 5 from the sheet, here's a hint: You will need to compute the integral as two integrals, one from -1 to 0 and one from 0 to 1, since the distance to the y-axis is |t^3|.

**Office hours this week:(4/21--4/25)** Wednesday and Thursday's are cancelled. You can see me before class on Wednesday 10:00--11:00 and on Friday from 1:00--2:00.

**Friday (4/25)**: Sorry about class today. My train from Chicago was delayed and hour. Note that I have changed the due date for the homework. I will grade it during the day on Thursday and you can pick it up in the afternoon outside my office.

**Office hours for the week (4/28--5/2)**Monday 3:15--4:15, Wednesday 4:00--5:00 and Friday 4:00--5:00.

**Review Session** Thursday 3:30--5:00 in 141 Altgeld (Note: No other office hours this day).
**Honors problem 4** There will be no fourth honors problem.

**Final Exam** I will post more information here as it becomes available:

--The final exam will be 8:00AM--11:00AM, Saturday May 3rd.

--The exam will cover 6.1--6.4, 6.6, 7.1, 8.1--8.8, 9.1--9.5.

--I will give you a sheet with various formulae.

--here is a review sheet together with the formula sheet you will be given with the exam.

In writing mathematics, the purpose should be to convey the facts/ideas/concepts at hand to the reader. This is
to be done so that the reader can, without verbal assistance from the writer, and without reading between the
lines, understand these facts/ideas/concepts. What I'm trying to say is: Make sure that what you write is
logically correct! My biggest pet peeve is the over usage of the equals sign "=". This symbol should only be
used when two quantities are equal. If they are equal, use "=", if not, don't use it. Don't be afraid to write
a sentence or two, or even a word, that intermediates between a set of equations:

Example:

f(x) = 3x + 2

so

f'(x) = 3.

Do __not__ write

f(x) = 3x +2 = f'(x)=3

or you will drive me crazy!!

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