Contact information:
Office: 327
Altgeld Hall
Office Tel: (217) 333-4284
Dept. FAX: (217) 333-9576
e-mail:reznick@math.uiuc.edu
I am in possession of your final exams, but you've been kicked out of the dorms, so you're probably on your way home. If you want to look at your exams, please watch this web-page for the announcement of a visitation towards the beginning of Spring 10. You cannot get your finals back: I am obligated to keep them for 12 months.
I am obligated to follow the University and Departmental rules, which require that I grade according to the plan announced at the beginning of the semester.
In a class of this size, there will probably be quite a few people who miss a cut-off by a very small amount. If you think about it, this would happen no matter where the cut-offs are set. If this happens to you, I know you will be unhappy. (When I was a student, and it happened to me, I was unhappy.) But it is unavoidable, and since consecutive marks are only 1/3 of a grade apart, it won't make a significant difference in the long run.
There have been some complaints about problem 9c, because it does not closely resemble a quiz problem or a problem on a previous exam. This is true. And it does resemble, closely, the process by which we used Riemann sums to calculate volumes of rotation, work, arc-length, etc. (See also item 2 in the 11/30 entry on preparation for test 3.) I am supposed to help you learn calculus, not master a list of 40 or 50 types of stylized calculus problems. When you run into calculus in your chosen discipline (and you probably will), it will be unpredictable in appearance and probably not one of those types. If a math professor gives one hard 5 point problem on a 200 point exam, it is not newsworthy enough for the Daily Illini.
Please read the Class organization for information on how the course is graded. At this point, I think it is unlikely that the B+/A- line will be curved below 90%.
Please also read the following part of the Student Code for the official rules about what to do in case you have three finals in a 24 hr period. The official algorithm is rather precise. In any case, you have to get it done before the last day of classes, which is Wednesday, December 9.
Wednesday's class will contain a relatively short overview of the course and review for the final, and there will be time at the end for you to evaluate my performance as instructor. Bring a sharp pencil!
1. Antiderivatives and indefinite integrals
2. Riemann sums and their interpretations
3. Area and definite integrals
4. The Fundamental Theorem of Calculus and average values
5. Integration using substitution
6. Volumes of rotation, using shells and using washers
7. Distance, work and arclength
You may be called on to use information from the topics of the last two exams, in the context of solving a problem from one of these categories. One exception: no epsilon/delta proofs.
Please bring a photo ID such as an I-card with you to the exam.
The office hours this week will be on Tuesday evening Dec. 1 from 7-9pm in 165 Everitt. This building is at the northeast corner of Green and Wright, and is across from Altgeld. No office hours on Wed. Dec. 2.
There will be the final quiz of the semester tomorrow (on 6.2,6.3,6.4), and I will also post a link to a "virtual quiz" on 6.5 and 8.1, along with the solutions. These are for your information and to help you prepare for Test 3 in two weeks. The homework for 12/1 was listed last week.
Enjoy your holiday and get some sleep.
I did a few volumes. One was the volume of a torus (bagel or doughnut) consisting of a circle of radius r, whose center is at distance R (> r) from an axis about which it is rotated. The volume is 2 Pi^2 R r^2. Another was a sphere of radius R from which a cylinder of radius Sqrt[R^2 - h^2] is removed, leaving a "cored apple" of height 2h. Whether you use shells or washers, the resulting volume of 4 Pi h^3/3 is independent of R. I then spoke about work, mostly covering the examples in the book, and the average value of a function, and moved on to arclength.
On Wednesday in class, I invite questions and will try to finish 8.1. After break, Monday 11/30 will be review for the test on Wednesday 12/2. The final two classes the last week will be an overall review and discussion of some optional topics which won't be on the Final.
The lecture summarized the material from the rest of the course, which is applications of integration in which Riemann sums estimate a quantity (volume, work, arc length), so that the quantity can be expressed as an integral. Examples were given in each instance with emphasis on shells and slabs. The critical distinction is whether is being sliced parallel to the axis of rotation or perpendicular to it. I also mentioned the midpoint rule for Riemann sums: pick xk* to be the midpoint of the interval, so xk* = (xk-1 + xk)/2.
In lecture, I derived the formula for the derivative (with respect to x) of the integral from p(x) to q(x) of f(t) with respect to t. I talked about areas between curves, especially those regions bounded by y=0, y=1, y= sin x, y= cos x and x=0 and x = pi/2. I then talked about volumes by rotation with an emphasis on the cone and the sphere. We will do integrations by shells and washers on Wednesday, as well as work, in the sense that physicists use the word.
The lecture finished off chapter five, with plenty of examples of integration by substitution. You need to do a lot of these to become comfortable with the method. Next topic: applications of integration!
In lecture, I got through 5.3 and 5.4, and hinted at 5.5, integration by substitution. The most exciting antiderivative covered was for f(x) = |x|: F(x) = x^2/2 if x > 0, 0 if x = 0, and -x^2/2 if x < 0. Here, F is differentiable for all x, F'(x) = |x|, and F'' is defined for all x, except x=0. The other topic of interest was the many different ways one can write the antiderivative for 2 sin(x) cos(x).
I did 4.7 #44 and talked about the importance of the domain of variables. I briefly discussed Newton's Method and Antiderivatives, which will not be on Test 2. For Wednesday, read 4.9 and 5.1 and bring questions to class.
Scores were overall, a little lower, but by less than I had expected. You did well. Don't relax now, many people's first semester grades are ruined by a lack of attention in the weeks just before Thanksgiving.
For Monday, read sections 5.1, 5.2, 5.3, 5.4.
Homework for Tuesday 11/3: 4.9 -- 7, 29, 59, 67;
5.1 -- 11, 13;
5.2 -- 1, 7, 39, 53;
5.3 -- 11, 15, 19, 23, 31, 35;
(5.3 -- 1 was erroneously given in lecture) or from the
book.
There is no quiz tomorrow, but there will be one on 11/5.
The lecture introduced Riemann sums and gave a few examples; you will not have to memorize 1 + ... + n = n(n+1)/2, etc, for the quizzes or exams. If such a formula is needed, it will be given.
Office hours before the exam are:
Zheng Li -- Th 3-5, F 3-4 in B1 Coble Hall
Ben Reiniger -- W 1:30-2:30, F1:30-2:30, B1 Coble Hall
Qianyi Zhao -- W 3:30 -4:30, South Lounge of Illini Union
Bruce Reznick -- W 4:30-6:00 241 Altgeld, Sunday night 7-9, 314 Altgeld.
There will be a quiz on Thursday, as usual, on the material covered in this week's homework. There will be no quiz next week, and there will be homework due next Thursday.
In class, I used antidifferentiation to discuss motion under the influence of gravity: in units of ft/sec, a body on which gravity is the only force will have its height given by y(t) = y(0) + y'(0)t - 16t^2. All questions about the body can be answered by looking at the graph of this function. I also started on section 5.1. The reading for next Wednesday's class is sections 5.1, 5.2 and 5.3. The homework for recitations on Thursday October 29 will be put on this webpage in the next couple of days.
I will have the usual open office hour on Wed. Oct. 21 from 4:30 to 6 and a special review session Sun. Oct. 25 from 7 to 9 in 314 Altgeld Hall. There will be no office hour on Wed. Oct. 28.
There will be a quiz, as usual, in section on Thursday, covering 4.4, 4.5 and 4.7, but mainly 4.4 and 4.7.
I did 4.7 #44 and talked about the importance of the domain of variables. I briefly discussed Newton's Method and Antiderivatives, which will not be on Test 2. For Wednesday, read 4.9 and 5.1 and bring questions to class.
For Monday, read sections 4.5, 4.7, 4.8 and 4.9.
Homework for Tuesday 10/20: 4.4 -- 7, 11, 19, 35;
4.5 -- 11, 27;
4.7 -- 3, 7, 11, 31, 35, 57
or from the
book..
The quiz will have one question on exponential growth, and will
otherwise cover sections 4.1, 4.2 and 4.3
I briefly discussed section 2.6 in the context of curve-sketching (4.3,4.5) and began to talk about L'Hopital's Rule. The main graph discussed in detail was f(x) = (x^2-1)(x^2-4).
For Monday, read sections 4.2, 4.3, 4.4.
Homework for Tuesday 10/13: 4.1 -- 3,7,47,51;
4.2 -- 1,11,23,25;
4.3 -- 9,11,25,33 and,
as a bonus, only for the adventurous, 4.3 -- 67, or from the
book..
Office hours are back to Wed. 4:30-6:00 in 241 Altgeld Hall. If the room is empty after 5:30 I might take off, so get there early.
The quiz on Thursday covers 3.8, 3.9 and 3.10.
Finished Ch.3 with a brief discussion of logarithmic differentiation and differentials, and covered section 4.1 along with the Intermediate Value Theorem. For Wednesday, read 4.2 and 4.3. Test 2 is three weeks from today
For Monday, read sections 3.10, 4.1 and 4.2.
Homework for Tuesday 9/26: 3.8 -- 5, 7, 13
3.9 -- 3, 15, 23, 31, 33
3.10 -- 15, 25, 39 or
from the
book..
Office hours are back to Wed. 4:30-6:00 in 241 Altgeld Hall. If the room is empty after 5:30 I might take off, so get there early.
In class, I covered 3.9 (Related rates = implicit differentiation with more than one variable) and 3.10 (linearity, differentials, approximating functions near "easy" values if you know the derivative.
The quiz is about 3.4, 3.5, 3.6, 3.7; not 3.8 (which will be on the next quiz.) the inverse trig derivatives to know are the derivatives for the inverse sine and the inverse tangent.
I feel obliged to say explicitly that no student in this class has my permission to upload any course material onto a third-party site. This includes any handwritten or typeset comments by me or by the textbook authors. Everything is copyright by the authors and we reserve the rights, whether we explicitly have said so or not. If you have given access to these materials to a site such as CourseHero, please remove them before the University lawyers find out.
In class, I covered 3.7 and 3.8, with an example from 3.5: the tangent line to the curve x^3 + xy + y^4 = 3 at P(1,1) via implicit differentiation, and having gotten the general formula for dy/dx, started to find the second derivative. I "covered" 3.7 by mentioning some of the examples. In 3.8, I derived the solution of the differential equation y' = ky by first arguing that f' = 0 implies that f is a constant and then by considering f(t) = e^{-kt}y, where y' = ky. (This confused a few people and I'll wrote this up in the next couple of days.) I also emphasized that in these problems, if you know the form of the solution, the issue is using the data as given to let you solve for the parameters.
I'm sending this in email as well:
Overall, the scores on the exam were quite good and there will be
no "curving". I'll have more to say in class on Monday. The C/D line
is about 70. If you got below 70 and feel the score accurately
reflects your calculus ability at this point, you might want to
consider switching to Math 115, Preparation for Calculus. The absolute
deadline is 4:00 PM, Wednesday September 30.
I enclose the following class-switching algorithm from the Mathematics
Advising Office:
WHAT TO DO: Go to 313 Altgeld Hall between 9-12 or 1-5pm weekdays, get form to
switch to Math 115, have it signed by Math 115 instructor, return form to 313
Altgeld Hall by 4pm, Sept. 30 at the latest.
Students who wish to make the switch MUST take Math 115 Exam 1 over trigonometry
on Monday, September 28 at 7pm or the makeup exam on Wednesday, October 7 at
6:45am (yes, 6:45 in the morning).
Note that students MAY NOT switch from Math 221 to Math 220.
The office hours this week will be on
Tuesday evening Sept. 22 from 7-9pm in 165 Everitt. This building is at
the northeast corner of Green and Wright, and is across from Altgeld.
No office hours on Wed. Sept. 23.
The first exam is on Wednesday 9/23 and will cover sections 2.1, 2.2,
2.3, 2.4, 2.5, 2.7, 2.8, 3.1, 3.2, 3.3, 3.4 and 3.6. (Not 2.6 and 3.5,
which will be on subsequent exams). The epsilon/delta definition of
the limit will be at most 10-15% of the exam.
How do you study for the test? First, at least scan through the
sections that will be covered. Then look at the notes you might have
from the lecture. Then look at the homework problems. Then look at the
quizzes. Every exam problem is one which would have "fit in" somewhere
either as a homework problem or a quiz problem or both. I know you
have no way to believe this before you've seen the first
test. You'll have to trust me.
Quick preview of exam instructions: closed book, closed notes, no
headphones, all cellphones off, no caps or sunglasses. I'll spend the
first 5-10 minutes on Monday reviewing, and there will be a lot of
reviewing in the Tuesday recitations. Some problems will be calculations, some may be word problems or
involve the visual interpretation of some graphs. The only proof would
be the epsilon-delta problem.
Also, you should know that the Intermediate Value Theorem and the cosecant and cotangent will not be tested on. I consider the major topics to be: Tangents and secants, average velocity and instantaneous velocity, intuitive limits and limit laws, the precise definition of a limit, continuity, definition of derivative at a point, derivative as a function, equation of a tangent line, derivatives of polynomials, exponentials, trigonometric functions and logarithms, the linearity of derivatives, the product and quotient rules and the chain rule.
How do you study for the test? First, at least scan through the
sections that will be covered. Then look at the notes you might have
from the lecture. Then look at the homework problems. Then look at the
quizzes. Every exam problem is one which would have "fit in" somewhere
either as a homework problem or a quiz problem or both. I know you
have no way to believe this before you've seen the first
test. You'll have to trust me.
Quick preview of exam instructions: closed book, closed notes, no
headphones, all cellphones off, no caps or sunglasses. I'll spend the
first 5-10 minutes on Monday reviewing, and there will be a lot of
reviewing in the Tuesday recitations.
Monday will feature a brief review; I'll answer questions and move on to 3.5 and 3.7 if there is time.
In the lecture, I covered sections 3.2 and 3.3. You will not be asked
to reproduce the proof of the product or quotient or chain rules, or
of the formulas for the limits of (sin h)/h or (cos h - 1)/h as h ->
0. However, you will be expected to use these results as needed.
I mentioned the Cab Calloway (1907-1994) song "Minnie the Moocher" in class,
because of its refrain "hi-de-hi-de-hi-de-ho" and its imitation in
the mnemonic for the quotient rule. Here is a YouTube link to
1958 version
. If you look around YouTube, you can find performances in a Betty Boop
cartoon from 1932 and in "The Blues Brothers" film from 1980.
Added 9/13/09: homework from the
book..
Homework for next Monday's lecture: re-read sections 2.1, 2.2, 2.3 and read 2.4 and 2.5.
Homework for Thursday's recitation: bring questions.
Homework for next Tuesday's recitation:
2.1 -- 1, 5; 2.2 -- 1, 7, 15; 2.3 -- 11, 13, 17, 25, 35;
crudely cut and pasted here.
Don't forget the resource of the solution manual and the back of the book and you can do more problems if you like and the TAs will look at your work. The first quiz will be in the recitation section on Thursday September 3.
Class organization , Syllabus and The ideas of calculus
For Wednesday's lecture:
Read sections 2.1, 2.2
and 2.3.
For Tuesday's recitation,
Reflect on your previous calculus experience in high school and look at the
syllabus for the course and think about two or three things you did not
understand. Write these down on a sheet of paper. Do NOT put your name on the
sheet of paper and turn them in to your recitation section.