## Math 221, Fall 2009: updates page

Here you can find updated information about the class.

Go to www.math.uiuc.edu/~clein/m221info_f09.html for general information about the class. To the bottom for exam information.

Week 1, 8/24, 8/26:

Assignments:

WebAssign homework: M221 F09 HW 1, due 7:30AM, Friday 8/28.

WebAssign homework: M221 F09 HW 2, due 7:30AM, Monday 8/31.

Class:

8/24: We went over the course information page. You should skim chapter 1 and make sure you are familiar with all of the following terms/concepts: functions, domain, range, graph of a function, increasing/decreasing functions, linear functions, polynomials, rational functions, trigonometric functions, one-to-one functions and inverses, exponential and logarithmic functions, laws for exponents and logarithms, combinations of functions (addition, subtraction, multiplication, divisition and composition). Read Sections 2.1 to learn more about where calculus comes from.

8/26: We went over sections 2.2 and 2.4 and tried to see how the intuitive notion of limit from 2.2 is made precise by the formal definition in section 2.4. I did an explicit example (where I think i misscalculated (.001)^2, which should have been .000001, instead of .00001 as I had written) proving that a certain limit exists using the definition. Finally, I mentioned that in practice this is not how we calculate limit but instead use the techniques described in section 2.3. You will see more examples of this type in your discussion sections tomorrow.

Notes:

Read 2.2 - 2.4 before class on Wednesday (just to get an idea of what we're going to do).

• To enter "ε" in WebAssign, just type the word "epsilon".
• For some reason (perhaps because I made last minute changes to the first assignment), your total score for your first assignment may not appear as the sum of the scores on each of the parts. Send me an email if this happens and I'll get it taken care of (though I may not write back to tell you I did.. you can just check your score again the next day).
• Unfortunately, it appears that you will not have free access to the online version of the textbook. Very sorry if I got anyone's hopes up.

Just a reminder (if you haven't read this far on the course information page), I have created a discussion group on google. If you'd like to join, read the instructions on that page under "Communication with instructors and classmates".

Week 2, 8/31, 9/2:
Assignments:

WebAssign homework: M221 F09 HW 3, due 7:30AM, THURSDAY 9/3.

WebAssign homework: M221 F09 HW 4, due 7:30AM, TUESDAY 9/8.

Class:

8/31: Today we talked about sections 2.6 and 2.5 (in that order). We described a "new" kind of limit; limits at infinity. We gave some examples of when such limits exist and related this to horizontal asymptotes. Then we talked about continuous functions a little bit; definition and why we care. Then we gave some examples and ended with our "toolkit of continuous functions" (theorem 7 of section 2.5) as well as how we can build other continuous functions from these (using theorems 4 and 9).

9/2: We talked about sections 2.7 and 2.8, finishing chapter 2. We used the limit to make precise the tangent line to the graph of a function and the instantaneous velocity of a moving object. Both of these are examples of the derivative of a function at some number a in the domain which we defined. We saw the derivative as a function itself and described how it relates to the function. We did various examples. Someone asked why we were working so hard to compute that the derivative of

f(x) = x3 - x
is
f'(x) = 3x2 - 1

The answer is that we are using the definition. You will be required to compute the derivative of some function using the definition both on an exam as well as on a quiz....

Notes:

If you haven't already read section 2.5 and 2.6, you should do that. Also read 2.7 and 2.8 for Wednesday's class... we're almost ready to define the derivative!!

If you'd like some help working (not necessarily homework) problems you can try Stewart's Tools for Enriching Caluclus which helps you work through problems in the book (the ones in red).

Week 3, 9/7, 9/9:

Assignments:

WebAssign homework: M221 F09 HW 5, due 7:30AM, SUNDAY 9/13 (note the extension due to technical difficulties with WebAssign)

Class:

9/7: Labor Day -- No class!!!

9/9: Professor Dunfield will cover class this day as I will be out of town.

Notes:

You will have your discussion section on Tuesday and Thursday. I now anticipate a quiz on Thursday, rather than Tuesady... sorrry for the misinformation.

Week 4, 9/14, 9/16:

Assignments:

WebAssign homework: M221 F09 HW 6, due 7:30AM, Friday 9/18.... Note that there are only 6 problems on this assignment. In addition to these problems, you should also work the following problems: § 3.3: 5, 11, 23, 33, 35, 37. § 3.4: 9, 17, 23, 37, 59, 77. These additional problems do not need to be turned in. You should check your answers in the back of the book.

Class:

9/14: Today we covered sections 3.3 and 3.4. This extends what we've done so far by providing us with some new functions that we can differentiate (trig functions; section 3.3) and a way of computing derivatives of functions built from others (specifically, compositions of functions---the derivative is given by the chain rule). We explained why the derivatives of the trig functions depend only on the derivatives of sin and cos, and explained the key limit need to compute these derivatives, namely

limx → 0   sin(x)/x = 1.
We ended with a discussion of the chain rule. We will talk about this some more on Wednesday.

Notes:

The point of making HW 6 short is to avoid having to spend too much time online with WebAssign until they are able to increase their capabilities.

Here is an updated review sheet for the midterm. It lists the various topics you will be responsible for on the first midterm and also gives a gigantic list of practice problems. I have decided to remove 3.5 from the midterm, which will cover all of chapter 2 and sections 3.1--3.4 and 3.6.

Wednesday 9/16: my office hours today will be moved. Instead of 10:00--11:00, I will be available from 11:00--1:00. I will also be available 10:00--11:00 on Friday this week because of Monday's exam.

Week 5, 9/21, 9/23:

Assignments:

Because of the exam this week, there is only one assignment, HW 7, due Sunday morning at 7:30AM. The intended due date is Friday morning, so you have an additional 2 days already built in, just in case WebAssign is malfunctioning at some point. Try to avoid their peak times, 8--11. In addition to the 6 problems on WebAssign, you should also work the following exercises from the book (again, these are not to be turned in, but you should check your answers in the back of the book and consult the TEC when available): Section 3.7: 9, 17, 19, 21. Section 3.8: 5, 9, 11, 17

Class:

9/21: Today you took the first midterm. You can find the solutions to the exam here. There were 4 different exams: (a), (b), (c), (d).

9/23: Today we discussed sections 3.7 and 3.8 on "real world" applications of calculus and one exponential growth and decay. Make sure you read those sections for more examples and further discussion. I also talked about the exam, see below. You will get your exams back tomorrow (9/24). Make sure you look over them carefully and check for any grading errors. You will have one week to have any grading errors fixed. Please see you TA's if you think you have found an error.

Notes:

I created an online feedback form here . To help the class run more smoothly, please take a minute to fill out the form and let me know what you do and don't like about the class. It is anonymous and voluntary and will not affect your grade. Thanks.

The scores on this exam were very high. The distribution was roughly as follows:

90--100: %50 of the class

80--89: %27

70--79: %13

< 70: %10

If you scored below 80/100, you should consider switching from this course into 115 as the exams will increase in difficulty as the semester progresses: I intend for the exams to fairly evaluate whether or not you have learned the material, but be aware that subject will become increasingly difficult, and in particular we will go well beyond what you learned in high school. Please consider the 115 option very seriously to avoid making hard decisions later. If you would like to switch, you need to do so soon. Here are the details sent from advising:

DEADLINE: 4:00 PM, Wednesday, September 30. Absolutely no students will be accepted in Math 115 after that point.

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.

Week 6, 9/28, 9/30:

Assignments:

WebAssign homework: M221 F09 HW 8, due 1:00PM, Thursday 10/1. In addition to these problems, also work the following exercises which will not be handed in. Section 3.5: 9, 13, 29, 41. Section 3.9: 15, 19, 25, 27.

WebAssign homework: M221 F09 HW 9, due 1:00PM Sunday 10/4. In addition, work the following exercises. You can check your answers in the back of the book. Section 3.10: 13, 17, 23. Chapter review, page 262: Practice differentiation: 1--49 odd problems.

Class:

9/28: Today we talked about sections 3.5 and 3.9. The first section is on implicit differentiation which gives us a way of finding the slope of the tangent line to a curve in the plane which is not necessarily the graph of a function (rather it need only look like a graph near the point in question). Then we talked about related rates problems, motived by a couple examples. The examples we discussed give you the basic idea of what this is about, and after reading the section you should be able to attack any of the problems in the book---remember, drawing a pictures can be very helpful!

9/30: Today we talked about linear approximations and differentials from sevction 3.10. Unfortunately, I ran out of time at the end and started to muck up the discussion of differentials. Take a look at pages 250 and 251 for the correct pictures associated to differentials (they're not that bad, I just got flustered!!).

Notes:

I will be gone this Wednesday 9/30 so my office hours will be moved to 12:00--1:00 Tuesday 9/29.

Week 7, 10/5, 10/7:

Assignments:

WebAssign homework: M221 F09 HW 10, due 2:00PM, Thursday 10/8. In addition to these problems, also work the following exercises which will not be handed in. Section 4.1: 3, 5, 31, 41, 49, 53; Section 4.7: 5, 11, 17, 27, 33.

WebAssign homework: M221 F09 HW 11, due 2:00PM, Sunday 10/11. In addition to these problems, also work the following exercises which will not be handed in. Section 4.3: 5, 11, 13, 19, 33, 37, 47, 53.

Class:

10/5: Today we talked about Sections 4.1 and 4.7. These sections explain how to use calculus to solve optimization problems---maximizing or minimizing a function. We discussed why/how this works, and did some examples. You should also look at page 324 "the first derivative test for absolute extreme values" which will come up naturally in the lecture on Wednesday.

10/7: Today we covered Section 4.3 and touched on Section 4.2. Section 4.3 describes what the derivates of a function tell you about the function. In particular, we learned about using the deriviative to find out where the function is increasing/decreasing and what this says about determining local max/min's. We also saw that the second derivative provides information about the shape of the graph---the sign determines the concavity. The purpose of Section 4.2 is to introduce and prove the mean value theorem. This is a very useful tool in calculus, and we hinted at why it's true (the proof is easy and is in the book), then we saw how to use it to prove that preceeding statements about the derivitive's influence on a function. We'll see the mean value theorem coming up again and again.

Notes:

The second exam is coming up soon---Thursday, October 21!!

Week 8, 10/12, 10/14:

Assignments:

WebAssign homework: M221 F09 HW 12, due 5:00PM, Thursday 10/15. Problems 5 and 6 are to be turned in to your TA during your discussion section on Thursday. After they have been graded, your scores for this problem will be updated. In addition to these problems, you should also work on the following problems which you can check in the back of the book (and these do not need to be turned in). Section 4.4: 1, 5, 9, 15, 21, 27, 29. Section 4.5: 5, 19, 31, 41, 49.

WebAssign homework: M221 F09 HW 13, due 4:00PM, Sunday 10/18. For problem 6 on this assignment, you should round to two decimal places. In addition to these problems, you should also work the following problems. You can check your answers in the back of the book (and these do not need to be turned in). Section 4.4: 39, 43, 51, 57, 61. Section 4.8: 7, 13, 39.

Class:

10/12: Today we covered section 4.5: The purpose of this section is to explain how we can use the techniques learned so far to sketch the graph of a function. We did two examples. Then we started section 4.4, which is on L'Hosptial's rule. This is technique for computing limits of ratios of functions when we cannot apply the usual limit laws. We will continue with this on Wednesday when we explain other situations when we can apply L'Hospital's rule.

Notes:

The second Midterm coming next Wednesday, 10/21!!

Here is the review sheet for the second midterm. There are TONS of practice problem and a week to practice. You should plan to do some problems every day between now and the midterm---don't let it sneak up on you!

Be aware that this exam will contain both related rates problems and optimization problems. These can require some thought to set them up so make sure you've practice plenty of these types of problems, and also make sure you can "breeze through" the other more mechanical problems. I'm not trying to "scare" the class---I want you to do well, so please make sure you prepare!

Week 9, 10/19, 10/21:

Assignments:

Do problems 1--15 odd from Section 4.9. These will not be turned in, but you should check your answers.

Class:

10/21: Exam 2!

Notes:

Week 10, 10/26, 10/28:

Assignments:

WebAssign homework: M221 F09 HW 14, due 5:00PM, Thursday 10/29. In addition to these problems, you should also work problems 13, 17, 19, 21, and 26 from Section 5.1.

WebAssign homework: M221 F09 HW 15, due 5:00PM, Sunday 11/1.

Class:

10/26: Today we covered Section 5.1. The point of this section is to develop some intuition for area, and to explain how we can define the area of regions where are not polygons. This leads to the notion of the definite integral, which we will define on Wednesday.

10/28: We covered Section 5.2 in which we defined the definite integral. We used the definition to compute the integral, partly to show that it can be done, but also to show that it's not fun. Next week we will learn the Fundamental Theorem of Calculus, which allows us to compute indefinite integrals.

Notes:

Here are the solutions to the second midterm, exams a, b, c, and d.

The grades on this exam were pretty good over all---the average was 79%. The percentage of scores in each of the ranges were as follows.

90--100: 21%

80--89: 30%

70--79: 26%

less than 70: 23%

So, over half the class score a B- or better.

Week 11, 11/2, 11/4:

Assignments:

WebAssign Homework: M221 F09 HW 16 due Thursday, 11/5 at 5:00PM.

WebAssign Homework: M221 F09 HW 17 due Sunday, 11/8 at 5:00PM.

Class:

11/2: Today we covered Section 5.3. We explained both parts of the fundamental theorem of calculus, and applied to to evaluate several indefinite integrals.

11/4: We covered Sections 5.4 and 5.5. The main point of 5.4 is to introduce new notation (the indefinite integral, which is just the antiderivative). Section 5.5 describes a new method for computing antiderivatives and integrals; substitution. This is a method which attempts to reverse an application of the chain rule. We did several examples.

Notes:

Week 12, 11/9, 11/11:

Assignments:

WebAssign Homework: M221 F09 HW 18 due Friday, 11/13 at 2:00PM.

WebASsign Homework: M221 F09 HW 19 due Sunday, 11/15 at 5:00PM.

Class:

11/9: Today we talked about areas bounded by curves, especially the area between two graphs. We talked about a few different examples. You should see more examples in your discussion sections tomorrow. I also tried to give some explanation of the delicacy of computing integrals of absolute values of functions... I failed and because of my mistakes, I likely confused a lot of you. I've typed some notes (found here) which hopefully clears this up. Sorry!!

Notes:

Week 13, 11/16, 11/18:

Assignments:

WebAssign Homework: M221 F09 HW 20 due Thursday, 11/19 at 5:00PM.

WebASsign Homework: M221 F09 HW 21 due Sunday, 11/22 at 5:00PM.

Class:

11/16: We covered Section 6.3 on volumes via cylindrical shells.

11/18: We covered Section 6.4 on work.

Notes:

Here is the review sheet for the third midterm with practice problems.

Week 14, 11/23, 11/25:

Assignments:

Class:

No class this week. Happy Thanksgiving!!!

Notes:

Week 15, 11/30, 12/2:

Assignments:

None this week.

Class:

11/30: We reviewed for the exam, especially chapter 6. 12/2: Midterm 3

Notes: