Reading Assignments for Calculus 1
Fall 2001, Math 101

September 2001

Be sure to check back often, because assignments may change!

I'll use Maple syntax for mathematical notation on this page.
All section and page numbers refer to sections from Ostebee/Zorn, Vol 1.

Due Friday 9/7, at 8am

• To read: all of the above documents, plus that from the textbook mentioned below.
• Pay attention to: all of it: I tried to address as many issues as I could think of. Any questions? Ask me (in person or by e-mail)!
• Reminder: Keep the hard copies of these documents in your folder. Make a note of exam dates, project due dates, and the due date of the final in your calendar.

Section 1.1: Functions, Calculus Style
Section 1.2: Graphs
Appendix A: Real Numbers and the Coordinate Plane

• To read: Section 1.1 through Example 6; Section 1.2 through Example 5. Read or skim through Appendix A with whatever depth you need to.
• Be sure to understand: Examples 5 and 6 from Section 1.1; Examples 3 and 4 from Section 1.2; All of Appendix A, of course.

E-mail Subject Line: Math 101 Your Name 9/7

1. Using the function m(x) defined in Example 4 on page 4, what is m(-4) exactly? Did you figure this out using the graph or the piecewise definition? Explain why you chose the method you did.
2. Consider the hot-air balloon whose altitude graph is shown in Example 5 on page 5. Is the balloon rising or falling at t = 3 minutes? Is the upward velocity positive or negative at t = 3 minutes?
3. In Example 2 on page 14, exactly how far above the x - axis is the curve when x=3?
4. In Example 3 on pages 14 and 15, the authors say that f (1) is approximately - 6, but that we'd need more information to know whether f (1) = - 6 exactly. What kind of information would tell us whether f (1) = -6?

Reminders:

• Always explain briefly how you arrive at each of your results. This time I asked "why or why not"; "explain", etc. I won't always, but it's implied.
• Start working on PS 1, listed at the bottom of this course's web page. . Plan on having it done by class on Monday morning. Bring questions to my office hours. (The time from Monday until it's due at the beginning of lab on Tuesday is intended for clearing up final difficulties and recopying the homework. Do not plan on beginning your homework Monday afternoon!)

Unfortunately, I can not respond individually to the reading assignments every day. I will, of course, respond to direct questions. There does not appear to be an easy way for me to automatically send you a "message received" note. Usually e-mail goes through fine, but sometimes messages do disappear without bouncing back to you. To be on the safe side, send yourself a copy every time you send me a response. Every now and then, ask me if there are any missing assignments, and if there are, forward your (dated) copy.

Due Monday 9/10 at 8am

Section 1.2 : Graphs
Section 1.3: Machine Graphics
Section 1.4: What Is A Function?

• To read: Finish Section 1.2, and read all of Sections 1.3 and 1.4 .
• Be sure to understand: Section 1.2: New Functions from Old
Section 1.3: Six views of the sine function, Examples 1 and 2
Section 1.4: Both definitions of a function, the five examples, and the definitions of domain and range, Periodic Functions, the symbolic view .

E-mail Subject Line: Math 101 Your Name 9/10

1. Suppose f (x) is any function. How does the graph of f (x)+2 compare with the graph of f (x)? The graph of 2 f(x) compare to f (x)?
2. Calculate h (1/2), where h is the third of the five examples in Section 1.4.
3. Let g (t)= the world's human population t years C.E, as in the second of the five examples in Section 1.4. What are the domain and range of g (t)?
4. Find the domain and range of m (x)=x 2.
5. How can you recognize a periodic function from its graph?

Reminders:

• Remember: HavePS 1 done (or as much done as possible) by Monday; I will spend 15 minutes Monday giving last-minute homework hints.
• Remember to come to lab Tuesday at 1:00pm.
• PS 1 (individual) is due at the beginning of lab.

Due Wednesday 9/12 at 8am

Section 1.5: A Field Guide To Elementary Functions
Appendix B: Lines and Linear Functions
Appendix C: Polynomial Algebra
Appendix E: Algebra of Exponentials
Appendix F: Algebra of Logarithms

• To read: Read through Exponential and Logarithmic Functions as Inverses in Section 1.5. Read or skim Appendices B , C, E, and F with whatever depth you need to -- I assume most of you will need to read Appendix F in a fair amount of detail.
• Be sure to understand: The appendices. In Section 1.5, all of Algebraic Functions , Example 2, and the discussion of asymptotes in Example 3, the definitions of exponential and logarithmic functions, the relationship between all graphs of exponential functions, the relationship between all graphs of logarithmic functions, the common points of each, and the relationship between the graph of a function bx and logbx.
• Please note: I know that this is a lot of material. Once we get through Section 1.5, we're going to spend an extra day practicing with the ideas. Furthermore, we'll be using these concepts later, and so you'll have more opportunities to really assimilate them as we go through the semester.

E-mail Subject Line: Math 101 Your Name 9/12

1. In Example 3 on page 54, what are the domain and range of the rational function r (x) ? What is the relationship between the domain, the range, and the asymptotes?
2. Is ey an exponential function? How about (Pi)x? ze?Why or why not?
3. If you were shown the graph of a monotonically increasing function, what would you look for to decide whether it could be an exponential function, or to eliminate that possibility?
4. What logarithm function corresponds to the exponential function 3x? How are the log function you found and 3x related?

Reminders:

• Start working on PS 2 Tuesday or Wednesday, and work on it throughout the week. This is a group assignment, so find a congenial person to work with (I prefer only 2 people in a group, although I know that occasionally a 3-person group is unavoidable.)

Due Friday 9/14 at 8am

Section 1.5: A Field Guide To Elementary Functions
Appendix G: Trigonometric Functions

• To read: Finish Section 1.5, and read or skim Appendix G.
• Be sure to understand: The sine and cosine functions defined as circular functions; every point on the unit circle corresponds to a value of both the sine and the cosine functions.

E-mail Subject Line: Math 101 Your Name 9/14

1. Can sin(x)=2 for some value of x? Why or why not? What are the domain and range of sin(x)?
2. Explain, in more detail than the book does, why sine and cosine are each 2 Pi periodic.
3. Evaluate sin2(38)+cos2(38) without a calculator. Explain (of course).

Reminder:

• As always come see me if you have any questions on PS 2, or any vague sense that you're not getting as much as you want to. Don't wait -- if you end up being lost, it's hard to recover.

Due Monday 9/17 at 8am

The Big Picture

• To read: Re-read all of Chapter 1 through Section 5, and those of Appendices A, B, C, E, F, and G that have covered material you're having difficulty with.
• Be sure to understand: More of it than you did the first time around!

No Reading Assignment due today

Reminder:

• If you have questions on PS 2 (or old problems, concepts), go to Meghan's help session Monday nights! E-mail her at mtracews before 5pm Monday to let her know you plan on being there.
• PS 2 is due Tuesday at the beginning of lab. As always, you and your group should have it as completely done as possible by Monday morning. Bring your last niggling questions to class Monday morning.
• Your group will turn in one joint version. Photocopy it before turning it in (and again when you get it back from the grader), so that you each have a copy for studying purposes (and so you have a record of your scores). Remember to pick up a cover sheet outside my office to fill out and turn in with your group problem set.

Due Wednesday 9/19 at 8am

Section 1.6 : New Functions From Old

• To read: Through Example 4
• Be sure to understand: The definition of the composition of two functions, the examples that shows that order matters.

E-mail Subject Line: Math 101 Your Name 9/19

1. Using f and g in Example 2, what is (g o f)(2)?
2. Let f(x)=x3 and g(x)=sin(x).
• What is (f o g)(x)?
• What is (g o f )(x)?

Reminder:

• Start working on PS 3 Tuesday or Wednesday, and work on it throughout the week.
• Exam 1 will be given in lab Tuesday 9/25. Start studying! Spread it out over many days, and be sure to not only do the study guide I will give you but also to re-read the text and your notes, and to re-do as many homework problems as you possibly can.

Due Friday 9/21 at 8am

Section 2.1: Amount Functions and Rate Functions: The Idea of A Derivative

• To read: Through page 103
• Be sure to understand: pages 94-96 on Rates, Amounts, and Cars; page 98-99 on The Slope of a Graph at a Point: Tangent Lines

E-mail Subject Line: Math 101 Your Name 9/21

Look at the graphs of P(t) and V(t) on page 95
1. Is the derivative of P positive or negative at t=5? Explain.
2. Is the second derivative of P positive or negative at t=5? Explain.
3. Give a value of t where the derivative of P is zero.
4. Give a value of t where the second derivative of P is zero.

Reminders:

• Plan on finishing PS 3 early, since it's covered on the exam!
• Once again, let me remind you to come to office hours. If you can't make my office hours, contact me about making an appointment.

Due Monday 9/24 at 8am

Questions and Answers for Exam 1

• To read: Re-read the text and your notes from the beginning of the semester up through Section 1.6
• Be sure to understand: All of it!

No reading assignment today!

Reminder:

• Have PS 3 done by Monday morning. It is covered on the exam, and it is due before you begin the exam.
• Review over the week-end, of course. Have tried every one of the sample problems, and have begun re-doing old homework.
• Bring questions to class Monday, both on new and old material.
• If you have questions on PS 3 (or old problems, concepts), go to Meghan's help session Monday nights! First, though, you have to e-mail her at mtracews before 5pm Monday to let her know you plan on being there.
• Before the exam Tuesday, write a "cheat sheet" if you want to. It must be only on one side of standard 8 1/2" x 11" paper, and it must be handwritten by you. You may put write anything on it you want to, but you must do the writing.
• Monday evening at 5pm is the 2nd annual Johnson lecture. I know the timing is not good, but many of you will be taking a break at about that time anyway. I'll be giving extra credit to those I see at the talk, but please dont' go if it will impact how much studying you get done! The title of the talk is Why Napster Doesn't Matter: Intellectual Property in the Age of Piracy by Gregory Rawlins, author of 'Moths to the Flame'.

Due Wednesday 9/26 at 8am

Section 2.1: Amount Functions and Rate Functions: The Idea of A Derivative

• To read: Re-read through page 103 again, really work at making sense of it. You may also want to read Section 2.2 tonight, so you don't have as much to read before Friday's class.
• Be sure to understand: The reading, better than before

E-mail Subject Line: Math 101 Your Name 9/26

1. What are the two meanings (or interpretations) of the derivative?
2. Suppose f(x)=k, a constant. What is f'(x)? Explain.

Reminders:

• Start PS 4 (group) Tuesday or Wednesday, and (as always) work on it throughout the week.
• Redoing the exam is an additional optional assignment. The main benefit of this is the act of redoing it and making sure you really understand the concepts, or clearing up confusion you didn't realize you had. This will not be graded as thoroughly as the actual exam; I'll just make a note you did it and return it to you along with solutions.

Due Friday 9/28 at 8am

Section 2.2: Estimating Derivatives: A Closer Look
Section 2.3 : The Geometry of Derivatives

• To read: All of Section 2.2; All of Section 2.3.
• Be sure to understand: Examples 1, 4, and 5 in Section 2.2. In Section 2.3, the extended example beginning on page 118; the definitions of stationary point, local maximum and minimum, global maximum and mininum, concave up and concave down; the first derivative test.

E-mail Subject Line: Math 101 Your Name 9/28

1. What does the term "locally linear" mean?
2. Explain why the derivative of f(x)=|x| does not exist at x=0.
3. Look at the graph of f' in Example 2 in Section 2.3.
1. Where does f have stationary points?
2. Where is f increasing?
3. Where is f concave up?

Here ends the reading for September
Go to the reading assignments for October!

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu

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