Fall 2000, Math 104

September 2000

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

All section and page numbers refer to sections from Ostebee/Zorn, Vol 2.

Due Friday 9/8, at 8am

• 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 in your folder. Make a note of exam dates, project due dates, and the due date of the final in your calendar.

Section 5.1: Areas and Integrals
Section 5.2: The Area Function
Section 5.3: The Fundamental Theorem of Calculus

• To read: All, but you may skim the proof of the Fundamental Theorem of Calculus beginning on page 373. The major ideas in these sections should be familiar to you.
• Be sure to understand: All the major ideas, of course, but especially the statements of the first and second forms of the Fundamental Theorem, and Example 3 in Section 5.3.

E-mail Subject Line: Math 104 Your Name 9/8

1. Does every continuous function have an antiderivative? Why or why not?
2. If f(x)=3x-5 and a=2, where is Af increasing? decreasing? Why?
3. Find the area between the x-axis and the graph of f(x)=x4+2 from x=1 to x=2. Explain, of course.

Reminders:

• 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.
• Come to lab at 1pm Tuesday.
• Find out this week's problem set assignment, listed at the bottom of this course's web page. .

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 9/11 at 8am

Section 5.4: Approximating Sums

• Be sure to understand: The figures on page 378 and the section Sigma Notation; Partitions beginning on page 380.

E-mail Subject Line: Math 104 Your Name 9/11

1. When approximating an integral, which would you expect to be more accurate: L10 or L100? Why?
2. Give an example of a partition of the interval [0,3].
3. What is a Riemann sum? Explain in your own words, not those of Ostebee and Zorn, of course.

Reminder:

• Don't forget to come to lab at 1:00 on Tuesday.
• PS 1 is due Wednesday.

This is an individual problem set. You're welcome to consult with your colleagues, but you must work on every part of this problem set and use your own words in describing the solutions.

• While problem sets are not due until Wednesday, each week treat it as if it's due Monday. Come to my office hours with questions, and bring remaining questions to class Monday. The time between Monday and Wednesday is intended only for writing the solutions in a clear and concise way that explains your thought processes. I do not set aside class time on Wednesdays for answering questions.
• If after class Monday, and office hours Monday and Tuesday, you have some remaining questions, please e-mail our TA Annie Machaffie (amachaff) before 5pm Tuesday, and tell her that you'd like to attend her evening help session Tuesday night at 8pm in A102.

Due Wednesday 9/13 at 8am

Problem Set Guidelines
Section 7.1 The Idea of Approximation

• Be sure to understand: The statement of Theorem 1

E-mail Subject Line: Math 104 Your Name 9/13

1. Why would we ever want to approximate an integral?
2. Give an example of a function that is monotone on the interval [0,2].
3. Let f(x)=x2. Does Theorem 1 apply to the integral int( f(x), x= -1. . 2) ? Explain.

Reminders:

• PS 1 (individual) is due Wednesday at 4pm. Make sure you read and follow the guidelines referred to above.
• Look at PS 2 on the course web page.

Due Friday 9/15 at 8am

Section 7.2 : More on Error: Left and Right Sums and the First Derivative

• Be sure to understand: The statement of Theorem 2

E-mail Subject Line: Math 104 Your Name 9/15

1. Explain in words what K1 is in Theorem 2.
2. Find a value for K1 for int( x2, x= -1. . 2).
3. Use Theorem 2 and your value for K1 to find an upper bound on the error when using L100 to approximate int( x2, x= -1. . 2).

Due Monday 9/18 at 8am

Project 1
Guide to Writing Mathematics

• Be sure to understand: What your client is asking you to do!

Reminders:

• Bring questions on PS 2 (group) to me before Monday.
• Bring any remaining questions to class on Monday.
• Lab is at 1:00 Tuesday.
• If after class Monday, and office hours, you still have questions remaining, please e-mail Annie (amachaff) before 5pm Tuesday to tell her you'd like to attend the help session Tuesday evening at 8pm in A102.

Due Wednesday 9/20 at 8am

Section 7.3 : Trapezoid Sums, Midpoint Sums, and the Second Derivative

• Be sure to understand: The statement of Theorem 3

E-mail Subject Line: Math 104 Your Name 9/20

1. Explain in words what K2 is in Theorem 2.
2. Find a value for K2 for int( x2, x= -1. . 2).
3. Use Theorem 3 and your value for K2 to find an upper bound on the error when using M100 to approximate int( x2, x= -1. . 2).

Reminder:

• PS 2 is due Wednesday. Your group should turn in a joint version. Photocopy it now (and again when you get it back from the grader), so that you each have a copy for studying purposes (and just so you have a record of your scores).
• Remember to note on your joint problem set who the "recorder" was--the person who did the writing. (A star by that person's name will suffice). Next time, switch recorders.
• Look at PS 3 on the course web page.

Due Friday 9/22 at 8am

The Big Picture

• Be sure to understand: Example 3

E-mail Subject Line: Math 104 Your Name 9/22

1. How many subdivisions does the trapezoid method require to approximate int( cos(x3), x = 0. . 1) with error less than 0.0001?

Reminder:

• You should have completed the calculations for your client (i.e. your project) by Friday, so that you can begin gathering your thoughts and writing your response. I suggest you plan on bringing a rough draft of your response to me during Monday or Tuesday's office hours.

Due Monday 9/25 at 8am

Section 3.8 : Inverse Trigonometric Functions and Their Derivatives

• To read: All, but you can skip the section on Inverse Trigonometric Functions and the Unit Circle.
note: For those who don't have Volume 1, Section 3.8 is in the back of Volume 2, starting on page 733.
• Be sure to understand:

E-mail Subject Line: Math 104 Your Name 9/25

1. What is the domain of the function arccos(x)? Why?
2. Why are we studying the inverse trig functions now?
3. Find one antiderivative of 1 / (1+x2).

Reminder:

• Bring questions on PS 3 to class on Monday. PS 3 is an individual assignment.
• If after class you still have questions, come to my office hours!
• Write a rough draft of you response to your client by Monday or Tuesday. Use the Guide to Writing Mathematics and the checklist to help you order your thoughts.
• If you have last lingering questions, and would like some additional help, our Calc assistant Annie is available Tuesday nights at 8pm. E-mail her by 5pm Tuesday at amachaff, and let her know you'd like to meet with her in A102.

Due Wednesday 9/27 at 8am

Section 6.1: Antiderivatives: The Idea
Section 6.2: Antidifferentiation by Substitution
Guide to Writing Mathematics

• Be sure to understand: Examples 3, 5, and 8 from Section 6.2

E-mail Subject Line: Math 104 Your Name 9/27

1. Explain the difference between a definite integral and an indefinite integral.
2. What are the three steps in the process of substitution?
3. Substitution attempts to undo one of the techniques of differentiation. Which one is it?

Reminders:

• PS 3 (individual) is due Wednesday.
• Look at PS 4 on the course web page.
• Begin putting the finishing touches on your letter to your client. If you have not already discussed your rough draft with me, please do so. I always feel badly for a group whose mathematics is correct but who didn't realize exactly what my expectations are.
• Have friends who are not in the class (and who have not had Calc 2) read your letter to your client, without telling them anything about it. Ask for their honest feedback: were they convinced by your explanations, without being confused? Did it flow well? Did they skip over parts, or were they able to follow it all?
• You have an exam on Tuesday 10/3. Make a study plan now.

Due Friday 9/29 at 8am

Section 9.1: Integration By Parts

• To read: Through page 497. Be warned that Example 8 is a bit slippery.
• Be sure to understand: The statement of Theorem 1 and Examples 1, 3, and 6

E-mail Subject Line: Math 104 Your Name 9/29

1. Integration by parts attempts to undo one of the techniques of differentiation. Which one is it?
2. Pick values for u and dv in the integral int( x * sin(x), x). Use parts to find an antiderivative for x * sin(x).

Reminders:

• Begin reviewing for the exam, if you haven't already.
• Project 1 is due Friday by 4pm.

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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