Spring 2000, Math 104

February 2000

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

Due Wednesday 2/2, at 8am

• Pay attention to: all of it: I tried to address as many issues as I could think of. Any questions? Ask me!
• Reminder: Keep these 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 2/2

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 Friday 2/4 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 2/4

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:

• PS 1 is due Friday.

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 Friday, each week treat it as if it's due Wednesday. Come to my office hours with questions, and bring remaining questions to class Wednesday. The time between Wednesday and Friday is intended only for writing the solutions in a clear and concise way that explains your thought processes.

Due Monday 2/7 at 8am

Section 7.1 The Idea of Approximation

• Be sure to understand: The statement of Theorem 1

E-mail Subject Line: Math 104 Your Name 2/7

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:

• Look at PS 2 on the course web page.

Due Wednesday 2/9 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 2/9

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).

Reminders:

• Bring questions on PS 2 to class on Wednesday. PS 2 is a group assignment.
• If after class you still have questions, come to office hours or e-mail Annie and arrange to meet her at ??? in A102 on Thursday evening.

Due Friday 2/11 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 2/11

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 Friday. 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. Remember to note on it who the "recorder" was--the person who did the writing. (A star by that person's name will suffice). Next time, switch recorders.
• If you have last lingering questions, and would like some additional help, our Calc assistant Annie is available Thursday nights. E-mail her by 5pm at amachaff, and let her know you'd like to meet with her in A102.

Due Monday 2/14 at 8am

Project 1
Guide to Writing Mathematics

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

E-mail Subject Line: Math 104 Your Name 2/14

Reminders:

• Look at PS 3 on the course web page.

Due Wednesday 2/16 at 8am

The Big Picture

• Be sure to understand: Example 3

Alert: Wednesday's class will be held in A102, rather than switching to 243. Instead, we will have Friday's class in Room 243. If I don't remember to mention it in lab, remind me!

E-mail Subject Line: Math 104 Your Name 2/16

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

Reminders:

• Bring questions on PS 3 to class on Wednesday. PS 3 is an individual assignment.
• If after class you still have questions, come to office hours or e-mail Annie and arrange to meet her at ??? in A102 on Thursday evening.

Due Friday 2/18 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
• Be sure to understand:

E-mail Subject Line: Math 104 Your Name 2/18

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:

• PS 3 (individual) is due Friday.
• If you have last lingering questions, and would like some additional help, our Calc assistant Annie is available Thursday nights. E-mail her by 5pm at amachaff, and let her know you'd like to meet with her in A102.
• 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 by Monday or Tuesday.

Due Monday 2/21 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 2/21

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:

• Look at PS 4 on the course web page.
• 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.
• You have an exam on Tuesday 2/29. Make a study plan now.

Due Wednesday 2/23 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 2/23

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:

• Bring questions on PS 4 (group) to class on Wednesday.
• If you have questions, come to office hours or e-mail Annie at amachaff and arrange to meet her at 9pm in A102 on Thursday evening.
• Fine-tune your response to your client. Have friends who are not in the class read it (without telling them what it's about) to see if they can figure out what the original question was and follow your solution easily. Ask them if they found it remotely interesting (they should).
• Begin reviewing for the exam.

Due Friday 2/25 at 8am

Section 9.1: Integration By Parts (continued)

• Be sure to understand: Example 8

E-mail Subject Line: Math 104 Your Name 2/25

Each integral can be evaluated using u-substitution or integration by parts. Which technique would you use in each case? Why?
1. int( x*cos(x), x)
2. int(x*cos(x2),x)

Reminder:

• PS 4 (group) is due Friday.
• If you have last lingering questions, and would like some additional help, our Calc assistant Annie is available Thursday nights. E-mail her by 5pm at amachaff, and let her know you'd like to meet with her in A102.
• Project 1 is due Friday.
• Continue reviewing for Exam 1.

Due Monday 2/28 at 8am

Q & A for Exam 1

• To read: Review Sections 5.1-5.4, 7.1-7.3, 3.8, and 6.2. Work on the study guide I gave you. Redo old problem sets.
• Be sure to understand: Everything, better than you did the first time you saw it.

Reminders:

• Look at PS 5 on the course web page.
• For the exam, I let you have a "cheat sheet" consisting of one 8 1/2 x 11 page of notes, front only, handwritten by you on that page :) (I'm trying to address all the finagling questions students have asked in the past!)
• The exam is during lab. You may begin taking it at 12:30pm. Don't forget to bring your calculator and your "cheat sheet".

Here ends the reading for February
Go to the reading assignments for March!

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 103
Norton, Massachusetts 02766-0930
TEL (508) 286-3970
FAX (508) 285-8278
jsklensk@wheatonma.edu

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