Reading Assignments for Calculus 2
Spring 2002, Math 104
January and February, 2002
Be sure to check back often, because assignments may change!
Last modified: February 11, 2002
I'll use Maple syntax for mathematical notation on this page.
All section and page numbers refer to sections from Ostebee/Zorn, Vol 2.
Due Wednesday 1/30, at 8am
guidelines for submitting reading assignments
suggestions for reading a math text
course policies
syllabus
- To read: all
- 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 1/30
Reading questions:
- Does every continuous function have an antiderivative? Why or why not?
- If f(x)=3x-5 and a=2, where is A_{f} increasing? decreasing? Why?
- Find the area between the x-axis and the graph of f(x)=x^{4}+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 in A102.
- Find out this week's problem set assignment, listed at the bottom of this course's
web page. .
Please Note:
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 2/1 at 8am
re-read:
Section 5.4: Approximating Sums
- To read: All
- 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 2/1
Reading questions:
- When approximating an integral, which would you expect to be more accurate:
L_{10} or L_{100}? Why?
- Give an example of a partition of the interval [0,3].
- What is a Riemann sum? Explain in your own words, not those of Ostebee and Zorn, of course.
Reminder:
- Please feel comfortable coming to my office hours. You don't need to make an appointment, just stop in. Remember that in a way, office hours are a part of Calculus -- everyone needs to ask questions outside of class sometime, so don't hesitate!
- Bring questions on the problem sets to my office hours. I only set aside 10-15 minutes in class on Mondays to answer questions for the week, so don't save your questions for that time. I don't do this because I assume you don't have questions, but precisely because I expect each of you to have many questions! I think it's best to give more personal attention to your questions than I can in class, so come by my office hours. Remember, you don't need to make an appointment to see me during office hours, just come by!
Due Monday 2/4 at 8am
Problem Set Guidelines
Section 7.1 The Idea of Approximation
- To read:
All
- Be sure to understand:
The statement of Theorem 1
E-mail Subject Line: Math 104 Your Name 2/4
Reading questions:
- Why would we ever want to approximate an integral?
- Give an example of a function that is monotone on the interval [0,2].
- Let f(x)=x^{2}. Does Theorem 1 apply to the integral int( f(x), x= -1. . 2) ? Explain.
Reminders:
- PS 1 (individual) is due Tuesday at 1pm. Make sure you read and follow the guidelines referred to above.
- If you have any last remaining questions on the problem set after coming to my office hours, bring them to class Monday.
- There may be a help session with the grader Monday night -- I don't have it set up yet (it's January 26th!), and I may not have time to change this when (and if) I get something set up.
Due Wednesday 2/6 at 8am
Section 7.2 : More on Error: Left and Right Sums and the First Derivative
- To read:
All
- Be sure to understand:
The statement of Theorem 2
E-mail Subject Line: Math 104 Your Name 2/6
Reading questions:
- Explain in words what K_{1} is in Theorem 2.
- Find a value for K_{1} for int( x^{2}, x= -1. . 2).
- Use Theorem 2 and your value for K_{1} to find an upper bound on the error when using L_{100} to approximate
int( x^{2}, x= -1. . 2).
Reminders:
- Look at PS 2 on the course web page.
Due Friday 2/8 at 8am
Section 7.3 : Trapezoid Sums, Midpoint Sums, and the Second Derivative
- To read:
All
- Be sure to understand:
The statement of Theorem 3
E-mail Subject Line: Math 104 Your Name 2/8
Reading questions:
- Explain in words what K_{2} is in Theorem 2.
- Find a value for K_{2} for int( x^{2}, x= -1. . 2).
- Use Theorem 3 and your value for K_{2} to find an upper bound on the error when using M_{100} to approximate int( x^{2}, x= -1. . 2).
Reminder:
- Remember to stop by my office hours as soon as you've struggled with something and can't resolve it! Don't let yourself get behind!
Due Monday 2/11 at 8am
Section 7.3: Trapezoid Sums, Midpoint Sums, and the Second Derivative
For Tuesday:
Project 1
Guide to Writing Mathematics
- To read: Re-read
- Be sure to understand:
All
No Reading Questions Today!
Reminders:
- Bring any remaining questions on PS 2 to class on Monday.
- If you still have questions after class, Rachel is available at 7:30 Monday evening to help you. e-mail her at rzeigowe before 5.
- Your group should turn in a joint version of PS 2. 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.
Due Wednesday 2/13 at 8am
Project 1
- To read:
Reread the project, and your work from Tuesday. You may also want to review Sections 7.1 - 7.3 and make sure that the ideas are all making sense to you.
No Reading questions today
Reminder:
- Look at PS 3 on the course web page.
- Keep working on the project.
Due Friday 2/15 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 2/15
Reading questions:
- What is the domain of the function arccos(x)? Why?
- Why are we studying the inverse trig functions now?
- Find one antiderivative of 1 / (1+x^{2}).
Reminder:
- I'm just going to keep on reminding you that coming to my office hours is important :)
Due Monday 2/18 at 8am
Section 6.1: Antiderivatives: The Idea
Section 6.2: Antidifferentiation by Substitution
Guide to Writing Mathematics
- To read: All
- Be sure to understand: Examples 3, 5, and 8 from Section 6.2
E-mail Subject Line: Math 104 Your Name 2/18
Reading questions:
- Explain the difference between a definite integral and an indefinite integral.
- What are the three steps in the process of substitution?
- Substitution attempts to undo one of the techniques of differentiation.
Which one is it?
Reminders:
- Bring questions on PS 3 to class on Monday. PS 3 is an individual assignment.
- If you still have questions after class, Rachel is available at 7:30 Monday evening to help you. e-mail her at rzeigowe before 5.
- You should have completed the calculations for your project by Monday, so that you can begin gathering your thoughts and writing your response. I urge you to bring a rough draft of your response to me during Tuesday or Wednesday's office hours. Use the
Guide to Writing Mathematics and the checklist to help you order your thoughts.
- You have an exam on Tuesday 2/26. Make a study plan now. Allow yourself at least 8 hours (preferably more), and be sure that redoing as many problems as possible is part of your plan.
Due Wednesday 2/20 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 2/20
Reading questions:
- Integration by parts attempts to undo one of the techniques of differentiation.
Which one is it?
- 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:
- 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, and which therefore ends up with a C on their project.
- 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?
Due Friday 2/22 at 8am
Section 9.1: Integration By Parts (continued)
- To read:
Reread the section
- Be sure to understand:
Example 8
E-mail Subject Line: Math 104 Your Name 2/22
Reading questions:
Each integral can be evaluated using u-substitution or integration by parts. Which technique would you use in each case? Why?
- int( x*cos(x), x)
- int(x*cos(x^{2}),x)
Reminder:
- Project 1 is due at 2pm Friday.
- Consider yourself nagged about coming to my office hours at the first sign of trouble. I don't want anyone falling through the cracks!
- Begin reviewing for the exam, if you haven't already.
Due Monday 2/25 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.
No Reading Questions Today
Reminders:
- Bring questions on PS 4 to class Monday. PS 4 will not be turned in, but it will be covered on the exam.
- If you still have questions after class, Rachel is available at 7:30 Monday evening to help you. e-mail her at rzeigowe before 5.
- For the exam, you may have a "cheat sheet" . Your cheat sheet must follow these guidelines:
- It must be on 8 1/2 x 11 paper (or smaller)
- There can only be writing on one side of the paper.
- Your notes must be in your handwriting. (No typing, no photocopying, no getting a friend to help you write it.) The handwriting must be on that paper (no photocopying pieces of your notes.)
- The exam is during lab. You may begin taking it at 12:30pm..
Due Wednesday 2/27 at 8am
Practice Antidifferentiating
- To read: re-read Section 9.1
- Be sure to understand: All
No Reading Questions Today
Reminders:
Here ends the reading for January and February
Go to the reading assignments for March!
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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