Spring 2003, Math 104

January and February, 2003

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

All section and page numbers refer to sections from Ostebee/Zorn, Volume 2, 2nd edition.

Due Wednesday 1/29, at 8am

• Pay attention to: all of it. Any questions? Please do ask me!

Section 5.1: Areas and Integrals
Section 5.2: The Area Function
Section 5.3: The Fundamental Theorem of Calculus
Section 3.4 Inverse Functions and Their Derivatives

• To read: Sections 5.1, 5.2, and 5.3 should be review; skim them to remind yourself of the ideas.
You can skim the beginning of Section 3.4 (Appendix S), but read the section Working with inverse trigonometric functions beginning on page S-8 carefully.
• Be sure to understand: The statements of both forms of the Fundamental Theorem of Calculus. The derivatives of the inverse trig functions.

E-mail Subject Line: Math 104 Your Name 1/29

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

Reminders:

• In these assignments, you should always briefly explain how you arrived at your answers.
• Come to lab at 1pm Tuesday in A102.
• Begin Problem Set 1, listed at the bottom of this course's web page. .

There does not appear to be an easy way for me to automatically send you a "message received" note. Because sometimes messages disappear, send yourself a copy of each reading assignment.

Due Friday 1/31 at 8am

Section 5.4 Finding Antiderivatives; The Method of Substitution

• Be sure to understand: Examples 6, 7, 9, and 13

E-mail Subject Line: Math 104 Your Name 1/31

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?

Reminder:

• The problem sets due each Tuesday reflect an entire week's worth of work, and you should be working on them throughout the week. Get in a group for this first one.
• Office hours are an important part of Calculus, so please don't hesitate to come to them! I only set aside 10-15 minutes in class on Mondays to answer questions on the week's problem set, so don't save your questions for that time--come to office hours, and get personal attention to your questions.
• Make sure you've read all the stuff I handed out in class and all the material on the course web page.

Due Monday 2/3 at 8am

Problem Set Guidelines
Section 5.6 Approximating Sums; The Integral as a Limit

• Be sure to understand:

E-mail Subject Line: Math 104 Your Name 2/3

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. Explain the idea of a Riemann sum in your own words.

Reminders:

• PS 1 (group) 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.
• If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.
• Your group will turn in one joint version of PS 1; the recopying should all be done by one person, the "primary author". Make a note on it who the "primary author" was this time, and switch next time.
• Be sure that each member of your group has a photocopy of the problem set you turn in, both for studying purposes and for your records.

Due Wednesday 2/5 at 8am

Section 6.1 Approximating Integrals Numerically

• Be sure to understand: The statements of Theorem 1 and Theorem 2

E-mail Subject Line: Math 104 Your Name 2/5

1. Why would we ever want to approximate an integral?
2. Let f(x)=x2 and I=int( f(x), x= -1. . 2). Does Theorem 1 apply to I? Explain.
3. Let f(x)=x2 and I=int( f(x), x= -1. . 2). Does Theorem 2 apply to I? Explain.

Reminders:

• Begin PS 2.

Due Friday 2/7 at 8am

Section 6.2 Error Bounds for Approximating Sums

• Be sure to understand: The statement of Theorem 3 and Example 6.

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

1. Explain in words what K1 is in Theorem 3.
2. Explain in words what K2 is in Theorem 3.
3. Find values for K1 and K2 for int( x3, x= -1. . 2).

Due Monday 2/10 at 8am

Section 6.2 Error Bounds for Approximating Sums

• Be sure to understand: Example 7

E-mail Subject Line: Math 104 Your Name 2/10

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

Reminders:

• Bring any remaining questions on PS 2 to class on Monday.
• If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.

Due Wednesday 2/12 at 8am

Work on Project 1

Reminder:

• Begin PS 3.

Due Friday 2/14 at 8am

Section 7.1 Measurement and the Definite Integral; Arc Length

• Be sure to understand: The Fact on page 416, Example 5, the Fact on page 419, and Example 8.

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

Let f(x)=sin(x)+10 and g(x)=2x-5.

1. Set up the integral that determines the area of the region bounded by y=f(x) and y=g(x) between x=-1 and x=3.
2. Set up the integral that gives the length of the curve y=g(x) from x=-1 to x=3.

Due Monday 2/17 at 8am

Section 7.2 Finding Volumes by Integration
Guide to Writing Mathematics

• Be sure to understand: The section Solids of revolution

E-mail Subject Line: Math 104 Your Name 2/17

1. Let R be the rectangle formed by the x-axis, the y-axis, and the lines y=1 and x=3. What is the shape of the solid formed when R is rotated about the x-axis?
2. Let T be the triangle formed by the lines y=x, x=1 and the x-axis. What is the shape of the solid formed when T is rotated about the x-axis?

Reminders:

• Bring questions on PS 3.
• If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.
• Do the best you can on your draft -- the better the draft, the more useful suggestions I can make

Due Wednesday 2/19 at 8am

Section 7.2 Finding Volumes by Integration

Reminders:

• Begin PS 4.

Due Friday 2/21 at 8am

Section 8.1 Integration by Parts(continued)

• Be sure to understand: Theorem 1. Be warned that Examples 8 and 9 can be a little slippery.

E-mail Subject Line: Math 104 Your Name 2/21

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).

Reminder:

• Exam 1 is Tuesday 2/25.

Due Monday 2/24 at 8am

Bring Questions for Exam 1

Reminders:

• PS 4 will not be turned in, but it will be covered on the exam.
• If you'd like to meet with Rachel Sunday night at 8pm in SC A118, please e-mail her by 5pm Sunday asking her to meet with you, and giving her a list of questions you have. Her e-mail address is rzeigowe.
• For the exam, you may have a "cheat sheet", consisting of handwritten notes on one side of an 8 1/2 x 11 (or smaller) piece of paper.
• You may begin taking the exam at 12:30pm Tuesday.

Due Wednesday 2/26 at 8am

Section 8.1 Integration by Parts

E-mail Subject Line: Math 104 Your Name 2/26

Each integral can be evaluated using u-substitution or integration by parts. Which technique would you use in each case? You do not need to evaluate the integral, but explain your choice.

1. int( x*cos(x), x)
2. int(x*cos(x2),x)

Reminders:

• Begin PS 5.

Due Friday 2/28 at 8am

More on Antidifferentiation

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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