Fall 2003, Math 104

September, 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 Friday 9/5 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

• To read: Sections 5.1, 5.2, and 5.3 should be review; read them as thoroughly as necessary to remind yourself of the ideas.
• Be sure to understand: The statements of both forms of the Fundamental Theorem of Calculus.

E-mail Subject Line: Math 104 Your Name 9/5

1. Why do you think it makes sense to call
int(f(x),x=a..b)/(b-a)
the average value?

Note: The text doesn't specifically address this; the reason I'm asking this is because this is exactly the sort of question you should be learning to ask yourself (and attempt to answer) when you read.

2. Find the signed area between x^5 and the x-axis from x=1 to x=2.
3. If f(x) is continuous, must it have an antiderivative? If your answer is yes, does tha tmean there must be a nice formula (or any formula at all) for the antiderivative?

Reminders:

• In these assignments, you should always briefly explain how you arrived at your answers.
• Begin Problem Set 1, listed at the bottom of this course's web page. . The problem sets due each Tuesday reflect an entire week's worth of work, and you should be working on them throughout the week.

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 Monday 9/8 at 8am

Section 3.4 Inverse Functions and Their Derivatives (Appendix S)

• To read: 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 various uses of the words "identity" and "inverse". The derivatives of the inverse trig functions.

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

1. What is the domain of the function arccos(x)? Why is this the domain?
2. Explain how we can tell lines which are neither horizontal nor vertical have inverses.
3. Why do you think we are studying the inverse trig functions now?
4. Find one antiderivative of 1 / (1+x2).

Reminder:

• Come to lab at 1pm Tuesday in A102.
• 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.
• Make sure you've read all the stuff I handed out in class and all the material on the course web page.

Due Wednesday 9/10 at 8am

Section 5.4 Finding Antiderivatives; The Method of Substitution

• To read: All. Remember to pay attention to tables and graphs; in particular, remind yourself why all of the basic antiderivatives in the table on page 333 are true, and begin to know them all.
• Be sure to understand: Examples 6, 7, 9, and 13 illustrate specific important points, but you should be paying attention to and doing your best to understand all the examples.

E-mail Subject Line: Math 104 Your Name 9/10

1. Explain the fundamental difference between a definite integral and an indefinite integral. Please go deeper than quoting "the first is a real number and the second is a family of functions" -- what real number does the definite integral represent? Why is the indefinite integral a family of functions?
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:

• Begin working on PS 2 (group).

Due Friday 9/12 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 9/12

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:

• Remember the problem sets due each Tuesday reflect the whole week-s worth of work, and should be worked on throughout the week.
• 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.

Due Monday 9/15 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 9/15

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:

• Rachel's help session is Monday night, 8pm-9pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Remember to give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• (Last reminder of the semester:) Come to lab Tuesday at 1pm, bring your completed problem set with you.
• Your group will turn in one joint version of PS 2; 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 9/17 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 9/17

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).

Reminders:

• Begin PS 3.
• Exam 1 will be Tuesday 9/23.

Due Friday 9/19 at 8am

Section 6.2 Error Bounds for Approximating Sums

• Be sure to understand: Example 7

E-mail Subject Line: Math 104 Your Name 9/19

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

Reminders:

• Begin studying now for the exam!

Due Monday 9/22 at 8am

Bring Questions for Exam 1

Reminders:

• Rachel's help session is Monday night, 8pm-9pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Remember to give her an idea of what you plan to ask her -- the numbers of the homework questions, problems from the study guide, or the topic that's causing difficulties.
• PS 3 will not be turned in, but it will be covered on the exam. Get questions on it out of the way before class!
• 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 9/24 at 8am

Work on Project 1

Reminder:

• Begin PS 4.

Due Friday 9/26 at 8am

Continue working on Project 1

Due Monday 9/29 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 9/29

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.

Reminder:

• The math for project 1 should be finished by Tuesday evening at the latest.
• Rachel's help session is Monday night, 8pm-9pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Remember to give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.

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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