Spring 2004, Math 101

April and May 2004

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

I'll use Maple syntax for some of the mathematical notation on this page. (Paying attention to how I type various expressions is a good way to absorb Maple notation). I will not use it when I think it will make the questions too difficult to read.
All section and page numbers refer to sections from Calculus from Graphical, Numerical, and Symbolic Points of View, Volume 1, 2nd Edition, by Ostebee and Zorn.

Due Friday 4/2 at 10am

Work on Project 2

Reminder:

• Begin PS 9.

Due Monday 4/5 at 10am

Section 4.7 Building Polynomials to Order: Taylor Polynomials

Reminder:

• Try to have the mathematical calculations for the project done by Monday morning.
• The deadline for receiving 100% on the Differentiation Exam is Monday at 3pm.
• Begin studying for Exam 2 over the week-end, if you haven't already.

Due Wednesday 4/7 at 10am

Bring Questions for Exam 2

Reminders:

• Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Get questions on PS 9 out of the way before class!
• For the exam, once again 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.
• As before, you may begin taking the exam at 12:30pm Thursday.

Due Friday 4/9 at 10am

Section 4.8 Why Continuity Matters

To read: All. Make sure to understand the statement of the Intermediate Value Theorem

E-mail Subject Line: Math 101 Name 4/9

1. What are the hypotheses of the Intermediate Value Theorem?
2. What is the conclusion of the Intermediate Value Theorem?

Reminder:

• Begin PS 10.
• If you haven't already, finish the calculations for the project.

Due Monday 4/12 at 10am

The Temperature at the Equator and the IVT

Reminder:

• If you want to, bring a rough draft of Project 2 to me for some feedback.

Due Wednesday 4/14 at 10am

Section 4.9 Why Differentiability: The Mean Value Theorem

To read: All. Be sure to understand the statement of the Mean Value Theorem and the section "What the MVT says."

E-mail Subject Line: Math 101 Name 4/14

1. What are the hypotheses of the Mean Value Theorem?
2. What is the conclusion of the Mean Value Theorem?
3. Explain the MVT using "car talk" -- that is, using velocity.

Reminders:

• Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Bring questions on PS 10.

Due Friday 4/16 at 10am

Section 5.1 Areas and Integrals

To read: All. Be sure to understand the definition of the integral, Example 2, and the section "Properties of the Integral" beginning on page 306.

E-mail Subject Line: Math 101 Name 4/16

1. What does the integral of a function f from x=a to x=b measure?
2. Is the integral of f(x)=5x from x=-1 to x=3 positive or negative?
Reminder:
• Project 2 is due by 4pm Friday.
• Begin PS 11.

Due Monday 4/19 at 10am

Section 5.2 The Area Function

To read: All. Make sure you understand the definition of the area function and Examples 2, 3, and 4.

E-mail Subject Line: Math 101 Name 4/19

1. Let f be any function. What does the area function Af(x) measure?
2. Let f(t)=t and let a=0. What is Af(1)?

Reminder:

• The deadline to receive 75% on the differentiation exam is Monday.

Due Wednesday 4/21 at 10am

Section 5.3 The Fundamental Theorem of Calculus

To read: All, but you can skip the proof of the FTC if you'd like: we'll look at a different approach in class.

E-mail Subject Line: Math 101 Name 4/21

1. Find the area between the x-axis and the graph of f(x)=x^3+4 from x=0 to x=3.
2. Does every continuous function have an antiderivative? Why or why not?
3. If f(x)=3*x-5 and a=2, where is Af increasing? Decreasing? Why?

Reminder:

• Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Bring questions on PS 11.

Due Friday 4/23 at 10am

Section 5.3 The Fundamental Theorem of Calculus

Reminder:

• Begin PS 12.

Due Monday 4/26 at 10am

Section 5.4 Finding Antiderivatives: The Method of Substitution

To read: All. Be sure to understand Examples 8, 9, and 10.

E-mail Subject Line: Math 101 Name 4/23

1. Explain the difference between a definite integral and an indefinite integral. I do not simply mean whether one is a number or a family, but what they each represent.
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?

Note:

• This reading assignment was originally assigned for this past Friday. If you already sent it to me, there's no need to send it to me again. If you didn't ... I guess you get a second chance!

Due Wednesday 4/28 at 10am

Bring Questions for Exam 3

Reminders:

• Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Get questions on PS 12 out of the way before class!
• As usual, 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 for the exam.
• As before, you may begin taking the exam at 12:30pm Thursday.

Due Friday 4/30 at 10am

Section 5.4 Finding Antiderivatives: The Method of Substitution

Reminder:

• Begin PS 13.

Due Monday 5/3 at 10am

Section 5.6 Approximating Sums: The Integral as a Limit

To read: All. Be sure to understand the definitionof a Riemann Sum and Example 3.

E-mail Subject Line: Math 101 Name 5/3

1. Explain, in your own words, the idea of using Riemann Sums to approximate integrals.
2. If f(x) is decreasing on [a,b], will Ln underestimate or overestimate the integral of f from a to b? How about Rn?

Due Wednesday 5/5 at 10am

Section 5.6 Approximating Sums: The Integral as a Limit

To read: Re-read this section, making sure it all makes sense to you now.

Reminder:

• Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Bring questions on PS 13.

Due Friday 5/7 at 10am

Here ends the reading for the Semester!

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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