Spring 2005, Math 101

April and May 2005

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 4/1 at 9am

Work on Project 2

Reminder:

• Begin PS 9.

Due Monday 4/4 at 9am

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 2:30pm.
• Begin studying for Exam 2 over the week-end, if you haven't already.

Due Wednesday 4/6 at 9am

Bring Questions for Exam 2

Reminders:

Class on Wednesday is in SC 243
• Get questions on PS 9 out of the way before class! PS 9 should be done before class today, so you can be focusing on reviewing.
• As you prepare for the exam, take advantage of the CLC and of my office hours.
• 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 4/8 at 9am

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 4/8

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. Get a good start on writing the letter.

Due Monday 4/11 at 9am

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 4/11

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.

Reminder:

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

Due Wednesday 4/13 at 9am

Section 4.9 Why Differentiability: The Mean Value Theorem

Reminders:

Class on Wednesday is in SC 243
• Keep on using the CLC and my office hours!
• Bring remaining questions on PS 10 to class.

Due Friday 4/15 at 9am

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 4/15

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 2:30pm Friday.
• Begin PS 11.

Due Monday 4/18 at 9am

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 4/18

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 4/20 at 9am

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 4/20

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:

Class on Wednesday is in SC 243
• Even if you've never been before, go to the CLC during its Calculus tutoring hours, and come see me during my office hours!
• Bring questions on PS 11.

Due Friday 4/22 at 9am

Section 5.3 The Fundamental Theorem of Calculus

Reminder:

• Begin PS 12.

Due Monday 4/25 at 9am

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 4/29

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?

Due Wednesday 4/27 at 9am

Bring Questions for Exam 3

Reminders:

Class on Wednesday is in SC 243
• Visit my office hours and visit the CLC while clearing up questions before the exam!
• Get questions on PS 12 out of the way before class. PS 12 should be done before class so that you can focus on reviewing.
• 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 4/29 at 9am

Section 5.4 Finding Antiderivatives: The Method of Substitution

Reminders:

• Begin PS 13.

Due Monday 5/2 at 9am

Section 5.4 Finding Antiderivatives: The Method of Substitution

Due Wednesday 5/4 at 9am

Section 5.6 Approximating Sums: The Integral as a Limit

E-mail Subject Line: Math 101 Name 5/4

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?
Reminder:
Class on Wednesday is in SC 243
• As the semester comes to a close, make the time to visit my office hours and the CLC.
• Bring remaining questions on PS 13 to class.

Due Friday 5/6 at 9am

Section 5.6 Approximating Sums: The Integral as a Limit

E-mail Subject Line: No Reading Questions Due Today (so you're done for the semester!)

Reminder:

• If anybody still hasn't passed the differentiation exam, the deadline to receive any credit at all (50%) is Friday at 2:30 pm.

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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