Reading Assignments for Calculus 1 with Econ Applications
Spring 2008, Math 102

April and May 2008

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 Wednesday 4/2 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 102 Name 4/2

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:

• The deadline for receiving 90% on the Differentiation Exam is Friday at 3pm.

Due Friday 4/4 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 102 Name 4/4

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:
• The deadline for receiving 90% on the Differentiation Exam is Friday at 3pm.
• The mathematical calculations for the project should be done by Friday afternoon.

Due Monday 4/7 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 102 Name 4/7

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:

• Bring remaining questions on PS 10 to class.
• If you haven't already, finish the calculations for the project, and get a good start on writing the letter. If you want to feedback on a rough draft, bring one by earlier enough that I have time.

Due Wednesday 4/9 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 102 Name 4/9

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?

Due Friday 4/11 at 9am

Section 5.3 The Fundamental Theorem of Calculus

Reminder:

• Project 2 is due by 3:00pm Friday.

Due Monday 4/14 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 102 Name 4/14

1. Explain the fundamental difference between a definite integral and an indefinite integral. Please go deeper than saying one has limits of integration and one doesn't. The first is a real number -- why? What does it represent? Then think similarly about an indefinite integral? Is it a real number? If not what is it? Why? What does it represent?
2. Substitution attempts to undo one of the techniques of differentiation. Which one is it?
3. What are the three steps in the process of substitution?

Reminder:

• Bring questions on PS 11.

Due Wednesday 4/16 at 9am

Section 5.4 Finding Antiderivatives: The Method of Substitution

Reminders:

• The deadline to receive 75% on the Diff Exam is Friday at 3pm.
• Exam 3 is on Tuesday 4/22. As usual, get an early start on PS 12.

Due Friday 4/18 at 9am

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 102 Name 4/18

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?
Reminders:
• The deadline to receive 75% on the differentiation exam is Friday at 3pm.

Due Monday 4/21 at 9am

Bring Questions for Exam 3

Reminders:

• Visit my office hours and visit the Kollett Center 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 Tuesday.

Due Wednesday 4/23 at 9am

Section 5.6 Approximating Sums: The Integral as a Limit

Due Friday 4/25 at 9am

Section 2.5 Differential Equations; Modelling Motion

To read: All. Be sure to understand the difference between solutions to algebraic equations and to differential equations; Examples 1, 2, 3, and 6.

E-mail Subject Line: Math 102 Name 4/25

1. Show that y(x)=x^(1/3) is a solution to the differential equation y'(x)=1/(3*y^2).
2. Solve the initial value problem y'(x)=5/x^2+4, y(1)=12.

Due Monday 4/28 at 9am

Section 2.5 Differential Equations; Modelling Motion

Due Wednesday 4/30 at 9am

TBA

1. TBA
Reminders:
• The deadline to receive 50% on the Diff Exam is Friday at 3pm.

Due Friday 5/2 at 9am

The Big Picture

To read: Review Section 5.6 and 2.5; begin reviewing the entire semester.

Reminders:

• The deadline to receive 50% on the Diff Exam is Friday at 3pm.
• The final will be Saturday, May 10, from 2pm-5pm.
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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