Spring 2004, Math 101

January and February 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 1/30 at 10am

Section 1.1: Functions, Calculus Style
Section 1.2: Graphs
Appendix B: Real Numbers and the Coordinate Plane

To read: The section How to Use This Book: Notes for Students beginning on page xvii. All of Sections 1.1 and 1.2. Also read or skim through Appendix B with whatever depth is necessary. If you find Appendix B unfamiliar or difficult, contact me immediately.

E-mail Subject Line: Math 101 Name 1/30

Let f(x)=x^2.

1. How is the graph of y=f(x)+3=x^2+3 related to the graph of y=f(x)? Why?
2. How is the graph of y=f(x+3)=(x+3)^2 related to the graph of y=f(x)? Why?
3. Which of f(x), f(x)+2, f(x+2) are even? odd?

Reminders:

• Come to lab Thursday at 1pm!
• In these assignments, you should always briefly explain how you arrived at your answers.
• Begin PS 1, listed at the bottom of this course's web page. . The problem sets due each Thursday 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 2/2 at 10am

Section 1.3 A Field Guide to Elementary Functions
Appendix C Lines and Linear Functions
Appendix D Polynomials and Rational Functions
Appendix E Algebra of Exponential and Logarithmic Functions
Appendix F Algebra of Trigonometric Functions

To read: All of Section 1.3. Be sure to understand the definition of the logarithm function base b and the definitions of sin(x) and cos(x) in terms of the unit circle. Read or skim through through the appendicies with whatever depth is necessary. If you find Appendix C, D or F unfamiliar or difficult, contact me immediately.

E-mail Subject Line: Math 101 Name 2/2

1. How are the functions f(x)=3^x and g(x)=log[3](x) related?
log[3](x) is Maple notation for log3(x).
2. What are some of the properties of sin(x)?

Reminders:

• Make sure you've read all the stuff I handed out in class and all the material on the course web page.
• The point of these reading assignments is to give you credit for reading and for beginning the learning process. I do not expect you to have completed learning the section by the time you answer these questions!

We learn by doing, so make a real effort at answering the questions each day, but don't be frustrated if some days you don't feel you're at all on the right track. Use this as an opportunity to identity the material you find particularly mysterious before class, so you know what to really focus on during class.

• Section 1.3 is an overview of the functions we'll be working with off and on throughout the semester. As long as you are fairly comfortable with trigonometry and polynomials, and have worked some with exponential functions, don't worry -- we'll be gaining familiarity with them throughout the semester. If you are not particularly comfortable with exponential functions or trig functions, use the time from now until we next work with them in depth to really work through the appropriate appendices.

Due Wednesday 2/4 at 10am

Problem Set Guidelines
Section 1.4 Amount Functions and Rate Functions: The Idea of the Derivative

To read: Through Example 4. Be sure to understand the section "Rates, amounts, and cars" beginning on page 36.

E-mail Subject Line: Math 101 Name 2/4

Look at the graphs of P(t) and V(t) in Figure 1 on page 37.

1. Is the derivative of P positive or negative at t=5? Explain.
2. Is the second derivative of P positive or negative at t=5? Explain.
3. give a value of t where the derivative of P is zero.

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.
• PS 1 (individual) is due Thursday at the beginning of lab. Make sure you read and follow the guidelines referred to above.
• If you have any remaining questions on the problem set after coming to my office hours, bring them to class Wednesday.

Due Friday 2/6 at 10am

Section 1.5 Estimating Derivatives: A Closer Look

To read: All. Make sure to understand Examples 3 and 4.

E-mail Subject Line: Math 101 Name 2/6

1. What does the term locally linear mean?
2. Explain why the derivative of f(x)=|x| does not exist at x=0.

Reminders:

• Begin Problem Set 2 (group).
• Office hours are an important part of Calculus, so please don't hesitate to come to them, whether your questions are big or small.

Due Monday 2/9 at 10am

Section 1.6 The Geometry of Derivatives

To read: All. Be sure to understand the definition of a stationary point and the difference between local and global maxima and minima.

E-mail Subject Line: Math 101 Name 2/9

Look at the graph of f ' in Example 2.

1. Where does f have stationary points? Why?
2. Where is f increasing? Why?
3. Where is f concave up? Why?

Due Wednesday 2/11 at 10am

Section 1.7 The Geometry of Higher Order Derivatives

To read: All. Think about why the Second Derivative Test makes sense.

E-mail Subject Line: Math 101 Name 2/11

Use the graphs of f, f ', f '' in Figure 3 on page 67.

1. By looking at the graph of f '', how can you tell where f is concave up and concave down?
2. By looking at the graph of f ', how can you tell where f is concave up and concave down?

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.
• 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.
• If, after coming to office hours, you still have questions on PS 2, bring them to class on Wednesday.
• 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 Friday 2/13 at 10am

Section 2.1 Defining the Derivative

To read: All. We'll talk about the formal definition of the derivative in detail during class.

E-mail Subject Line: Math 101 Name 2/13

1. Let f(x)=x^3. Find the slope of the secant line from x=-2 to x=4.
2. For a function f, what does the difference quotient ( f(a+h) - f(h) )/h measure?
3. Let f(x)=x^3. What is the average rate of change of f from x=-2 to x=4?
Reminders:
• Begin PS 3.

Due Monday 2/16 at 10am

Section 2.2 Derivatives of Power Functions and Polynomials

To read: Through Theorem 4 on page 97. Be sure to understand Examples 1 and 2.

E-mail Subject Line: Math 101 Name 2/16

1. What is the derivative of f(x)=x^3?
2. Let f(x)=x^(1/3) (i.e. the cube root of x). Use the graph of y=f(x) to explain why f'(x) does not exist at x=0.
Reminder:
• The mathematical solutions for Project 1 should be done by Monday afternoon.
• Read the guidelines and the checklist before beginning to write your letter.
• Begin writing the letter no later than Monday afternoon. It is not easy to do, and the more effort your group puts into it, the more helpful my comments can be.

Due Wednesday 2/18 at 10am

Section 2.3 Limits

To read: Through Theorem 6. Be sure to understand Example 4 and the definitions of left-hand and right-hand limits.

E-mail Subject Line: Math 101 Name 2/18

1. Let g(x)=(x^2-9)/(x-3), as in Example 2.
1. Is g(x) defined at x=3? Why or why not?
2. What is limit(g(x),x=3)? Why?
2. Is f(x)=|x| continuous at x=0? Why or why not?

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 3 to class.

Due Friday 2/20 at 10am

Work on Project 1

Reminder:

• Begin PS 4. This problem set will not be collected, but should be completely done by the beginning of class on Wednesday.

Due Monday 2/23 at 10am

Section 2.4 Using Derivative and Antiderivative Formulas

To read: All. Be sure to understand the definition of an antiderivative and Theorems 8, 9, and 10.

E-mail Subject Line: Math 101 Name 2/23

1. Explain in your own words what an antiderivative of a function g(x) is.
2. How many antiderivatives does f(x)=3x^2 have? Why?

Reminder:

• Begin studying for Exam 1 no later than this week-end (2/21 and 2/22).

Due Wednesday 2/25 at 10am

Bring Questions for Exam 1

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 4 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 Thursday.

Due Friday 2/27 at 10am

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 101 Name 2/27

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.

Reminder:

• Begin PS 5.
• Continue working on your draft of Project 1.

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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