Spring 2001, Math 101

April 2001

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

All section and page numbers refer to sections from Ostebee/Zorn, Vol 1.

Due Monday 4/2 at 8am

Practice Differentiating

• To read: Nothing new; review the product rule, the quotient rule, and the chain rule.
• To read for Tuesday's lab: The project I will hand out in class Monday.
• Be sure to understand: How to use the various rules. Begin to be able to combine them.

Reminders:

• Bring questions on PS 8 to class Monday. I will not answer questions on the exam in class, but would be delighted to answer any questions (or at least to give you hints) during office hours. PS 8 and PS 8.5 are both due Tuesday at 4:00 pm.
• The Differentiation Exam is Friday.
• Please come to Carol's help sessions and my office hours.

Due Wednesday 4/4 at 8am

Project 2

• Be sure to understand: what you're being asked to do.

Reminders:

• The Differentiation Exam is Friday.
• Look at PS 9 (individual).

Due Friday 4/6 at 8am

Section 4.6: Optimization

• To read: Through Example 5
• Be sure to understand: The discussion on pages 297-298 beginning with Local vs Global Extreme Values and continuing through Example 3

E-mail Subject Line: Math 101 Your Name 4/6

1. What is the difference between a cricital point of f and a stationary point of f?
2. Where can the maximum and minimum values of a continuous function occur on a closed interval?

Reminder:

• Practice for the Differentiation Exam, which will be at the beginning of class (don't be late--You'll only have 15 minutes to take it.)

Due Monday 4/9 at 8am

Section 4.6: Optimization

• Be sure to understand: Pay especial attention in Examples 3 to how the constraint y= - 2x+2 was used to change the distance formula from one of two variables (distance = sqrt(x^2+y^2)) to one involving only a single variable.

1. Read for Tuesday: All of Section 4.1
2. Be sure to understand: Examples 3 and 6.

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

1. Suppose you are trying to minimize the volume of a soda can, given that you want the volume to be 12 oz. What equation are you trying to optimize, and what is the constraint equation?

Reminder:

• Important: To get 100% on the Differentiation Exam, you have to pass it by 3pm Wednesday (that means it must be done by then!) So don't waste any time! Start coming to my office and re-taking it. If you don't know how to do something, come and ask me!!!!
• Bring questions on PS 9 to class Monday.
• Please come to Carol's help sessions and my office hours.

Due Wednesday 4/11 at 8am

Section 4.1 : Differential Equations and Their Solutions
Section 4.2: More Differential Equations: Modeling Growth

• To read: All of Section 4.1, if you didn't get it done for Tuesday. In Section 4.2, read Theorem 1 on page 256, the sections on radioactive decay and biological populations on pages 259-260, and the afterword: Discrete vs Continuous Growth beginning on page 264.
• Be sure to understand: Examples 3 and 6 in Section 4.1, as I mentioned for Tuesday. In Section 4.2, The statement of Theorem 1, and Examples 3 and 4.

E-mail Subject Line: Math 101 Your Name 4/11

1. Is y(t)=sin(t) a solution of the differential equation y'' = -y?
2. Find a solution to the initial value problem
y'=3y, y(0)=30.

Reminder:

• Wednesday is the last day to get 100% on the Differentiation Exam, so please come live in my office if necessary!
• Look at PS 10 (group).

Due Friday 4/13 at 8am

Section 410: Why Continuity Matters

• Be sure to understand: The statement of the Intermedate Value Theorem, Example 2

E-mail Subject Line: Math 101 Your Name 4/13

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

Reminders:

• Project 2 has been postponed. It is now due Wednesday 4/18 at 4:00pm.
• If you missed your chance to get 100% on the Differentiation Exam, don't miss your chance to get 80 points on it! The deadline for that has been postponed until Wednesday! Practice, come to me with questions, etc.

Due Monday 4/16 at 8am

Section 4.11: Why Differentiability Matters; The Mean Value Theorem

• To read: Through page 334. Really do read this for Monday, even though we haven't started talking about Section 4.10 yet -- we'll be talking about Section 4.11 on Tuesday in lab.
• Be sure to understand: The statement of the Mean Value Theorem, the section What the MVT says on page 333, Question 1 and Theorem on page 334.

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

1. What are the hypotheses of the Mean Value Theorem?
2. What are the conclusions of the Mean Value Theorem?
3. Explain the MVT using "car talk" (that is, position, velocity, etc).

Reminder:

• The last day to get 80 points on the differentation exam is Wednesday. After that, it goes down to 50 points -- but only until Monday 4/23.
• Bring questions on PS 10 to class Monday. As always, take advantage of Carol's help sessions and my office hours!
• Exam 3 is a week from Tuesday.

Due Wednesday 4/18 at 8am

Re-read Section 4.10 and Section 4.11

• To read: Re-read both sections and really make sense of what the IVT, EVT, and MVT actually say and mean.
• Be sure to understand: What we can do with the various theorems.

Reminders:

• The last day to get 80 points on the differentiation exam is Wednesday.
• Spread studying for the exam out over several days.
• Remember: ideal studying includes re-reading the text (taking notes on key ideas), re-reading class notes, doing the sample problems I give you, re-doing as many homework problems as possible, and looking over old exams to see what types of mistakes you made before.

Due Friday 4/20 at 8am

Section 5.1: Areas and Integrals

• Be sure to understand: The definition of the integral on page 342; Example 2; the section Properties of the Integral beginning on page 345

E-mail Subject Line: Math 101 Your Name 4/20

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? Why?

Reminders:

• Monday is the last day to get any points on the differentiation exam.
• Study!
• As always, the exam covers the current problem set, so get an early start on it.

Due Monday 4/23 at 8am

Questions and Answers for Exam 3

• To read: Re-read everything since Exam 2 (and, if necessary, prior material as well, of course).
• Be sure to understand: All of it!

Reminder:

• Do all the problems due Tuesday before Monday's class, as this new material will be on the exam.
• Work out all the sample problems I gave you, and begin re-doing as many homework problems as possible.
• Write down at least one question on the material to hand to me at the beginning of class Monday.
• Before the exam Tuesday, write a "cheat sheet" if you want to. Same rules as before.

Due Wednesday 4/25 at 8am

Section 5.2: The Area Function

• Be sure to understand: The definition of the area function on page 357; Examples 1 and 2

E-mail Subject Line: Math 101 Your Name 4/25

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)?

Reminders:

• Look at PS 12 (group). Re-doing Exam 3 is PS 12.5 (individual and optional).

Due Friday 4/27 at 8am

The Area Function

• Be sure to understand: Everything much better the second time around

E-mail Subject Line: Math 101 Your Name 4/27

Suppose that f (x) = 4x+2. Let Af(x) be the area function from 0 to x of f.
1. What is Af(1)?
2. What is Af(x), if x>0?

Reminders:

Due Monday 4/30 at 8am

Section 5.3: The Fundamental Theorem of Calculus

• To read: All, although you may skim the proof of the FTC beginning on page 373-we'll prove it a different way in class.
• Be sure to understand: The statement of both the first and second forms of the FTC; Example 3

E-mail Subject Line: Math 101 Your Name 4/30

1. Find the area between the x-axis and the graph of f(x)=x3+4 from x=0 to x=3.
2. Does every continuous function have an antiderivative? Why or why not?
3. What is the difference between a definite integral and an indefinite integral?

Reminder:

• Bring questions on PS 12 to class Monday. As always, take advantage of Carol's' help sessions and my office hours!
• Bring questions on PS 12.5 (re-doing the exam) to my office hours. Both are due Tuesday.
• The final exam is Wednesday May 9 at 2pm. I don't know as of writing this on January 9 where it will be. Check this spot again, or check your e-mail, or listen in class for the announcement.
• The final will be cumulative, of course. Begin reviewing now (or sooner) and get help on anything you never understood, or used to understand and don't anymore, or mostly understand ... (Please do NOT be embarassed to ask me about something from the very beginning tha tyou never understood! Better late than never, after all.)

Here ends the reading for April
Go to the reading assignments for May!

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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