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

Reading questions:

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

Reading questions:

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.
3. Check your answer to (1) by differentiating your result and seeing if your result and its derivative satisfy the IVP.

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

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

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

Reading questions:

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

Reading questions:

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.

No Reading Questions Today 6

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

• To read: All
• 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

Reading questions:

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!

No reading questions today!

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

• To read: All
• 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

Reading questions:

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

• To read: Re-read Sections 5.1 and 5.2
• Be sure to understand: Everything much better the second time around

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

Reading questions:

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

Reading questions:

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.)