Homework due 02/02/09

Do problems 12, 13, 16 & 19 on page 203.

Homework due 01/30/09

Do problems 11 and 17 on page 203.

Tips for Optimization Problems:

1. (a) Write down all that you know about a particular situation. This includes equations you can form and the constants and variables involved.

(b) Sketch any diagrams that help establish the way in which the quantities are related.

2. Figure out what quantity you are trying to maximize or minimize.

3. Find a function for this quantity in terms of the variables involved. In the case of more than one variable, try and express the functions in terms of only one variable through substitution.

4. Consider a reasonable domain for your function given the context of the problem. Check end behavior given the domain.

5. Find all Critical Points.

Homework due 01/29/09

After looking over the entire structure of the problem we answered in class which was to find the dimensions of the aluminum can, 12 oz in volume, that would minimize the surface area (amount of aluminum) used. Make sure you understand how we managed to verify that our values after using calculus were in fact the ones that would minimize the surface area. Then, consider the dimensions of the can we have found to be most economical and consider it containing soda. Next answer the following:

An actual can of Coca Cola is not a perfect cylindrical container and its dimensions do not correspond to those that minimize the material cost of manufacturing the can found above. The radius of an actual can is 3.413125 centimeters and height is 12.22375 centimeters. Why do you think that an actual Coca Cola can does not have the dimensions found by the optimization problem above?

History of Calculus - January 22nd

Dr. Adrian Rice has been a professor at Randolph-Macon College in Ashland, VA and is an emminant historian of mathematics, with 18th and 19th century math as his specialty. He received his Ph.D. from Middlesex University, London, in 1997. He also holds masters and bachelors degrees from King's College London, and University College London, respectively. He came to Randolph-Macon in September 1999 after having served as a visiting professor at the University of Virginia from 1998-1999, and a lecturer at Middlesex University from 1995 to 1998. For more information on Dr. Rice and his publications please visit http://faculty.rmc.edu/adrice/public_html/ .

He will be talking to us about the history of calculus; the circumstances surrounding its emergence, the key personalities involved and what other breakthroughs it has shaped. Please bring any questions you might have about the history of calculus and why it would be important to learn it. You can also generate some questions by commenting on this post if you would like for certain things to be discussed during his talk. We will meet in SAC on Thursday, January 22nd.

Take-Home Test Discussion Post

You may comment on this post to pitch questions about the test. The test is due Friday, January 23rd.

Homework due 01/15/09

Do problems on page 136-137; # 35, 37 & 44 - 47.

Homework due 01/13/09

Do problems 1, 2, 5, 6, 7 & 9 on page 136 of your textbook. You may want to keep your formula sheets or your notes from class on the rules of differentiation handy when attempting these.