Week #6
I know some of you are finding the material hard, especially the quizzes. Please continue to work hard, your efforts will pay off. Don't let minor setbacks discourage your desire to learn.
Remember Monday's a holiday!
New bonus questions have been posted, see the sidebar for more information. Number 2 is tough and number 4 is easy (use the definition for absolute value, and divide it into cases), at least I think so. The hint for number 2 is actually given in Example 1 (page 60) of Stewart's textbook. Again, you can work together on these, but you need to write up your own solutions.
At this point, you should be able derive the rules for differentiation that I presented in class. Also, please look at the textbook's proof of the Quotient Rule, and the rules that immediately follow it. The next rule we need to do is the Chain Rule, and for many that will be a toughest one. No proof will be given for the Chain Rule though. We'll also do the derivatives of the trigonometric functions and then finally implicit differentiation. Once the rules are written, we just need to practice them to work out the nuisances that perplex many students when taking derivatives of functions. Rules, however, are a lot easier than using the definition and I think most of you will agree after some practice.
Next week will largely entail working with the rules to find derivatives. If time permits we will use implicit differentiation to solve 'related rate' word problems.
P.S.: The holiday link is from MIT. Many of you may be interested, especially if you like alternative views on commonly held beliefs (this is also a must read if you can trace your roots to España or Taino indian.). However, lest you think the world is divided between evil and good, I leave you with a quote:
"There never was, there never will be, nor is there now, a man who is always blamed, or a man who is always praised."
This translated quote (original text in Pali) is attributed to Siddhartha Gautama in the Dhammapada, but in fact may have been culled from other sources.
posted by Ron Bannon at
10/08/2004 06:20:00 AM
6 Comments:
A brand spanking new survey this week, consider participating in this very unscientific and unofficial opinion poll.
By
Ron Bannon, at 7:24 AM
Oops... i did it again... unforgivable mistakes on the quiz. The material is presented clearly though... I guess I should brush up on my "anti-nervous" skills.
Gbenga
By
Anonymous, at 4:27 PM
Bonus problems (page 63, problems 2) often conjure up images of historical mathematics. With that in mind, I'd like to mention the oldest surviving and most influential text from Chinese civilization, The Nine Chapters on the Mathematical Art by Jiuzhang Suanshu. It was written more than 2,000 years ago and codifies (actually nine chapters worth) what the Chinese knew about mathematics at that point in time. In the eighth chapter, the techniques of solving beginning linear algebra problems (Guassian elimination which you learned about in MTH-119) is presented.
By
Ron Bannon, at 9:07 AM
Also do the extra credit work, they'll help even out the scores in the end. I know errors are easy to make, especially on quizzes and exams. Although more difficult, you should have less errors on the assigned extra credits.
Furthermore, everyone is encouraged to seek advice and help on the extra credits. Just write-up your own solutions.
By
Ron Bannon, at 7:34 PM
I wonder if the innocent looking TI-89, completely harmless (well except if you throw it at someone, >:)) will be allowed on tomorrow's quiz... it is important to note though that everyday the scientific world explores for new ways to make life easy. Now, I'm not advocating laziness, but believe if its there... use it! :)
p.s. i believe in, and adhere completely to the academic honor code.
Gbenga
By
Anonymous, at 5:01 PM
Well, maybe I'm just a senseless Luddite, and so I believe that science, or technology for that matter, has not made our lives easier. We have become dehumanized, and no longer know our place in this Universe.
Enough already, I guess tomorrow we should take a vote. But to be perfectly honest, tomorrow's quiz does not require a calculator.
By
Ron Bannon, at 6:54 PM
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