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Wednesday, April 26, 2006

Perseverance


Would you agree? Have you had lots of perseverance lately?



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Sunday, April 23, 2006

The DaVinci Code Quest Sunday



It started last week. Google releases one puzzle each day for 24 days until the movie "The Da Vinci Code" is released in May. So far 7 puzzles have been released. You have to solve the puzzle to reveal a clue. Then you have to answer the clue question(s) to advance to the next puzzle. You can win a prize for solving all 24 puzzles. Now I realize this is all about marketing and they're really just trying to get as many of us as possible to go see the movie but the puzzles are really cool! Google searching often helps to find the answers. One of the puzzle questions can be answered using The Fundamental Principle of Counting and the very first (sudoku-like) puzzle uses a couple of mathematical symbols.

Challenge 1: What is the question that can be solved using The Fundamental Principle of Counting and how do you use the counting principle to find the answer?

Challenge 2: What mathematical symbol is used in the very first puzzle and what number does it represent? (Not the "delta," in a later puzzle it has a different meaning.)

You have to sign up for a Google Homepage in order to play, but that's a free and very useful service. After that you can begin the game. Click on the US button to start 24 days of fun! (Actually, 17 because you could work through the first eight today.) Don't forget to also find the answers to the Challenge Questions above!. ;-)



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Tuesday, April 18, 2006

Higher Order Derivatives




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Thursday, April 13, 2006

doing-- understanding---

Thank you so much for sharing what you are learning. I’ve been carefully reading your scribes trying to learn along with you, knowing that I’d probably understand better if I was on the “doing” end as you are when you are scribing. I remember this old saying:

What I hear, I forget.
What I see, I remember.
What I do, I understand. - Kung Fu Tzu (Confucius)


I’ve found this is very true for me, especially when I am learning something new on the computer, trying to understand how a teaching strategy might work, or teaching myself a new recipe.

I wondered--- have you found this is true for you also? How do you find your scribes help you understand all that you learn in calculus? Does “doing” help you understand in your other courses too? Or may be not?

Best,
Lani



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Tuesday, April 11, 2006

The derivative of a constant times a function and the derivative of a power function

The derivative of a power function




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Sunday, April 09, 2006

Four Colour Sunday!


You may have heard that any map can be coloured with four colours in such a way that neighbouring countries receive different colours. That it can be always done is one thing. How to do it is another. Are you ready to start colouring?

(Thanks again to Think Again!)



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Wednesday, April 05, 2006

Scribe! The Chain Rule, and song

Hi this is Van, and doing the weekly scribe. So, let's get this started. Yay!, no pictures to put in or make!, I love my job, anyways onto the scribe.



So, we started the class off with our 4 question, multiple choice quiz. 8 minutes long. Then we did practice questions. Which were:

a f(x) = 4x³- 1x²+5x - 7

b g(x) = (2x² - 1) ( x³ - 4x + 3)

c h(x) = 2x - 3
x² - 4

This is our first class after spring break, so I completely forgot about the Product rule and Quotient rule. So Mr. K teaches us a song that helps us remember them both. Here it goes.

The quotient rule you wish to know is lowdy high minus highdy low.
Put a line and down below
Denominator squared will go
The product rule you have in rhyme
Is one prime two plus one two prime

You sing it in a way, that makes it sound like twinkle twinkle little star.

So after the questions we are given a question that looks like this

x²-3x

We've never dealt with a problem like this before. So, we apply Function DeComposition and it looks like this.

f(x) = x
g(x) = x²-3x

We are then given a rule. For situations like this. It's called the Chain Rule. And the chain rule says this:

F(x) = f(g(x))
F'(x) = f'(g(x)) - g'(x)

So we implement this new found rule onto our question.

F(x) = x² - 3x
= (x²-3x)^½

f(x) = x^½
g(x) = x² - 3x
f'(x) = ½ x^½
g'(x) = 2x - 3

F'(x) = ½(x² - 3x)^-½ ٠ 2x - 3


So, after we went through our first example, we did another one

h(x) = (x³ - 3x)²
h(x) = f(g(x))
h'(x) = 2(x³ - 3x)(3x²-3)
= 2[3x^5 - 12x³ + 9x
= 6x^5 - 24x³ + 18x

That was using our chain rule. Here's if we do it manually without the chain rule.

h(x) = (x³ - 3x)(x³ - 3x)
= x^6 - 6x^4 + 9x²
h'(x) = 6x^5 - 24x³ + 18x

It may look easier, but Mr. K says, use the chain rule. It will be much more efficient when you advance further into Calculus.

Homework in the white and orange book is... all questions up to and including Page 77 and in the blue book is page 20.

Thank you, and next scribe can only be one other person... Temesgen. (2 person class, wee)

once again, I don't know how to place square roots over things. Annoying



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Tuesday, April 04, 2006

derivative of a quotient rule and derivative of a product rule


















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Sunday, April 02, 2006

Roboclaw Sunday!


Move the robot arm to pick up the ball. Clean, simple design. I got to level 19. I died. It's a doozy!



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Scribing once a week? Possibilities?


Van noted scribing once a week is a lot of work. Yes it is! How might an “idealist” confront the possibilities of those scribes?



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