Calculus Final Project 2010

Math is ruling the world

I'm not sure if I'm being sarcastic right now, but this article was truly interesting to me. It explained the close relationships between mathematics, numbers and our daily life containing internet.

Cover story starts with the giant title saying that math will rock the world which is totally true. It starts the article with the system that organize, and structures any written information published by its context, concept, and theme. By doing so, it says that it needs numbers and math to accomplish it. In one sense this sounds totally new to someone, but in other side, this is just a basic common sense that already has been known to the public.

Since the beginning of the construction of computer, math always has always been in people's life style. Like it stated in the article, math is essential to everyday life. Everything is organized with math equations, and everything is programed with algorithms online, and companies have been dealing with their costumers and products based on mathematical models.

Issue of privacy has to come right after that. In the several articles in the cover story it stated about how individual's privacy is becoming public by the development of technology based on math. People's lives have been monitored and gathered as a data for the bigger companies. This is one of the greatest fear that people might have. For the company they have to do this research in order to gain biggest possible profit that could be happen.

Mathematician will be the largest group of people who are ruling the world. It is true that most of the job will provide math skills. Highest rates of mathematics elites will gain the most profit. Math will rock the world; it has been and it will.

Scribe Post Feb 19th

Related Rates!!

Followed by last scribe post, in this post we will talk about the extension of Porky Problem.

This post will follow the exploration done in class: Section 4.9 A: Related Rates Warm Up

(http://www.ehow.com/how-does_4696774_credit-card-companies-use-calculus.html)

Review!

Calculus is the mathematics of change, and everything changes with respect to time.

In algebra we study the relationship between variables.

In calculus we study the relationship between the rate of change of variables.

There are infinite amount of scenarios that can be produced.

- A bathtub is filling at the rate of 2gal/min

- A balloon is deflating at a rate of 3 cubic centimeters/second

- A football is kicked with an initial upward velocity of 30yd/s

Lets translate these scenarios into mathematical models!

all theses scenarios are rates volume changing respect to time.

Now let's play with some real related rates problems!

Make sure you have the exploration in front of you!

Rippling Water Problem

- This problem deals with the radius of the circle, and the area.

Therefore we should write out the equation involving two different variables.

Let A be Area

Now we are using Implicit Differentiation

to express the rate of change of the area of the circle with respect to time t.

Process starts with stating that this equation will be derived with respect to variable.

Use chain rule to implicitly differentiate the equation.

This is the hardest part where everyone is having hard time, or at least some of us!!

It is simple, let's look at again.

- This is our original equation

each of variables, in this case A and r, is a function composed with t.

Since the letter r itself is a function, outside function is squared, and inside function is r

Using chain rule,

derive the outside, leave inside alone

- We get the result.

now we have to multiply the derivative of inside function, which is r'

However, since the function r is the function of t, we can also write out the derivative of r in different form.

It's the change in numerator over change in denominator.

This is why there is additional fraction representing derivative after each implicit differentiations.

This is how to do the implicit differentiation relating two different rates.

Rest of the question and answers are posted in Bru's post of Friday's class.

If there is any additional question, please let me know.

-Hyunhwa-

:0 Our next Scribe Post will be by Skirdude

See Math

Derivative of the inverse function and its application

1. Derivative of the original function is equal to the one over derivative of the inverse function with mirror point of the original function.

2. only if function f(x) is invertible.

3. Volume is an invertible function.

4.

5.

(1) Black :

(2) Red :

(3) Orange: : Tangent line of the V(r)

(4) Green : : Tangent line of the r(V)

6. Combine two tangent line equation

Data table shows that x value and y value is equal; therefore, this two tangent ling function is invertible and the the values of functions are reciprocals.

7. I attended the virtual class, because of the reason that the virtual class gives me more time to spend on the subject, and less pressure from other student.

Technology, Information, and Education

2. Mark Twain said, "Never let formal education get in the way of your learning." What did he mean by that? Is technology blurring the boundary between formal and informal learning?

People are curious about things that the formal education could not cover. Knowledge from school isn't what the whole world is filled with. There are lot more information that can be earned out of the school, and sometimes it is more beneficial to get outside of the formal education. Formal education is limited, it cannot provide every single aspect that individual seeks to earn, and here is where mark Twain's quote comes in. "Never let formal education get in the way of your learning." It can only mean one thing. Don't stop seeking for an answer when someone is trying to get just because school doesn't give an answer. Keep striving to find an answer even from outside of the school. Use what you can from outside to find and complete your thirst of knowledge.

Technology is getter better over the course of time flows. Our method of learning changed from social talking into getting it from the text, and now we are learning if from communicating with people who we have no idea who they are. We are in the world of online where the whole world is considered as one town. It is a town formed under the development of internet. Also this was the turning point of our method of learning. Instead of getting information from books, people ask questions to other people online. This led students to have their classes online as well. Students find the information online, do homework online, and even communicate people online.

Back to the question of formal education, actually because the technology is developed and our method of learning changed, boundary of formal education is no more clear enough to conflict our thoughts. Formal learning is what we get from school; however, by providing online classes and online blog posting as homework, we now have no clear boundary between formal and informal education. We all use the information off online, and it is all became our base of knowledge. Development in technology changed our way of receiving information, and it blurred the boundary of formal and informal education.

This is one article I found about how information has been presented to people, and how it will be.

Where is Everyone?

Product Rule

This forum post is showing the differences between textbook definitions and online definitions of the product rule. On our textbook, product rule was clearly defined with in the box. It also gave us the proof with the general definition of the derivative. It also provides simpler definition of the product rule with not only with letters, but also with words. On the other hand, online version of the definition of the product rule I found provided audio and video description of the definition. It was easier for me to understand with someone talking to me; therefore, I thought that online version I found had more clear description. However if someone wants to know more about product rule not simply about how to solve the problem, one should go through the textbook to learn about the product rule.

Product Rule:

Example:

Mind Map of Review on Semester One