Math is Super

This article really made me think about my future. It seems as though, if you want to be someone with influence in the world, your best bet is to become a math major. Baker talks of how math greatly influences the world we live in. Although i did not fully understand the relationship, I understood that it math is very critical in the world today. Most everything in our daily lives can be analyzed in number because of patterns that exist. Words, movements and emotions can all be described in numbers. Its all quite amazing. Businesses use these patterns to predict what we people want in order to sell products and such. Internet, for example, is monitored by computers that gather data from keywords that we type to build a sort of profile of each person in order to see what we want. These companies use the data to advertise their products. Though this analyzation of the internet, companies can find out what is popular among people fairly easily. This is a concern to many because it is in some way an invasion of our privacy.  There are debates regarding the monitoring of the internet and phones in congress. On the hand, these computers can pick up suspicious behavior that could help with the war on terrorism. Companies are working to protect privacy as well as get enough info to build good data. All these companies are at the frontier of the technological movement of mathematics playing a huge part in our daily lives. And the workers at these companies are kids straight out of college who are good at math. And they make a good amount of money if they score a big idea that another company wants to buy. Its a good place to be, which make me consider taking that route. Plus, the US needs more locals to be these math geniuses because so many of the people working at these companies are foreign born. Its also kind of scary how much math can do. How it can predict what people want and how it can pick up conversations through computers that were intended for few people. Our whole way of life is being converted into numbers. Although computers have the capability to cure illnesses and stuff in is important to note that eventually they may turn on us like they did in terminator, just a thought. In conclusion, like Baker states, it is a good time to know math because it is what is moving the world forward. 

Some nice pics

Super sick scribe post

Hey y'all. This is Wednesday's (27th) scribe post. Enjoy!

 

Firstly, we went over the quiz because a number of us did not do so hot. I was personally upset with myself for missing the first problem in which we were given a point of a function and asked what the derivative was. The derivative of a point is the slope of the tangent line so all I had to do was draw the tangent line and find its slope by counting squares. I do not know how I missed such a simple problem. Hurray to Bru for lowering the effect of quizzes on our grades.

 

Secondly, in class we went over what an Explicit function is. An explicit function or equation is the form that we normally write or see an equation. It is an equation that defines Y as a function of X.

 

 Ex. Y=2x+3

 

The expression on the right explains how Y is related to X. This is called an explicit equation because it comes from the same root as “explain”, which is precisely what it does.

 

 

An equation that is not set up in the “Y equals…” form, only implies that Y is a function of X and therefore, it is called an implicit function. Deriving an implicit function can be easier than deriving an explicit function depending on how the equation is set up. This is called implicit differentiation.

 

Ex.  Y-2x=3

 

To derive an implicit function: You do not have to reset up the equation. You simply derive the terms in the equation and replace Y with Y’. Then solve for Y’ and the result is your derivative. Lets try it out.

 

Y-2x=3     The equation

 

Y’-2=0       taking the derivative of the terms using the power rule.

 

Y’=2         Solving for the derivative

 

 

It is as simple as that, especially when you take the derivative of such an easy equation. And we can check if this is right by finding the derivative explicitly.

 

Y=2x+3       The explicit form of the equation

 

Y’=2           Finding the derivative using the power rule.

 

 

Now lets try the last problem on the exploration we were supposed to finish for homework. First let us solve the problem explicitly.

 

Y³=X⁷                         The equation

 

Y=X^7/3                        We must isolate Y for the right side to explain how Y is related to X. Now we derive

 

Y’=7/3X^4/3                                      Power Rule

 

So lets see if this matches up with the result we get from implicit differentiation.

 

Y³=X⁷                           The equation

 

3Y² x Y’=7X⁶                                We’ve derived the equation and multiplied all the Y terms by Y’

 

Y’=7X⁶/3Y²                                     We isolate Y’ so as to figure out what it equals

 

Y’=7X⁶/3(X^7/3)²             We know from the explicit equation that Y=X^7/3

 

Y’=7X⁶/3X^14/3                              Simplify and then simplify even more

 

Y’=7/3X^4/3                                      Check

 

                                                                      We must’ve done it right because Y’ prime equals the same thing when we solved the equation both explicitly and implicitly. Yay

 

 

 

So another day in the world of calcultopia comes to an end. Another battle won but many more lay in our path to the ultimate answer of calculus. $@… Or something like that. Next scribe is Winn Plot

 

J-tron foteen

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Experience Life

One's intelligence is often determined through scores on test or grades in school, which is okay but not ideal. Schools teach students skills that are considered important to succeed in life such as math, science and a good knowledge of our history and language. These things are important but I think what people really need to succeed is experience. People to need to see what is going on in the world. Traveling the world and learning from uncommon sources is essential in my opinion. School does a good job at preparing students for the future but people need to see the world for themselves. It is very common for students in europe to travel between grade school and college. A formal education doesn't necessarily get in the way of one's intelligence but I think that it may make someone naive to the world around them. In the US, it is not as common to take a year off because it is considered lazy. This is where I think a formal education inhibits one's intelligence. Many kids go straight to college before experiencing the world for themselves, if they travel at all, and don't apply the skills they learn to the world around them. The education students get in college will mean a lot more if they have a good amount of life experiences first. I think that it is important to travel and learn from other sources than a school teacher.

Product Rule

I thought that the textbook gave a good explanation of the product rule. The examples of the product rule being done on functions was easy to follow and it had a box stating the product rule verbally. "Derivative of first times second, plus first times derivative of second..And don't forget the chain rule". Although the textbook was good, the site I found was really nice because it had figures that moved and showed the product rule in affect. The figure showed the relation the two functions and their derivatives and you could manipulate the components. Overall, I liked the site better because of the figure but if I had not read the textbook first, I may have not understood the site as much. The product rule as the site stated, is {f(x)g(x)}^'=f(x)g^'(x) +f^'(x)g(x).

ex.  y = x²(3x+1)

First you take the derivative of the first equation (2x) multiplied by the second, which equals 6x^2+2x

Plus the derivative of the second equation (3) multiplied by the first, which is 3x^2

and it all comes out to 9x^2+2x.....I think

Let me know if this is right!

super sick map