Calculus Final Project 2010

Ski Movie Final Project

The purpose of this final project is to help us understand related rates through teaching them ourselves. We are also hoping that we can help to teach others and challenge them to a new Related Rates problem. About all everyday scenarios, such as skiing, contain some bit of calculus. We are proposing a scenario, in which two skiers are skiing away from each other. We are going to calculate the rate at which the distance between them is changing. This problem was created by skirdude, secret and Flying Slug.

Two skiers are having an extreme day on Snowmass Mountain. They have been skiing together all day, dropping fatty cliffs and schralping mad gnar. Its the end of the day, and they are getting tired, so they now decide they both want to go down different runs. They are total math buffs and decide to turn this into an awesome Related Rates problem!

You can find our solution here!

And a big shout out to the crew at Aspen for being very patient with us and giving us tons of help!

Future Math

It seems to me that every year there is new, incredibly ground breaking technology. Math included. This technology always is portrayed as the "future." Its gonna change the world around us! Well, I believe that we do that by ourselves. We already have the technologies to change our world, how we use should be the most pressing issue.

Currently, everything we create is built in order to streamline the process. As shown in the article, shopping is included. The fact that a company has the rights to what music I'll be buying next, or my favorite author may, in fact, be quite frightening. I am a believer in the fact that the more this technology piles on, the more cautious we need to be about how we use it. Computers already have capabilities far beyond that of any human. As a race, we need to hold true to our roots. We must embrace technology in a way that we do not inhibit our natural tendencies.

I don't mean to be all superficial and such, but is this really that far from possible?...

Alright, maybe thats a little far fetched. But, I would say that we are likely on our way there.

I think that all this technology is definitely beneficial and could greatly change the world we live in. It has the opportunity to benefit all of us. However, I would stress that we should keep in mind where we would like to be, and where we are going.

Related Rates 2.0

What are Related Rates?

http://www.donself.com/images/confused-baby.bmp

A related rate problem has a few qualities:

a. 2 changing quantities

b. Hopefully enough information about those quantities

c. And (as with most Calculus problems) asks you to figure out the rate at which on is changing

There are a few tricks to helping you solve these most complex problems:

1. DRAW A PICTURE!

You might think your too cool for school... but guess what? Your not.

Drawing a picture gives you time to organize and think, which could help with a breakthrough.

2. Identify the quantities

Determine and label, which quantities can change (variables) and which are constants?

Again, keeping these organized is your road to success.

3. Algebra, Algebra, Algebra...

Write your equation... remember what you learned in Algebra? You should!

4. Calculus... your new friend

Use your newly sharpened Calculus skills to differentiate the equation. This should be easy as pie... right?

5. Find the rates of change

Dissect the problem. Find out what quantities could be rates of change (I'm talking about units here!)

6. Substitute!

Here comes the fun. Now you can work with your sweet equation to answer the problem.

Wait! Don't forget... this was a word problem if I remember correctly. Which means......?

Answer in a complete sentence, with units of course.

This is a good site to practice... in case you feel you need to work on your skills.

I know that this is the kind of problems we were doing last week, but just a little play by play to help anyone who is still confused out.

Don't forget the take home quiz assigned in class... all about Related Rates.

And we have a new final project about Related Rates coming up, so start brainstorming and coming up with fun creative ideas.

The next scribe will be Blitzen.

http://www.timtim.com/public/images/drawings/large/Skier.gif

-Skirdude-

Ski Math!

The Matterhorn

Glacier

Tiroler Grostle

The Bowl

Not here...

Choices, Choices

1. Derivative of the Inverse Function: For any point (a,b) on an invertible function the derivative of the inverse of the function evaluated at b is equal to the reciprocal of the derivative of the function evaluated at a.

2. In Symbols:

3. Volume of a Sphere:

Invertible? YES!

4. Inverse of a Sphere:

5.

Red:

Blue:

Green:

Orange:

6. (1/4pi) is the inverse of 4pi

7. Why Class? I chose to come to the class room because I know that otherwise I wouldn't have had the complete focus I have in class room setting. I know that, me personally, I need to have visual immersion in a subject, which class can do, and I even sometimes lose that focus in class, without all the distractions the online world has.

New Generation

I chose to assess the 4th question, asking "what should schools be teaching?" given the current changing technologies and young minds. After viewing the video, it is beyond obvious that the world is changing, and drastically. It is hard to even evaluate what we should be teaching students, because as stated, it will likely be outdated before they can even use the information. And if that’s not the case, there will likely be a computer that can do it for them. Maybe we should be working on how to defeat armies of Transformers like in the movies, so far that seems to be the only really likely outcome.

But actually, we are in need of some radical changes. I am under the belief that our generation could suffer a great deal if we do not change our motives. The challenges being left behind by our predecessors could prove to be beyond the abilities of our age group. We face problems such as, but not limited to, incredible environmental setbacks, immense economic responsibilities, and widespread international conflict. We, as a demographic, are the most influential and strongly recruited by companies. We posses much more influence than is recognized. Why not use this authority to change the industries?

My thoughts are that we should shift our efforts from teaching and focusing students on singular skills and careers, to cultivating brains that have the ability asses the current dilemmas. A generation of problem solvers who are incredibly motivated and ready for the tasks at hand. Currently, our generation receives so much pressure regarding our test scores, college choice, and early careers that many kids end up “burnt out” before they even have their first job. Instead, these students should be leaving school incredibly prepared and excited to change the world.

Awesome Product Rule Video!

I found this video to be exceptionally helpful. While the book did in fact strip everything of "frills," as previously stated, so did this video. It also provided examples, step by step, of different styles of a product property problem. The video used actual number examples, beyond "u" and "v", like the book does, which I find to be tremendously confusing. I'm hoping the source of this video, will be able to provide help with many more properties and rules.

Product Rule: Derivative of first times second, plus first times derivative of second

f '(x)= f '(x) • g(x) + f(x) • g'(x)

Example: h(x)= (sinx)(x^6 + x)

h '(x)= (cosx)(x^6 + x) + (sinx)(5x^5 + 1)

Best Mind Map 2010!