Sunday, January 31, 2016

Calculus BC 2015-2016 January: Advanced Integration Techniques!

Calculus BC 2015-2016 January
Advanced Integration Techniques!
UNIT08 was all Integration By Parts, Integration By Partial Fractions and Differential Equations. We talked about several quotient rules for ln(x), arcsin(x), arctan(x) in addition to Integration By Partial Fractions. We applied these techniques to Variable Separable Differential Equations for Exponential Growth and Decay, Newton's Law of Heating and Cooling as well as Logistics! 

Don't forget limits involving L'Hopital's rule. Be 1 with your inner Lindsay Lohan!

We also got to play with slope fields to solve DiffEqus Graphically when all these great integration techniques failed to provide us with Closed Form Analytic AntiDerivative Functions. Last but not least, we wrote a program on the TI nSpire CX CAS for Euler's Method to solve DiffEqus Numerically! We used examples from the Harvard Calculus text to work on our Word Problems involving DiffEqus.


Units and Number Sense Mater!

Calculus BC + TI-nSpire CX CAS

Well, that's all folks!

preCalculus 2015-2016 January: Matrices and Linear Programming!

preCalculus 2015-2016 January

Matrices and Linear Programming!

We spent all of January on finding Points Of Intersection! We focused primarily on Linear Equations in 2D and 3D. As such, Elimination Method was King. So, we followed that with Augmented Matrices and Gauss-Jordan Elimination. Then we worked with Cramer's Rule. Finally we developed a Matrix Algebra and found we could solve Matrix Equations with an Inverse Matrix. 

Then we tackled nonLinear Equations with the Substitution Method and played with a simple case of John Nash's (RIP) Theorem: Linear Programming. Fun was had by all!

Number Sense and Units Mater!

NEW preCalculus + TI-84plusC

Well, that's all folks!

Friday, January 1, 2016

Happy New Year 2016!

Happy New Year 2016!
Now that it's 2016, I suppose that it's time for a New Year's Resolution: 

"I resolve not to get so upset every time I see a blatant disregard for the proper use of units!" 

This problem shows up everywhere. I think that you'd be very surprised by just how ubiquitous this issue actually is. Take a look at just a few examples below.

Verizon To The Rescue!
This audio clip, turned YouTube video, is one of the most infamous examples of this complete disregard for number sense and dimensional analysis. Suffice it to say that an approximate 36000 KB data overage times 0.002 cents per KB is billed at approximately $72???

Potato Farmer
Me: My dear sir, that's quite a sign you have!
Farmer: Why, yes, we are having a big sale.
Me: I can see that! This sale is amazing!
Farmer: May I interest you in some potatoes?
Me: Certainly, I'll take 100lbs.
Farmer: Dear me, how wonderful...
Farmer: Just a minute while I fetch 100 bags!
Me: Thank you, take your time, no hurry...
Farmer: There you go, done loading your car.
Me: Here you are, my good man...
Me: You get a nice new crisp $1 bill...
Farmer: What's the meaning of this?
Me: You did such a fine job, keep the change!
Me: I know, it's way too generous,
Me: but I think you've earned it!
Farmer: This is an outrage!
Me: No, no, you can keep the change. 
Me: After all, with the extra penny,
Me: you can get a whole pound too...
Me: with change to spare, no less!

Library Matron
Clearly, the Library Matron meant 10 cents per page printed from the PC Lab. However, under the unwritten rules of "Truth In Advertising" I would be fully within my rights to demand 10 printed pages for a single penny, no?

Deli Guy
The Deli Guy is guilty of the same gross negligence of proper units. Did he mean 50 cents per sandwich? Shall we just give him a pass? No, say I, no more Mr Nice Guy! We can't let this slide anymore. Keep this up and it will soon be the end of civilization as we know it! How about 5 cents for 10 sandwiches?

Tile Store
The Tile Store is guilty of this mortal sin as well? So, shall we pay our 69 cents per tile and meekly walk away shaking our collective heads without uttering so much as a single cough in derision? No, I will make my order and pay 69 cents for 100 tiles! Maybe I'll take 1000 tiles off the clerk's hands for a measly $6.90! Why stop there, how about 10000.... OK, ok, now this is getting out of hand!

Parting Blow
Sorry, I have no further commentary. This last example just takes the cake!

Wait, just when you thought it could not get any worse, there's more:

One more: this is opens up a whole other can of worms! This is a neighbor's mailbox. His street address is 226 Such-And-Such Lane.

Well, that's all folks,
A. Jorge Garcia
Applied Math, Physics and CS
2015 NYS Secondary Math PAEMST Nominee

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