## Saturday, May 24, 2014

### Teaching Math 4R: Calculus UNIT5A: Applications! (LAST POST THIS SCHOOL YEAR IN THIS THREAD)

Teaching Math 4R:
Calculus UNIT5A: Applications!

LAST POST THIS SCHOOL YEAR IN THIS THREAD:
Quarter IV Weeks 5&6: 5/12-5/23
We covered a number of loose ends in UNIT5A. We played around with Optimization, Related Rates, Accumulator Functions and Volumes of Revolution!

This is the last post in this thread for this year as next week is Final Review and then we have In-Class Finals. I think we had a successful year. You have all our ScreenCasts, SmartNotes and SAGE WorkSheets for the whole year right here in this post! However, next year I think I'm rerecording my ScreenCasts with my current mic. The beginning of the year had poor audio. Also, I think I can use SAGE more.

Hope you had fun learning SAGE with us this year. Have a great Summer, see you next year!

SAGE Calculus UNIT5A: Applications

Bye Bye Period 3, Math 4H preCalc
You will be missed!

Bye Bye Period 4, Math 4R-11 preCalc
You will be missed!

Bye Bye Period 7, Math 4R-11 preCalc
You will be missed!

Quarter IV Weeks 3&4: 4/28-5/09
We finished UNIT5 on Anti-Derivatives with a lot of python programming in SAGE for Riemann Sums!

Here's a number crunching version of nLRTE in a SAGECELL.

Here's a graphical version of gLRTE also in a SAGECELL.

These programs calculate Left Sums, Right Sums, Trap Sums and trap Errors. You can change f(x), a, b and n and recalculate everything on the fly! The graphical version, gives numerical output as well as a graph of the rectangles and allows for GUI input.

Quarter IV Weeks 1&2: 4/14-4/25
We started UNIT5 on Anti-Derivatives 2 weeks ago and will continue UNIT5 for 2 weeks more. UNIT2 was 2 weeks on the Definition of the Derivative. UNIT3 was 2 weeks on Product Rule, Quotient Rule and Chain Rule. Now, UNIT5 is 4 weeks on Definite and Indefinite Integrals, Differential Equations and Riemann Sums!

SAGE Calculus UNIT5 Anti-Deivatives:

Quarter III Weeks 7&8: 3/24-4/04
We finished UNIT2 of Calculus with the Definition of the Derivative as the limit of the Difference Quotient. We also started UNIT3 about the Product Rule and the Quotient Rule. We had fun on April Fool's day (see video 302). Chain rule in next week!

SAGE Calculus UNIT3 Derivative Rules:

Quarter III Weeks 5&6: 3/10-3/21
We finished CH3 Rational Functions. I always like to end preCalculus this way as Rational Functions is a rich topic for introducing limits at infinity and limits at a point. Then we started UNIT2 of Calculus with the Definition of the Derivative as the limit of the Difference Quotient.

We already figured out the Power Rule as well as the derivatives of sin(x), cos(x) and exp(x) not to mention 1/x and sqrt(x) which are really Power Rule anyway!

Take a look at our SagePub directory above. We've been using SAGECELL in class a lot lately. I've been saving these cells as worksheets on the Clemson server to share here.

SAGE Calculus UNIT2 Limits:

Quarter III Weeks 3&4: 2/24-3/7
We didn't get much accomplished these past few weeks with all the Snow Days and February Break! We did, nevertheless, get to finish the PreCalc text doing CH3 Rational Functions. We also talked about Linear, Quadratic, Power and Polynomial Functions. I love to end on this topic as its a nice intro to Limits! Next unit starts Calculus! We also started using the SAGECELL server (see video).

SAGE Chapter 3 Rational Functions:

Quarter III Weeks 1&2: 2/3-2/14
We didn't get much accomplished these past few weeks with a Delayed Opening and so many SnowDays of late! We did somehow finish CH4: Polynomials. We talked about Real Roots, Complex Roots and InEqualities. After February Break we'll cover CH3 Rational Functions before starting Calculus!

NOTE TO SELF:
BTW, we had problems scheduling our Midterm this year. I think that next year I'll leave CH5 for after Midterms so we have more time for Review! So, we will cover Chapters 12,11,10,9,4. Then we Review and have an in class Midterm. After Midterm week, we can cover CH5 and CH3 and then Calculus! We can be a bit more SAGE intensive next year too, now that I have all my SAGE worksheets. Maybe we'll try using http://cloud.sagemath.org or http://sagecell.sagemath.org too.

SAGE Chapter 4 Polynomials:

TI83 Chapter 4 Polynomials:

Quarter II Weeks 8&9: 1/13-1/24
We finished Chapter 5 all about Inverse Functions like Exponential and Logarithmic Functions. This week we worked on solving exponential and logarithmic equations as well as real world problems aka word problems and problem solving.

Next week is the last week of the quarter and then we have midterm week. As I look over Quarter II, I find that we had precious little time for SAGE in class. We focused on the basics of SAGE and python during Quarter I. This Quarter, I still used SAGE, but I posted my SAGE WorkSheets on Edmodo after class for those who still wanted to follow along any new topic with SAGE.

Our in class midterm was delayed until the week after midterms. So, there won't be much new here until 2/10/14!

Quarter II Week 7: 1/6-1/10
We continued Chapter 5 all about Inverse Functions like Exponential and Logarithmic Functions. We focused on using exponents to cancel logs and visa versa in order to solve equations!

Quarter II Week 6: 12/16-12/20
We started Chapter 5 all about Inverse Functions like Exponential and Logarithmic Functions. Of course, Friday was PreCalculus Caroling Day!

SAGE Chapter 5 Inverses:

TI83 Chapter 5 Inverses:

Quarter II Weeks 4&5: 12/2-12/13
We finished Chapter 9 all about CIS(theta) and Vectors. We focused the last week or so on dot products and cross products (see below)!

Quarter II Week 3: 11/25-11/29
We started Chapter 9 all about Vectors. Actually, we started with CIS(theta) and Complex Arithmetic! We stuck to reference angles mostly and no tech was harmed in the making of our screencast (as yet). It was a short week due to Thanksgiving. So, we had Take Home Tuesday on CIS(theta) and GAMEDAY on Wednesday. Fun was had by all!

SAGE Chapter 9 Vectors:

TI83 Chapter 9 Vectors:

Quarter II Week 2: 11/18-11/22
We finished Chapter 10 all about Conics. This week we focused on Parametric graphs and Word Problems. Next we will cover CH9 Vectors starting with CIS(theta).

Quarter II Week 1: 11/11-11/15
We continued Chapter 10 all about Conics. This week we focused on Polar graphs. We talked about converting General Form Conics to Polar Form instead on Completing the Square in the case of rotated graphs! Next weeks now is about Parametrics.

Quarter I Week 9: 11/4-11/8
We started Chapter 10 all about Conics. This week we focused on Completing The Square as a method to convert General Form conics into Standard Form Parabolas, Ellipses and Hyperbolas. We also focused on graphing Standard Form Conics without any tech! Next week is about Polar graphs and 2 weeks from now is about Parametrics. We're going to need TI83s or SAGE for that....

SAGE Chapter 10 Conics:

TI83 Chapter 10 Conics:

Quarter I Week 8: 10/28-11/1
We are finished with Chapter 11 about Matrices! We had a test on Friday. We are starting Chapter 10: Conics next week.

Quarter I Week 7: 10/21-10/25
We are almost finished with Chapter 11 about Matrices. This week focused on nonLinear Systems. Then we reviewed solving Linear Systems using Determinants or Matrix Inverses. We even had a preQuiz on Thursday and a Quiz on Friday on Linear Systems. Next week we cover the last topic in CH11: Linear Programming. The preTest this Thursday and Test this Friday will include all the nonLinear and Linear Systems as well as Linear Programming.

Quarter I Week 6: 10/14-10/18
We continued Chapter 11 about Matrices. This week focused on Matrix Arithmetic and Matrix Algebra. First we need to know how to add, subtract, multiply and divide before we can do the Algebra, aka Arithmetic backwards! BTW, we aren't really dividing, we're multiplying by the reciprocal. So, we used reciprocals to solve Matrix Equations.

Quarter I Week 5: 10/07-10/11
Out sick.... However, I did start using DropBox, see above!

Quarter I Week 4: 9/30-10/04
We started Chapter 11 about Matrices this week! We started by reviewing 2x2 Systems Algebraically and Graphically. Then we introduced Guass-Jordan Elimination using Augmented Matrices!

SAGE Chapter 11 Matrices:

TI83 Chapter 11 Matrices:

Quarter I Week 3: 9/23-9/27
We finished CH12 this week with a test! Our last topics included Proof By Induction and The Binomial Expansion Theorem!

Quarter I Week 2: 9/16-9/20
This week we covered Geometric Sequences and Induction! Included below you will find ScreenCasts based on TI83 and SAGE. I also have SmartNotes from the TI83 ScreenCasts as well as SAGE Worksheets for the SAGE ScreenCasts!

Quarter I Week 1: 9/9-9/30:
PreCalculus is all new this year:
(1) My preCalculus for Juniors classes started the school year with Chapter 12 this year! We start with Chapter 12 so we don't waste a lot of time reviewing topics from Chapters 1 and 2 which are about solving Linear Equations and Quadratics! So, when midyear is upon us, we can switch to Calculus without skipping important topics at the end of the preCalculus text. As such, we cover as much preCalculus as we can in the Fall Semester and as much AP Calculus AB material as we can in the Spring in preparation for Calculus next year!

(2) We are using a Computer Algebra System called SAGE instead of the TI83. The grand experiment this year is to see how well students learn the Math while learning to code in python at the same time!

(3) We will be learning a lot of python in class. You can learn some python code on your own too with this online, interactive textbook!

I actually have 2 different preCalculus classes. PreCalculus 4R and preCalculus 4H cover the same material and is comprised mostly of Juniors. The difference between these to groups is that 4R takes AP Calculus AB next year and 4H takes AP Calculus BC. Also, we cover material a little more in-depth for the 4H student and our tests may be a bit more challenging.

SAGE Chapter 12 Sequences:

TI83 Chapter 12 Sequences:

Well, that's all folks!

Sincerely,
A. Jorge Garcia
Applied Math, Physics and CS

Teaching with Technology,
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