Teaching Math 4R:

Calculus UNIT5: Anti-Derivatives is Finished!

__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.

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:

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:

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:

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!

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:

__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!

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!

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__

__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!

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*

*http://shadowfaxrant.blogspot.com*

http://www.youtube.com/calcpage2009

2013 NYS Secondary Math PAEMST Nomineehttp://www.youtube.com/calcpage2009

2013 NYS Secondary Math PAEMST Nominee

*Teaching with Technology,*

*pastebin youtube slideshare*

*mathforum apcommunity*

*sage ebay*
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