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E-mail: seanbird@covenantchristian.org

Calculus Physics More

 

 Summer 2012 TI-Nspire & TI-Nspire CAS summer workshop Beginner level - Connecting Math & Science OR High School Mathematics

  Algebra Getting Started with the TI-Nspire Summer Institute 2012  at Covenant Christian High School, Indianapolis, IN

 

 

    The sections refer to Paul Foerster's Calculus: Concepts and Applications 1st ed.

    These tns files can be used on your computer with the TI-NspireTM CAS software (download for free 30-day trial). The software comes with the retail purchase of a handheld. DON'T throw this away.

      They can be saved and then sent to your handheld with the TI-Nspire software or using the free computer link software

    The files are designed to work on students' handhelds or software in the 'handheld view'.

TI-Nspire CX CAS Primer for OS3_2.pdf  updated Summer 2012 for OS 3.2. The corresponding Word document: TI-NspireCASprimerCX.doc

 

TI-NspireCAS primer.doc or pdf by Sean Bird - updated Aug 2010 for OS 2.1 Touchpad!!

A guide to learn the features and become comfortable with the TI-Nspire CAS, especially designed for TI-83/84 users. Page 11-12 are to be handed in on the first day of school. This assignment also will equip students with a philosophical motivation to study mathematics.

TI-NspireCAS primer w/ Reardon edit.doc or pdf (0.5MB)  - This is similar to the Calculus summer assignment I gave my students, but the 'homework' problems on the last pages are what Tom Reardon used at his public high school in Ohio (pg 13 has answers).  The majority of this document is still written for the 2.1OS, but you could especially use the last pages.

You are welcome to modify the Word documents to suit your needs. Please share your improvements/modifications.

 

Parent Night for Calculus - new in 2010,  1 page overview of calculus tns file

 

Scavenger_Hunt_TI_Nspire_CAS_Touchpad_CalculusBird.docx Get to know the Calculator page  (pdf)

You may want to install the Nspire fonts for Word documents to show up correctly.

 

What is Calculus?                12727    20min (1st day activity)
Local Linearity                       10890   10-15min (no tns required for this introductory activity)
X-treme Calculus Part 2      11488  40-45min (motion - CBR2 extension)
Exponentially Fast Deriv      11612  40-45min* (CAS active)
RelatingRates.tns                11643   45min*  typo in Word doc fixed Student.doc
Gettin' the Swing                   11689  40-45min (sinusoidal derivative - CBR2 ext.)
Helicopter Bungee Jump    11761  40min*
Infestation to Extermination 11856   40min* (exp growth/decay, DEs, CAS ext)
Sum Rectangles                  12100   15min (Riemann sums,  area "program")
FTC Changed History          12148   15-20min
Average Roller Coaster       12215  15min (average value & ave rate of change)
Area Accumulation               12241   15min for part 1
Volume by Cross Sections 12281   <15min for part 1
Slope Fields Forever            12321  20min (CAS extension deSolve)
Charged Up                           12369  20min (CAS deSolve, application of DEs)
[BC] Gateway Arc Length     12440  15min* (CAS)
[BC] Parametric Race & Slope 12516   15min*
[BC] Polar Necessities        12559   15min*
AP CalcExamPrep.tns         12624  20min*action-consequence-reflect(Click to the left for the tns file updated for OS 3.1, and the AP Exam format changes that began May 2011. Here is an improved student worksheet)    

I would also highly recommend any activity that is designated with the hand symbol (see ctrl click on the handheld). These files are Action-Consequence activities referred to as Calculus Nspired.

* means that the teacher notes of this activity sites which AP problems relate to the topic.

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I gave the following survey to my students on November 8, 2007, after they had used the TI-Nspire CAS for the first 9 weeks: TI-nspireSurvey.doc

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ParametricFriend.tns Parametric graphing on the TI-Nspire is shown with some visual enhancements

PolarFriend.tns This 'Polar Graphing Friend', similar to the 'Parametric Friend' above, is an aid to make teaching, learning, and exploring polar graphs easier with the TI-Nspire. I think the polar graph 'paper' on one of the first pages of PolarFriend.tns can be a valuable resources with the TI-Nspire Navigator.
I've even come up with a reasonable way to shade the area of a polar graph from 0 to some theta2. Some screen shots of this will be coming soon to my blog (3/24/09) 

 

Here are some of the tns files I've made and used in my AP Calc class '07-'08

Explor01_1.tns updated

Explor01_2.tns

Explor01_4.tns updated

Sec2_3.tns new Explores limits graphically, numerically (table) and algebraically - including epsilon-delta Sec2_3Nspire09.pdf  - screen shots from class notes

 

Explor02_4.tns updated dynamic file which explores piece-wise functions Limits from left & right, continuity, sliders.

Sec2_4.tns

Sec2.5 Pathman.tns and handout.pdf or doc

Sec3_6.tns

Sec4_1ProdRule.tns

Sec6_1.tns

 

derivsteps.tns This is a modification of a French file that I found on ti.bank.free.fr

The Aussie site http://www.interactivemaths.net/node/134 said this about it: "Type in your function and this clever TI-Nspire program will find the derivative and show all of the setting out. Marvellous!"

Sec7_4slopefield x+y ic dynamic.tns Thanks to John Hanna's slope field file on his Nspire site we were able to get a dynamic visual of slope fields and particular 'numeric' solutions from the initial conditions.

slopefield.tns

Sec7_5EulerMethod.tns  Numerical approximation method to graph a DE. This file introduces Euler's method and helps set up a spreadsheet.

 

BoxProbByBird.tns I've used this file to demonstrate the uses of Nspire and I began Section 8.3 class by having students work through this example problem that reminds them of a physics activity regarding buoyancy and a penny boat.

Sec8_3MaxMin.tns This Nspire document includes two dynamic problems:

an example problem (maximize area of a rectangle under a curve)

and problem #9 (minimize distance between origin and function)

Sec8_4bAreaBetweenCurves.tns

This document includes updates to Riemann Sum "programs" so that lrs2, mrs2, and rrs2(b,a,n) are defined for two functions. Once f1(x) and f2(x) are defined the area of the rectangle between two functions can be calculated for large n.

ALSO the proof for #17 is dynamically demonstrated - Area of parabolic region is 2/3 of the area of circumscribed rectangle.

area.tns updated Put this file in MyLib so that you can access the area approximation methods from any document. After refreshing the libraries, on the TI-Nspire CAS you can find the program in Catalog 6 (or Catalog 5 with the TI-Nspire) or type, for example area\rsa(b,a,n).  View some of the file as a pdf  areaRiemann.pdf  (See TI activity exchange - search 12100)

rs(b,a,n) is Riemann Sum from a to b with n subintervals. Delta x = (b-a)/n. Solutions are exact (if mode set for auto).

rsa(b,a,n) give approximate or decimal solutions for left, right, midpt Riemanns and trapezoid, Simpsons and numeric integral

rsa2(b,a,n) does the above but it finds the area between f1(x) and f2(x) where f1 is the higher function.

rsl(b,a,n) Riemann sums from the left hand.

rsr(b,a,n) Riemann sums from the right

rsm(b,a,n) midpoint Riemann sums

trap(b,a,n) trapezoid approximation

sr(b,a,n) Simpson's Rule

 

Sec8_5Volume&Area.tns

AP Calc problems on the Nspire

Sec8_5Vol10&12.tns  Dynamic volume by rotation

Sec8_5VolumeMC.tns Volumes of square or semicircle cross sections illustrated

Sec8_6VolCylShell.tns Animated and dynamic illustration of Cylindrical Shells method of rotated volumes. This is not on the AP exam. However, it is a beneficial topic to think about to see general methods of finding volume & discerning when one method is superior.

Sec8_7Arc Length Nspire ppt (modification of a Greg Kelly ppt )

Sec8_7ArcLengthProb30.tns Arc Length exploration

Section 8.9 Polar func+polar_tracing.tns (by John Hanna)

heart.tns  Some of the hearts are polar. But there is also a heart that is an implicit equation. Another one consists of radicals & inverse trig functions. Enjoy the following link for a summary or if you don't have a TI-Nspire HEARTS.pdf

Sec8_9prob13.tns  What 3 things are wrong with how the area was solved on the first page?

ch8studycards.tns Q&A about what you need to know regarding critical points, point of inflection, max/min problems, volume, arc length & polar. Helpful equation to know. Mostly taken from our Stuff You Must Know Cold

 

227bird.pdf Notes from my T3 Dallas presentation TI-Nspire™ CAS Primer and Calculus with TI-Nspire™ Technology and SMART Board™ Technology (Also available on my TTT & NCTM site )

 

Sec9.8Review.tns Reviewing integrals -Compare the area between 0 and k with k and pi. Also definite integral. Methods of integration. This file was designed on the handheld.

 

Sec12_04TaylorSeriesNspire.ppt (modification of a Greg Kelly ppt )

- CovenantBird youtube channel

- My Calculus site

- TI User Group site

- My blog with many Nspire articles

 

Instruction videos for TI-Nspire handheld and software

atomic learning ti_nspire

 

GREAT INTRO VIDEOS!!! This is interactive key- pressing practice.

 

 

 

 

 

 

 

 

 

Math Nspired

 

timath.com

 

Nelson Sousa's site

 

Piman's tipsNtricks

 

John Hanna's site

 

tiphysics.com

 

 

 

 

 

 

 

 

 

 

 

 

 

pathman

 

 

 

 

StudyCards-

theorems

Integrals

Critical Points & Volume...

series

derivatives

limits

 

 

 

PTT.ppt

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sliders_How_To.tns modified for the handheld from John Hanna (see above)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

last updated

July 18, 2012

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We celebrated my 8 year old's birthday after the Indy Nspire User Group meeting.