Texas Instruments: TI-36X Pro and TI-30X Pro Mathprint

 Essentially, the Texas Instruments TI-36X Pro and the TI-30X MathPrint are functionally equivalent.  What makes the two calculators different?

*  The TI-36X Pro is sold in the United States and in lot of the world, with the TI-30X MathPrint is sold primarily from Europe.  I ordered my TI-30X Pro MathPrint from the United Kingdom.  

Product pages from Texas Instruments:

TI-36X Pro (United States and Canada)

https://education.ti.com/en/products/calculators/scientific-calculators/ti-36x-pro

TI-30X MathPrint (Denmark, in Danish):

https://education.ti.com/da/products/calculators/scientific-calculators/ti-30x-pro-mp#specifications

Australia has a TI-30XPlus MathPrint, which is styled like the TI-30X Pro MathPrint, but without calculus functions.

https://education.ti.com/en-au/products/calculators/scientific-calculators/ti-30x-plus-mp?category=overview

*  Thanks to the body of the calculator being curved, the TI-36X Pro is slightly bigger than the TI-30X Pro MathPrint. 

*  The screen on the TI-36X Pro is a curved trapezoid, while the screen of the TI-30X Pro MathPrint has is rectangular.  

*  The TI-36X Pro has a circular arrow keypad while the TI-30X Pro MathPrint has a rectangular arrow keypad.  

* The TI-30X Pro Math print has black characters, while the TI-36X Pro has blue characters.

* The font on the keys of the TI-30X Pro Math are larger than than the font on the TI-36X Pro's keys.

Here are some pictures.

Either calculator is worth buying.  You  can see my review of the TI-36X Pro from 2011 here:

http://edspi31415.blogspot.com/2011/04/ti-36-pro-review.html

P.S. I still wish the TI-36X Pro/TI-30X Pro MathPrint had an alpha key instead of one key to press multiple times to get different variables.  That is my biggest gripe. 

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Calculus: Scaled Integration

Calculus:  Scaled Integration

Introduction

The take the integral:

∫( f(x) dx, A, B) 

The integral can be transformed to new limits C and D via linear transformation:

∫( f(x) dx, A, B) → ∫( g(y) dy, C, D)

Where the interval [ C, D ] has the smaller range than [ A, B ].

Set the transformation to:

y = m*x + β

C = m*A + β

D = m*B + β

Solving for m, β:

(C - D) = (A - B) * m

m = (C - D) / (A - B)

and

β = C - A * m = D - B * m

Solving y = m*x + β for x:

x = 1/m * (y - β)

Taking the derivative of both sides:

dx = 1/m  dy

The transformed integral:

∫( f(x) dx, A, B) → 1/m * ∫( f(1/m * (y - β)) dy, C, D)

Examples

Example 1:  

∫(x^2 - 5 dx, 10 ,16) but scale the integration interval to [1, 2].

A = 10, B = 16, C = 1, D = 2

m = (1 - 2)/(10 - 16) = 1/6,  1/m = 6

β = 1 - 10 * 1/6 = -2/3

x = 6 * (y + 2/3) = 6 * y + 4

Transformed Integral:

6 * ∫( (6*y + 4)^2 - 5 dy, 1, 2) = 1008

Example 2:

∫( e^x * ln(x + 2) dx, 0, 5) but scale the integration to [0, 1].

A = 0, B = 5, C = 0, D = 1

m = -1/-5 = 1/5,  1/m = 5

β = 0 - 0 * 1/5 = 0

x = 5 * y

Transformed Integral:

5 * ∫( e^(5 * y) * ln(5 * y + 2) dy, 0, 1) ≈ 262.8586594

Numerical integrals were calculated with the TI-36X Pro.  

When trying the Simpson's rule or Trapezoid rule, I find the smaller range does not really give better estimates.  But I am presenting the technique and if this helps in the future, great.  

Coming up:

July 11 - July 15, 2022:  TI-58 and TI-59 Week

Next Regular Blog:  July 23, 2022

Eddie  

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.