ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Moko on October 18, 2012, 10:38:24 pm

Title: Eulers's Method-CAS?
Post by: Moko on October 18, 2012, 10:38:24 pm: I think it is possible to apply Euler's method on the Ti-nSpire CX because I've found it in the first section of the book button,
it says:

Euler(Expr, Var, depVar, {Var0, VarMax}

I have no idea what to put in...if someone can help out, that'd be awesome!
Title: Re: Eulers's Method-CAS?
Post by: Lasercookie on October 18, 2012, 11:12:53 pm: You're missing a few arguments there:

$euler(\text{Expr}, \text{Var}, \text{depVar}, \{\text{Var0}, \text{VarMax}\},\text{depVar0}, \text{VarStep})$

There's a bit more to it, but that gets it working.

$\frac{d}{d\text{Var}}(\text{DepVar}) = \text{Expr}(\text{Var},{DepVar})$

So depVar will usually be y, Var will usually be x or t.

$\{\text{Var0}, \text{VarMax}\}$ is your start / end point. VarStep is your step size. depVar0 is your initial y-value.

Let's try an exam question: VCAA 2010 Exam 2 MC Q12

$euler(\frac{x+2}{x^2+2x+1},x,y,\{0,0.1\},2,0.1)$ which for 0.1 gives an answer of 2.2, option E.
Title: Re: Eulers's Method-CAS?
Post by: Moko on October 20, 2012, 04:58:31 pm: Thanks a lot man :D...this will save a lot of time in the exam I'm sure
Title: Re: Eulers's Method-CAS?
Post by: VCE_2012 on October 29, 2012, 08:44:54 pm: Quote from: laseredd on October 18, 2012, 11:12:53 pm
You're missing a few arguments there:

$euler(\text{Expr}, \text{Var}, \text{depVar}, \{\text{Var0}, \text{VarMax}\},\text{depVar0}, \text{VarStep})$

There's a bit more to it, but that gets it working.

$\frac{d}{d\text{Var}}(\text{DepVar}) = \text{Expr}(\text{Var},{DepVar})$

So depVar will usually be y, Var will usually be x or t.

$\{\text{Var0}, \text{VarMax}\}$ is your start / end point. VarStep is your step size. depVar0 is your initial y-value.

Let's try an exam question: VCAA 2010 Exam 2 MC Q12

$euler(\frac{x+2}{x^2+2x+1},x,y,\{0,0.1\},2,0.1)$ which for 0.1 gives an answer of 2.2, option E.

Nice, I've design my own program using the spread sheet but it doesn't work when there's a y-variable in the DE. I'm just wandering, with the operator you've used to demonstrate how it works, would it work if there's a y-value in the DE?
Title: Re: Eulers's Method-CAS?
Post by: Lasercookie on October 29, 2012, 09:13:34 pm: Quote from: VCE_2012 on October 29, 2012, 08:44:54 pm
Nice, I've design my own program using the spread sheet but it doesn't work when there's a y-variable in the DE. I'm just wandering, with the operator you've used to demonstrate how it works, would it work if there's a y-value in the DE?
Just tried it then and it works for me. Play around with the function yourself (check the TI-nspire manual for more info on it, search for the pdf of that on google if you don't have it in hardcopy)