PARTIAL FRACTION EXPANSION

[wagonwheel]

Can the TI-89 Titanium do partial fraction expansion?

For example: (S+5) / ((S+1)(S+3)) will solve into 2/(S+1) + -1/(S+3) which can now be Laplace transformed. NOTE: in the expansion I allowed S to = -3 and -1.

Thank you in advance for any help.

[DifEqRules]

F2 (Algebra) -> 2 (Expand) your expression

[dantegl]

I've been trying to do this and the expand comand with not work if the poles are complex conjugates. Anyone know of another method to do this? Thanks!

[expressbeat]

This thread is prob. dead, but in case anyone else stumble across it -

There is a way do it with complex roots but its somewhat time consuming, esp. if you're trying to do this with limited time. What I'd do is this:

First set the mode to Exact (Mode>F2>scroll down to Exact/Approx). Otherwise your Ti-89 won't separate all terms.

1. Determine the complex roots (you can use F2>Complex>cZeros() for this) and rewrite the expression with all the roots separated out. for example:

1/((x+5)(x^2+9)) = 1/((x+5)(x+3i)(x-3i))

2. Substitute all the i's with the letter i (alpha>9).

3. Use F2>Expand(). Wait until it's done.

4. Look through the result. You will get the right fractions, but there will be multiple polynomials for each term. For example, the x+3i fraction in the above example will look like this:

1/(10(3i-5)(x+3i)) - 1/(30i(x+3i))

5. At this point you'll have to collect the terms, which is the time consuming part. I couldn't use the built in algebra functions to do it automatically, so I had to copy-paste each pair of fractions by selecting it with the [up-arrow] button, then F1>Copy. However, if you isolate the constants and then Define i=sqrt(-1) you WILL get the right numerator for the quotient. For example:

1/(10(3i-5)) - 1/(30i)
>> Define i=sqrt(-1)
Done
>> 1/(10(3i-5)) - 1/(30i)
-1/68+5/204*i
>> approx(-1/68+5/204*i)
-0.01471+0.02451*i

which IS the correct numerator for the A/(x+3i) term.

If you Define i=sqrt(-1) too early the calculator will recombine some of the terms, and your numerators won't be constant. I couldn't figure out a way to prevent that.

As I said, good luck doing this on an exam with limited time. However, it very well may be faster than doing it on paper, and more reliable if you check your input. It may be a good technique to check your answers, e.g. if you do the expansion, and than type it in your calculator and isolate 1 root, and check if it's the same as the manual result.

Good luck.

[arrowvitaly]