Seeking calculator suggestions for solving linear equations with complex coefficients

I had a TI-60 and a TI-68 years back that would do this. These were about $30 calculators, as I recall, and I don't think they are available anymore. At least I haven't seen them in a long time. (Maybe eBay?) I used the linear solving capability a few times just to play with it (new toy), but I really never used it much in actual practice. It just seemed easier for me to keep track of everything by putting it on paper. Easier error checking too. That's just me and personal preferences though. I'm sure with practice it would be a quick solve on the calculator.

Nels

...., he said judgementally.

Those of us who actually teach might disagree.

I have yet to see a calculator that can help with a problem like, "Prove that R[x] is a vector space over R."

dave

Tee-hee... I'm afraid you mean "... best possible within the constraints of the testing situation." :-(

My choice for "best possible" outside of that would be a high-powered notebook PC with a good CAS on it, such as Maple or Mathematica or MathCAD. It would also come with a full alpha-numeric keyboard, no extra charge. But it would probably be frowned upon during tests. (Darn.) However, for solving problems (both real-world and imaginary), these would have immense potential, well worth the (somewhat massive) time & effort needed to learn to use them.

-- Vincent Johns Please feel free to quote anything I say here.

I suppose that was really snobby of Michael to say, "With all respect." What did you want, somebody to come up and say, "Hey fella, I found that calculator you need for $19.95 at Wal-Mart, and I can bring beer and pizza over tonight and teach you to use it?" You got a very good response outlining an opinion that you probably don't need an expensive calculator to do lengthy linear equations, and you responded like a complete ass.

For the record, I like an HP-15C, but even then, I didn't really need it until I was required to do successive approximation problems. It has programming functionality which is what it sounds like you will need, and this should be available in a less expensive calculator. It also has reverse Polish notation, which is very handy for complex equations. Do you know RPN? If you really want a specific recommendation, you should ask your instructor.

About Michael's comment on entering the system of equations, you are probably going to have to do that pre-test, pre-class, when programming the calculator, provided you are given the form of the equations to be encountered prior to testing. If you don't have pre-made forms, then it's just as he says; it might be as easy to do it by hand.

Now, apologize to Michael, you lout. And no, I didn't smile when I said that.

There are a variety of Hewitt-Packard callculators that will solve systems of linear equations with complex cefficients.

The HP 49 series, for example will solve them either in equation form or matrix-vector form or augmented matrix form (by matrixrow reduction), and in exact or approximate form.

If a calculator is required for the course there should be a specified model, or models and this information should be available from the school. If not, I would question the quality of the school. If the instructor is incapable of setting proper specifications, he isn't much of a teacher.

I've got nothing against people using calculators to do error-prone arithmetic, but I would make two points:

(1) Solving systems of linear equations with complex coefficients has got nothing to do with calculators.

(2) If a test is a test of whether one has the appropriate calculator or not, it should be called that and shouldn't affect in any way affect ones grade in electronics.

That makes sense ...the source of reply, not the rightness of it. You must be far removed from reality. The calculator is a tool to be used on occasion. There are other tools thatr serve as well and beter in some circumstances. The myths surrounding the need for calculator and computer are being demolished daily. One of the best compliments I experienced was from a class where neither were used [although I have taught the use of both.] A year later, one student thanked me with, "We are teaching the other kids how to do their trig." You have no idea of what you speak.

Best Match for a high school student's needs.

For electronics (associate degree level) we just use a TI-36X solar. It does Log/anti-log for dB calculations, ENGineering units, fractions, sin/cos/tan,etc. I also bought a TI-84+ which as they said is a bugger to enter in complex problems and you would need to study the manual for it over Xmas break to understand it. I recommend a notebook with Matlab or MuPad(free) if the instructor lets you but ask first if it is permitted on the tests. TI-36X is best for doing 98% of all the problems you will see. Nanu5871

I think you will find that for the most part, TI-36X will do nice for calculations and MultiSim 7,8, or comparable will be best for the rest of the electronics stuff. I have never seen any electronics tech or engineer bother with using the TI-84,89,etc or other overpowered calculator. They always use a simple engineering calculator and simulation software. Save money, headaches, and stress....but if you insist, I would be glad to sell my TI-84+ silver edition for $129 to you...if you just gotta have the overpowered calculator in your hands. Nanu5871

No, it doesn't. But learning the means, methods, why's and wherefores does NOT mean that they are quick and easy to do by hand,accurately, under testing conditions.

Therefore, (Though I'm sure I wont' change the mind of a single instructor), either- give *purely theoretical* tests- no numbers at all. or- give *few enough* problems that the students will for sure have no trouble doing the math by hand. And, along those lines, since it is an artificially induced situation, make the numbers ones that don't turn into crazy huge-denominator fractions, etc. Instructors want to test for understanding, not calculating ability, right? That's why I think all-theoretical tests are the way to go. My engineering professors thru college often did that, and it sure didnt' make the tests easier.

you do have to know how to set up and solve a complex-coefficient matrix in order to even enter it into the calculator. If you want the students to prove that they can do complex-coefficient math by hand, that's another test entirely.

my 0.02, k wallace

that's exactly what my next point was, did you read it?

To use numbers that work out 'well' in the complex coefficient matrix, OR give few enough problems that you know they can be solved in the time alloted - since the point is not to test arithmetic skills, but understanding of the electronic circuits (which is where this all started, and where, with inductors IIRC, you have to know how/when to use them).

I don't know how many tests I took in college where I understood the material just fine, but there was SO much to do on the test that i was scrambling to finish in the time alloted. And I'm a med-to-fast worker.

k wallace

I think you might be missing the point. Fractions are taught using the simplest of values, so children can grasp the concept. You can use simple values without getting into some generalised algebraic form. The concept does not change when the values become more complicated [for them], but that does not validate teaching fractions using 177ths and so using a calculator that does fractions. What one does do is to use halves, quarters, thirds, fifths ....common smaller values and their multiples. Once the concept i learned *then* ny values will do. *Then* the concept can be generalised into algebraic form. So it was that geometry and trig was taught using simple radical values [and so the need to learn that arithmetic as well.] What could be simpler than the symbolic representation of sqrt(3) and sqrt(5)? It is still introduced using the simplest of values. The two triangles found in the geometry set still used in schools are sufficient to give a large enough sample of values to study trignometry on the whole. Using other values again does not validate the use of the calculator from the start.

Yes, the calculator should be used when the study develops into more "realistic" situations, but that comes next, not first, and to learn a concept, it is *best* to use simple values at first without any effort to learn something new at the same time. In the study of trig, for example, the study can be extrapolated *after* learning the basic concepts, using finer accuracy in measurement and calculation of angles, and so using the calculator to advantage.

I just picked up the Sharp EL-506VB on sale at Circuit City for $6.99 (Reg. $19.99):

http://64.233.161.104/search?q=cache:wC0TiDXL0lYJ:

I was mainly looking for just a simple "checkbook calculator" (and maybe for some whim-of-the-moment equation I may have churning in my head and I'm away from the 'puter! P=)--but at that price...

~Kaimbridge~

----- Wanted-Kaimbridge (w/mugshot!):

Perhaps we can agree to disagree on this a little, since there are valid arguments either way. Perhaps we agree that there is a use, but overuse is a considerable problem in junior and high school at least. I can certainly see the validity in college and university, but even there it is not something that must be worn constantly. There are problems of a type and nature that can be readily solved without.

Consider a simpler true case study: In high school, after much effort the student understood that to change from mm to cm he had to divide by ten. He *would not* let go of his calculator.

Anothr: The girl [family friends] who was in a pink fit, saying she "hated" geonetry ...just a few days befor her exam. She had gone through the study using Geometer's Sketchpad, a very useful tool. Tutoring her so that she could say, "Is that all there is to it?" took two hours and the old geometry set.

I can't speak for what you might have have to do, but although I saw others struggling mightily through an exam, I have on occasion finished the same exam with time enough to go over the results and then have still ample time to spare. One factor is relative preparedness, a factor I've seen as a teacher watching the efforts of many students over the years. We can be our own worst enemy at times. It can happen in the pressure of an exam, as the question becomes clear or not before answering. That is not to say that occasionally an exam can not be prepared thoughtlessly. It does say that it might also be a matter of perspective. Even with the calculator, I've seen those competent enough, but still not skilled enough to use it readily, and every effort is time-consuming. As with the study on hand itself, there needs to be sometimes inordinate time and effort spent in practice, and the tool can for some get in the way, rather than be an advantage. Again, it's a matter of perspective and relative ease of use.

....just one perspective. It's still a matter of the OP talking to the prof and getting the reply he wants ...do you need the claculator for the exam.

I absolutely agree with the above. Overuse (and use when *thinking* would be a better tool) holds kids in HS back from learning concepts, finding those 'shortcuts' that we do in our heads (all the trig root-two, root-three stuff I'm thinking of now) that lead to a complete and connected understanding.

regards, k wallace

Easy. The calculator is still useful after you graduate. :-)

I agree, the TI-89 works really well. When you are entering the matrix values using the matrix editor, you can even enter unreduced expressions, and in freely intermixed polar/rectangular form, which are solved and entered into the matrix cell by pressing the enter key. Then just use the rref function and you have your solutions.

-- john