Integration and derivation commands on HP-49g+



#7

I'm a bit confused about the derivation and integration capabilities of the CAS system with respect to indefinite math.

Please, can anyone confirm the following? (Of course these should work only with non approx flags set.)

for integration with respect to the X variable, use INTVX
for integration with respect to any other variable, use RISCH (BTW, what's the origin of this name?)
for derivation with respect to the X variable, use DERVX
for integration with respect to any other variable, use DERIV
Am I right? Is there any other way? Thanks in advance.

-- Antonio


#8

I have a 50G, but it should be similar to a 49G+.

The INTVX and DERVX commands (and other "VX" commands, such as SOLVEVX and SIGMAVX), use whatever independent variable is stored in {HOME CASDIR VX}. The default value for VX is "X", but you can change this to "Y" or "t" or any other variable, by adjusting the "Indep var" setting in MODE CAS. For example:

If you have X in VX, then INTVX(8) returns 8X

If you have Y in VX, then INTVX(8) returns 8Y

If you have t in VX, then INTVX(8) returns 8t

Since the VX commands automatically use whatever independent variable in VX, you don't need to specify the independent variable.

Alternatively, you can use DERIV instead of DERVX, or RISCH instead of INTVX. However, these commands ignore VX, and expect you to specify the independent variable. For example:

RISCH(8,X) returns 8X

RISCH(8,Y) returns 8Y

RISCH(8,t) returns 8t

DERIV and RISCH might be preferable if you were working with several different independent variables. Suppose, for example, that you were taking partial derivatives of functions with respect to X, Y, and Z. If you used DERVX, you would have to keep resetting the variable in VX. It would probably be easier to use DERIV instead.

The term "RISCH" presumably refers to the Risch algorithm for finding antiderivatives


Edited: 10 Jan 2007, 4:42 p.m.


#9

Thank you Norris...

For that wonderful explanation of the "VX" functionality...I was a bit murky on how it worked myself (this after reading the users guide!). I have one question: Why can't the users guide offer as concise and coherant an explanation as you just did??
Can you re-write the entire users guide in the style you just demonstrated and post it??? (just kidding of course...well, maybe...)

Best regards, Hal


#10

Sorry, I have no plans to rewrite the HP50G User's Guide. However, I do agree that it could be improved.

I wonder if perhaps the "Wikipedia" approach could generate some good free documentation for the 50G. There might not be anyone out there who wants to write a whole manual, but there might be lots of people in the HP community who would be willing to describe and review one feature at a time. Who knows, you might generate a User's Manual that was actually written by users.

Edited: 10 Jan 2007, 8:00 p.m.


#11

Nice job on integration. Wasn't asked or answered - as a part of efficiencies offered by the cas VX approach - I find it much easier To use the X variable when I can because of the assumption by cas of x also makes use of the x key in the 50 assumed alphabetic. This to me represents nearly half of the time gained, i.e. having the x key always shifted to alphabetic for the primary variable of integration, especially if you repeat that variable more than once plus dX.

Ron

PS That user-friendly feature was not on my 49 g+, only my 50.

Regards,

Ron

#12

Thank you, Norris,

very precise and helpful.

-- Antonio


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