OT: Memorial Day Math Challenge

Looks like you'd have to use the chain rule thrice over. Wolfram Alpha can't find a solution in any reasonable amount of time, the free Web version at least, so it seems unlikely to be anything nice.

Maybe if someone has a copy of Mathematica they could crank it through that.

d/dx A*tanh(B*sinh(x)) =

4AB*cosh(x)*cosh^2(B*sinh(x))/(cosh(2B*sinh(x)) + 1)^2, at least. Yuck.

Oops, that's the "alternate form." It's also AB*cosh(x)*sech^2(B*sinh(x)).

Huh? Isn't it...

d/dx A*TANH(B*SINH(x)) = A*B*COSH(x)/(COSH^2(B*SINH(x)) ...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
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| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 

             I'm looking for work... see my website.

A very good polynomial approximation to the tanh(x) function that I've used in the past, given by Maple, is:

(-.67436811832e-5+(.2468149110712040+(.583691066395175e-1+.3357335044280075e-1*x)*x)*x)/(.2464845986383725+(.609347197060491e-1+(.1086202599228572+.2874707922475963e-1*x)*x)*x)

This is over the interval 0 to 3.1. If you need a different interval the coefficients would need to be recomputed, but if you're using polynomial approximations taking derivatives will be much easier.

Yep ;-) ...Jim Thompson

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| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142   Skype: Contacts Only  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 

             I'm looking for work... see my website.

Yep, Wolfram spits out a bunch of different forms, and I was looking at the wrong one.

VIN = x

*TANH%28B*SINH%28Z*TANH%28Q*x%29%29%29

--sp

--
Best regards,  
Spehro Pefhany 
Amazon link for AoE 3rd Edition:            http://tinyurl.com/ntrpwu8

Thanks, Spehro! I had it, but was unsure of myself ;-) ...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142   Skype: Contacts Only  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 

             I'm looking for work... see my website.

' Hmm. How come it gives it to you but just sits there spinning for ten minutes for me? Not fair.

Maxima does it just fine:

2 2 A B Q sech (vin Q) Z cosh(tanh(vin Q) Z) sech (B sinh(tanh(vin Q) Z))

Jim, didn't they may you learn calculus in school? What, did you go and forget it?

--
Tim Wescott 
Control systems, embedded software and circuit design 
I'm looking for work!  See my website if you're interested 
http://www.wescottdesign.com

I didn't forget... it was just so messy, I was unsure of myself, and was using the group as a verifier.

I had five semesters of Calculus at MIT... all the way thru tensors... loved every minute and got straight A's ;-) ...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142   Skype: Contacts Only  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 

             I'm looking for work... see my website.

That's not a challenge, it's just mundane drudgery...

Supposedly this is a challenge:

Doubling Your Accuracy

An unbiased instrument for measuring distances makes random errors whose di stribution has standard deviation sigma. You are allowed two measurements a ll told to estimate the lengths of two cylindrical rods, one clearly longer than the other. Can you do better than to take one measurement on each rod ? (An unbiased instrument is one that on average gives the true measure.)

I think math can be a psychological event for some. Number 1 daughter absolutely freezes up during a math exam... but she got admitted to Scripps College (and got a grant) on the basis of her poetry ;-)

Strangely, she's very good at programming, as is number 1 son.

Number 2 daughter and number 2 son (now deceased) are calm creatures and whiz thru math. She's a chemist... what can I say ?:-}

My nightmare was economics... Samuelson no less... first pass thru... F, second pass thru... D :-( slept thru most of the class time. ...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142   Skype: Contacts Only  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 

                          In Memoriam... 
                       Duane Lee Thompson 
                October 31, 1972 - April 20,2006 
          4th Child, 2nd Son, of Jim & Naomi Thompson 
                     Victim of Colon Cancer

Hate to admit it, but I repeated the same calculus semester three times (twice at night) and never twigged. Too dependent on graphical analogies, perhaps - just couldn't trust (or remember) the tables. Got so that even the simplest forms froze me; just the SIGHT of the notation........

My younger brother won prizes........

RL

To program well requires a considerable aesthetic and literate capability.

Clifford Heath.

Measure the sum of the lengths (S) and the difference between them (D) (i.e. place the rods end-to-end and *measure* the sum and difference directly rather than measuring individually then adding/subtracting).

The longer rod has length (S+D)/2, the shorter rod (S-D)/2. Assuming the errors follow a normal distribution, the calculated lengths will have standard deviation sigma/sqrt(2) (i.e. the variance (=sigma^2) will be halved).

MIT has a bunch of its calculus classes online now. Its differential equations lectures are really good!

I've not accessed them, but I understand that MIT now offers _much_ course material on-line for free... including many EE courses. ...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142   Skype: Contacts Only  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 

             I'm looking for work... see my website.

Not common sense, and a familiarity with end-use?

RL