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Education: UK
"Oz" wrote in message ... Gordon Couger writes Computers do away with the need for some calculus. You can just work it out the long way. Sure, and that's true of many real life problems. However if you don't understand the concept of calculus then you are doing it by rote. Further it's easy to simplify and find an analytic solution that should be close to the answer to check that your result looks plausible. One engineer was trying to find the volume of a stream profiles at different levels with a computer program. That is a classic area under a curve problem and she couldn't covert it to code. Since the data was on a X, Y data it was all straight lines. Each section of the stream could just be solve using the area of a triangle added to the are of he rectangle above it. When summed up in a recursive function it took about a half page of code and a hour to show her how to do it. Indeed. The very same method that, taken to the limit, is used to prove integration. Hmm, I can't quite see why recursion is needed if I understand the problem as stated. A recurcusive soluouton that goes all the way throught to the other side of the channel calulates the avergate and returns the area and return the area to the incantaion that called where it is summed wiht the area of that incantation and so on until the function fails back to the point it return the area in the stream. It is all done with volitile variables and no house keeping. There was a chanle and they want to fill it with number of levels of water and I could resue it without any dependance or effect outside the function its self. We had a lot of that kind of data and it could drop in anywhere with no side effects. I doubt she understood recursion but she did get the point about simplifying the problem. Quite. Mindless following by rote using tools you don't understand often results in someone getting cut. For an engineer anything difficult enough to require calculus has a look up table anyway In 8 years of solving problems for engineers I never used calculus once. Maybe they could solve the ones that needed calculus and just brought me the hard ones. It's more than that, often. Frequently simple calculus is used to generate the basic cell, which is then used numerically for the real (and thus often tedious, analytically) life problem. I set in on a course on open channel flow that the first words were you all know what vector is 6 of them define a point in space, 3 of those can be discarded because they are a mirror image of the other three and that is called a tensor and tensor will be noted this way. Then he spent six weeks defining a term u* then the math got hairy describing turbulent flow. Anytime I needed a complex function on a computer I reduced it to a look up table if at all possible because speed was always a problem. I have algorithms for integer square roots, fixed point trig functions and a host of other math tricks many that avoided division because of all the machine cycles it uses. These are for working on micro controllers that run at 2 MHz. The biggest use of them if for engine controller in automobiles. Of course the resolution of the data the computer reads is low and the granularity of its actions so course crude approximation of many trig functions and such work in many cases. Complex high resolution functions are useless when you out put choices are limited to 16. Gordon Gordon |
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Education: UK | sci.agriculture |