use of differential eqs in computer science

[ehtisham]

example(equation) where diff.eqs. are useful in computer science

[Mike Dubbeld]

Not much turnover on these forums. Computer programs are sometimes used to solve DE's because they have no exact analytical solution they have to be approximated by iteration using numerical methods. As someone working in a corporation you might be asked to do this but if you are not familiar with DE's you would have a lot of trouble. Formulating DE's is more of an engineering thing.

 

Not only that but when you say 'computer science' you no doubt are pertaining to a Boolean-Church-Turing machine/digital beast. But there are such things as analog computers and that puts you squarely into the realm of differential equations. Continuous analog functions/block diagrams/transfer functions and feedback control systems. Electrical circuit analogs of billion dollar bridges and sky scrappers that have similar differential equations. It costs only a few dollars to build and test an electrical circuit but no one goes around building billion dollar buildings to see if they are structurally sound when built this way or that way.

 

Analog computers are far faster than digital computers and one example of such a beast is an air speed indicator and other pilot instruments. By learning systems engineering with block diagrams/transfer functions in the form of Laplace transforms to represent governing DE's of some system, given a set of initial conditions and boundary conditions you can brainlessly construct an algorithm for solution on a computer by numerical iteration/approximation of solution.

 

Any 6 year old can be a programmer. The same can't be said about formulating and solving DE's. Calculators use analog computers. They take things like the discharge rate on a capacitor as output and feed it into an analog to digital interface where it is digitized for LCD or LQD display digits. Also there is convolution and Fourier series - representing square waves by analog smooth waves - how do you modulate a set of pulses of digital output into a modem to be multiplexed with a few thousand other modulated signals and shot up to a satellite and sent to the other side of the planet and demux'ed and de-modulated on the other end? Wave superposition. Analog. DE's again. How does you CPU design interface with the outside world?

[D H]

Not much turnover on these forums.

Several reasons for a lack of an answer to this question.

• The OP asked a question that is too open-ended. Your answer is 25 times longer than the question, and you did not come close to giving a full response. I'm not belittling your post; a full response would require a book.
  
• The OP is too lazy to deserve an answer. He couldn't even bother to use punctuation. All it takes to find an excellent answer is a quick google search.
  
• The OP might well be trying to cheat. If you had answered in a timely manner you would have just done the OP's homework for him.

[Pangloss]

Yeah I agree with DH. That was a nice reply, though, Mike. Thanks for taking the time.

[Mike Dubbeld]

I think my answer is a good answer. I see the poster as likely complaining about having to learn DE's as a computer science major - what are they good for? I didn't see the post until recently and since no one else responded that makes my post about 100 percent better than the rest...... I don't really care if I answer homework questions either. A lot of times people think they can just get an answer on the web but for things in math and science on tests chances are you have to show your work and the person getting a homework answer will likely see the answer is so complicated that even if they do copy it they could not explain it in class and it will not help them on a test anyway.

 

It is for good reason there are so few people in school doing science and mathematics. I have a ton of math books but most of them totally suck unless you already know the subject. The arrogance in most math books is beyond belief --- "and so it is obvious that---" No, many times nothing about it is obvious in any way shape or form. Skipping 10 or 20 steps is not elegance it is lazy egoism. I have a bad attitude toward the priesthood of mathematics. (Another thing that irks me no end is how many mistakes authors make. It is very difficult to prove an author wrong when you are just learning something new.) Its simply not good enough in schools to teach without explicitly showing what good it is for which again is what this thread is about. I can take my knowledge of partial differential equations down to Borders Books and with about 2 dollars get a cup of coffee with it.....

 

Curiouser and Curiouser, cried Alice.

[peatantics]

Mike, I think you asked a reasonable question. "Not much turnover on these forums" is a statement not a question and in fact your entire question is rhetorical or self answering in my humble mumbled jumbled opinion. The vast majority of people on this planet know only how to push the buttons on their ""LITTLE BLACK BOX INSPECTOR GADGETS". The requirement to know how the object works is not needed since when something IS in or on or over or under or through or before or past it fails the answer is as they know is

The user of a system is the one who pays for that system. The number of users of that system make that system a viable proposition. A is A is YES I KNOW self referential. For it not to be circular would mean that iteration would soon become unpopular. While the wiki is available as a source material it at the very least is as good of a black box as we have ever known. Dennis Diderot after all offended the members of certain guilds on publishing trade secrets in his, the first Encyclopédie. n-joyed=peat<%~))>