I was playing around with Maple 11 and made something that some of you who are new to calculus might have fun with.
As already mentioned in my blog here, I'm new to this kind of math and very new to Maple and am currently just having a lot of fun playing around and learning a few things in the process.
You will need Maple 11 to use the worksheet. The worksheet can be downloaded via a link at either HTML page.
with Animated gif: AreaBtwnCurvesAnimated_AniGif.html
without Animated gif: AreaBtwnCurvesAnimated.html
That's a very interesting article.
Being a software developer myself, I have an opportunity to see both the usefulness and disadvantage of the use of software for the learning process, from both the user and developer point of view.
I doubt that there can be much of an argument in regard to the usefulness of not only computational devices, but also software as analytical tools. However, I believe that the usefulness or disadvantage of the same as tools for learning, relies upon a lot of issues. One of the main problems with the use of software isn't usually the software itself, but a user's lack of understanding of not just the software being used, but the use of computer systems in general.
Although the computer and it's software of today is multi-tasking, the interface is not as much so, as one is led to believe it is. There was a time not very long ago when, along with programming languages, entire computer systems became "object oriented". In other words, tasks were bundled together and referred to as "objects", creating a defined, yet somewhat obscure access to the individual tasks. In my opinion, part of the problem with some software developers these days, is the assumption that because they know where to look, and have more/less put reference material where it "belongs" within the piles of help style documentation, that a user will also know where to access it. I think it would make all software (including Maple) much simpler to use and especially to learn in the first place if it came with a wall chart showing the various paths to the desired destinations within the reference material. Much of the computer related hardware these days have even taken such an approach, but unfortunately, they have swung the pendulum in the other direction by providing such a "schematical approach" without including much, if anything in the way of written material.
The linearity of the interraction between user and software these days, can greatly impede the learning process, since the learning of the software can greatly interfere with the learning of that which the software is attempting to teach. Once the software is learned, then the advantage of the use thereof is much greater than would be possible without the software. The biggest problem is that the learning of computers and software, unless that happens to be one's field of study, is in itself a total waste of time, yet is required in order to reap the benefits of their usage. It's kinda like, if you were to give a hand-held calculator to someone who has always used an abacus and then asked him to perform a simple mathematical calculation. Something that would take a brief moment using the abacus, would require first the learning of the hand-held calculator before the calculation could be performed. Yet once usage of the hand-held calculator was learned, the ability to perform not only simple, but complex calculations using the hand-held calculator would greatly exceed the ability to do the same using the abacus.
I look forward to the day when mathematical computer software becomes object oriented, and the creators of it provide material in the form of wall charts, or something similar - which in my opinion make the learning process so much simpler and provides the leap to the actual benefit of the software much shorter. As mentioned, or at least implied, learning Maple, as with learning practically any software is simple for me because of my experience as a software developer. However, I can only recollect my early years learning computers and the software that make them useful, to have an understanding of the problems and resulting frustration that might be encountered by those with little experience with such things.
It would be my assumption that worksheet mode would always be at least slightly more dependable and less likely to have errors due to erroneous keystrokes and accidental or misplaced input from the mouse. More speed would seem likely, if for no other reason, due to the number and types of events that have to be looked at and dealt with within the type of "document mode" (that appears to be expanding and growing) that may have nothing to do with what the user might be wanting to accomplish.
It's an extremely complex task to take an application in the direction that Maple is taking their document interface - I give them a great deal of credit for having the courage to do so.
It would be my assumption that worksheet mode would always be at least slightly more dependable and less likely to have errors due to erroneous keystrokes and accidental or misplaced input from the mouse. More speed would seem likely, if for no other reason, due to the number and types of events that have to be looked at and dealt with within the type of "document mode" (that appears to be expanding and growing) that may have nothing to do with what the user might be wanting to accomplish.
It's an extremely complex task to take an application in the direction that Maple is taking their document interface - I give them a great deal of credit for having the courage to do so.
Tom - Thanks for your comments.
I know what you mean about the learning of c-pointers. That was a tough subject for me to grasp as well. Then came the learning of Object-Oriented programming - something my little pea-brain had an even tougher time with. Fortunately, the learning of such things is behind me, and I now have a great deal of appreciation for the existance of such a way of doing the things they were designed to do.
I found that the following, because of the plot display order, displays a filled area between the two of approximately.
(int(sin(x), x = 0 .. .8767))-(int(x^2, x = 0 .. .8767))
P1 := plot(x^2, x = 0 .. .9, filled = true, color = white):
P1b := plot(x^2, x = 0 .. .9+.3, filled = false, color = red):
P2 := plot(sin(x), x = 0 .. .9, color = blue):
P2b := plot(sin(x), x = 0 .. .9, filled = true, color = COLOR(RGB, .7, .7, .99)):
display([P1, P1b, P2, P2b], view = [0 .. 1, 0 .. 1])
a picture
Is there a function in Maple to quickly determine the point(s) of intersection between two plots?
I found that the following, because of the plot display order, displays a filled area between the two of approximately.
(int(sin(x), x = 0 .. .8767))-(int(x^2, x = 0 .. .8767))
P1 := plot(x^2, x = 0 .. .9, filled = true, color = white):
P1b := plot(x^2, x = 0 .. .9+.3, filled = false, color = red):
P2 := plot(sin(x), x = 0 .. .9, color = blue):
P2b := plot(sin(x), x = 0 .. .9, filled = true, color = COLOR(RGB, .7, .7, .99)):
display([P1, P1b, P2, P2b], view = [0 .. 1, 0 .. 1])
a picture
Is there a function in Maple to quickly determine the point(s) of intersection between two plots?
Carl, I downloaded the worksheet for the first pendulum a day or two ago and am still looking at it. The second looks even more interesting. You must teach a very interesting class!
I wonder if when Maple first loaded, McAfee asked if it should allow it access
and you inadvertently answered, "no". I've done something like that in the past.
If you think that may have happened, you may need to go into the settings for
McAfee and allow it access from there.
There's more about the required access at:
"http://www.maplesoft.com/support/faqs/Maple7/Installation/7.aspx"
I hope I'm posting this suggestion in the right place.
Being a C programmer, I wonder if I may be the only one who would like to see a simpler syntax for conditional statemets. For example in C, a statement or another conditional is always assumed to follow a conditional expression, so there is no "then" and an expression is always ended with the same bracket that it began with, so there is no "end if", "od", or "end"..
Tim
