I have a degree in Mathematics and Physics from the Danish University Aarhus, comparable to a masters degree with thesis - majoring in Mathematics. In 1991-92 I was a visting scholar at UCLA, Los Angeles, following graduate courses in Applied Mathematics. Since 1992 I have been a teacher in a high school (gymnasium) in Denmark. Special interests: Applied mathematics, graphics and popularizing Mathematics.

MaplePrimes Activity

These are replies submitted by erik10

@acer Thanks for your reply. I now realize the element-wise operator can be used in much more general situations than just multiplication of two lists! Good to know.

What I meant with my second question was if it is possible to solve equations for each item in the list. Lists E and m are given with units. I want a list m with units, which items are the solution to the equation E = 1/2*m*v^2. I know I can isolate m in the equation and use the ~ operator to get the list asked for. It would be nice though, if solve could be applied to each item in the list. NB! Students today aren't that good at manually isolating a variable, so it would be convenient to avoid it, if possible?



@Carl Love Thanks a lot, that solved by problem at hand. I was trying to make many calculations of the same kind at the same time, like in a Excel worksheet. Now for future use, I would like to extend my question.


1. question: What if I wanted to make a more general operation on every item in the list, say taking the squareroot of every item in the list, still including units?


2. question: Is it even possible making a list of solutions to a certain equation? For example:



and then using the formula E = 1/2*m*v^2 to find a list of velocities, v?




@Rouben Rostamian  Thank you a lot for your contribution. I apprciate it. The solution seems very good. I guess then that Least Square is the appropriate method to solve this kind of problem. 

After this succesful solution, let me take the question one step further: Now it might happen that a population is not in Hardy-Weinberg Equilibrium, but still the Least Square method will provide a set of solutions. Let's assume it is decided that the given Phenotype frequencies are subject to some error bounds (it could be absolutely or relative), then is there a way to decide if there are a solution for the allel-frequencies which imply the 'corrected' Phenotype frequencies to be within the bounds mentioned? (and provide the solution)



@jzivku I actually already have contacted, because I didn't get any response from here. I am waiting for an answer at the moment.


@Preben Alsholm Big thanks! First time I notice this LSSolve command. It works just great! It doesn't matter how many free parameters. Now I only have to consider if I should use it to estimate the elevation, the initial velocity and the Air resistance coefficient or maybe only the latter. By making a combined plot, including the Physical data and the theoretical curve (with "time points" added), I get a very good impression about the quality of the fit!


@Carl Love Maybe I was too loose in my description. In fact my discreet data is from an experiment with a throw in physics. Considering the ball to have an air resistance proportional to it's velocity, I want to find a coefficient of air resistance, named k. I wanted to make a fit with the theoretical solution, given initial velocity and elevation. This analytic solution have two coordinates depending on time: x(t) and y(t), assuming the throw taking place in a vertical plane. Obviously the fit can't be done seperately, because I will probably end up with two different optimal values for k! My discreet data consist of a column of times T and two columns of the corresponding x and y values, named X and Y. All data is imported from Excel.

Previously I have done the fitting in a manual way: Importing the X and Y column of data from Excel without any time data, making a combined plot consisting of the scatterplot of (X,Y) and the theoretical curve. Since the problem only involves one free parameter, it is not that difficult to manually find by simple trial and error, until the curve fits the data well. I just wanted to know if it could be done automatically in Maple? Also it would be very helpful in other situations containing more than one parameter! 

NB! The throw could also be modelled with a model in which the force of resistance is proportional to the square of the velocity. This is a different question, because only numerical solutions exixts here ...



@Preben Alsholm Your suggestion worked! I did place an abs around Drag, though, but that amounts to the same. Apparently Maple did try out some negative values of Drag and turned into troubles.

Besides adding output = parametervalues to the fit command did give me the optimal value of Drag.

Thanks a lot!



@Alex Smith You are probably right. Using this multiplikation factor will avoid the need for the lengthy convert command. And besides: the student will learn something!


A minor correction to the picture:



@Preben Alsholm 

As mentioned it was the person responsible for IT at our school who experienced problems. I will very soon test it myself. We are using Document Mode and 2Dmath. Also I will install Windows 10 from scratch (ISO file). I just need to take backup and clone my harddrive, not to take any chances ...



I read your comment on Windows 10 support from June. The man handling IT at our school has tested Maple 2015 on a Windows 64 bit machine and he received error messages. I haven't tried it myself yet, though. If this example is not unusual, it can be a severe problem, because students buying new Windows computers will likely buy one with Windows 10 pretty soon. And quite a few students will get into trouble. I think it is crucial that Maplesoft will produce an update before the the release of Maple 2016. It cannot wait until then, I am pretty sure. Also quite a few using Windows 7 or 8 might well choose the free upgrade in the coming weeks ...




It will not surprise me if there are some Maple stuff that won't run properly in the browser. But if part of it works it could be a good choice in that situation.

When dealing with stuff intended for my students there are no problems: Then we will use Maple itself of course (They all have a timelimited student license for it). So no need for Maple Player here.

The other completely different situation is when a user (not necessarily my students) find my website. Let's assume I have a Maple animation for them to watch, BUT they just need to download Maple Player via a link. Well, I think very few users, maybe 9 out of 10 will probably forget about it and just watch the other stuff on the page. It is my impression very few users will actually take the time or effort to download and install this application. Besides they might even be unsure of the security of this application? Not that many people know about Maple. 

So I hope I am making it clear: 99% of the time I am using Maple by myself or with my students - sharing mw files via MapleCloud. They even turn in homework solved in Maple! Then in 1% af the cases I would like to put an illustration or Maple animation on my website for (other) people to watch or interact with. Here I prefer it to run in the Browser.   

@Markiyan Hirnyk 

I didn't know about MapleWWW. It is definitely something I will check out soon. Thanks!



Forgot to comment on Maple T.A. We have had presentations for this tool at a Lecture. The idea looks very promising, but my impression is that it still lacks some 'ease of use' to get widespread. It is still a bit too complicated for ordinary teachers to produce quizzes of a medium complexity. Hopefully it will be improved in v11. Also I think it requires a 'package' or library of already produced quizzes, for people to start on ... 

When those obstacles are overcome, I think it will be very valuable for tests, but not the least for students to test themselves on a daily basis.





Thanks for reminding me that MapleCloud has gone viral, making it possible to sent another person an URL to find it. That is really a great step.

According to using MapleCloud, I have done so since it started up about five years or so ago :) In my classes, we have sent material to one another. Besides I have been using the Opaque option to use it to turn in test solutions.



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