erik10

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.

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These are questions asked by erik10

Dear Maple users

I have been investigating the one-dimensional Wave Equation for the vibrating string with fixed endpoints. Before trying to use Maple for a solution, I surfed on Google and stumbled upon a solution given in a GeoGebra animation:

https://www.geogebra.org/m/eKkFV8uz

I succeded in making a similar animation in Maple. See the attached Maple file: The last line is out-commented in order for the file not to be too big (saving many frames...). Remove the # and recalculate, select the animation object and eventually resize it. Then hit the Play Button in the Toolbar. It should work very much like the animation above. 

Now my question: I assume the numerical solution is solved using the Finite Difference Scheme in the background? How do I receive the numerical data, which lies behind the animation? Is it possible to evaluate the solution at specific (x,t) points?

I am quite impressed that GeoGebra can solve this PDE, by the way!

Regards,

Erik

Wave_Equation_-_vibrating_string2.mw

Dear Maple users

I have a possibly quite easy question: How do I calculate or refer to a partial derivative evaluated at some specific point? The Maple documentation was no help to me in this regard. I hope the picture below indicate what I am looking for. I am using Maple 2D notation, but not excited about using the vertical line as evaluation. What ways can it be accomplished?

 

Erik

 

 

Dear Maple users

Let's say I want to plot a line containing a parameter, for example (a+2)*x+6, where a is the parameter. When using the following Explore command:

Explore(plot((a+2)*x+6, x = -5 .. 5, view = -10 .. 10), parameters = [a = -4.0 .. 3], initialvalues = [a = 1])

I will be able to change the value of a by using the slider. The actual value of a is currently displayed as well. Now, However, I want to have the current value of the slope of the line displayed as I move the slider. How is this done? When using a print command inside the Explore command the value of a+2 is not displayed, rather "a+2". Can I use some kind of component?

I hope someone can help. 

NB! I constructed this rather doll example, just to make it simple.

Regards, Erik

 

Below I wanted Maple to calculate the 4. degree Taylorpolynomium of a function f around x = 7. As shown below, Maple delivers a polynomial, but not a function definition. In other words one cannot have the polynomial evaluated at a specific value. The reason for this is obvious: The value 3 of x is passed to the command, implying 3 = 7 is a parameter to the command: Therefore the error message. I solved the problem by using the unapply command, but this operation is a bit tedious. I think I remember there is another more simple operator to make the same happen in Maple. I hope someone can remind me of that one!

Regards,

Erik

 

 

Dear Maple users

I was using the animation command to create an animation consisting of a running sine curve with a ball following the curve, as shown below. I wonder if it is possible to create it with the Explore command too? Or is this command more limited? I need to be able to add more animations, like I can with the display command ...

Regards, Erik.

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