Scott03

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These are answers submitted by Scott03

With Maple 11, there is a package for importing data from an excel spreadsheet (ExcelTools).  The Data Import Assistant from the Tools>Assistants menu can also be used for this.  If the spreadsheet was exported as a delimited file, both Maple 10 and 11 can read in this file (see ImportData and ImportMatrix help pages).  Please note that only the numerical data is brought in, no formulas that used in the cells to get the values are imported in.  If you are just wanting data from one cell, you can just copy and paste into Maple.

If you combine Maple with the Database Integration toolbox you can connect Maple to "JDBC-compliant databases, such as Microsoft® SQL Server, Microsoft® Access, Sybase™, Oracle®, IBM® DB2®, and MySQL®".  More information can be found on Maple's webpage here.

 

Scott

The plotting with axis labels in multiples of pi is something new to Maple 11 and can be done fairly easily.  For example the tips and techniques that Maplesoft put out last April (can be found here) has a section on how this can be set.  As for drawing polygons with the angles labeled, to my knowledge there is no automatic way to do this.  One way is to combine the polygon plot with a Text plot with the angle values and the location to start the text.  The second option is to draw in the text after the polygon is plotted by using the plot annotation (also discussed in the above tips document).

 

Scott

Oops.  I am sorry that I didn't double check the Get statements before posting.

 Here is the updated worksheet

View 185_Maplet_det_updated.mw on MapleNet or Download 185_Maplet_det_updated.mw
View file details

 

Scott

Here is some simple code that may do what you are looking for.  This Maplet will give four boxes for a 2x2 matrix, a button to get the determinant and a box to the left of the button for the result.

This is a simple exampel and can be procedure could be rewritten to be more efficient.

 

Edit: Please see the post below for the corrected worksheet


Scott

One option to get both the solutions is with the avoid option for fsolve.  It would look something like this

fsolve([exp(x) - 2*cos(x) = 0],x=-3..3);

fsolve([exp(x) - 2*cos(x) = 0],x=-3..3,avoid=%);

 

This tells fsolve to avoid the solution that was given in the previous output (which should be the line above if it was executed first).

 

Another options is to use the Roots command found in the Student:-Calculus1 package.  The following will give both those solutions you were looking for in one output

Student:-Calculus1:-Roots(exp(x)-2*cos(x), x = -3 .. 3, 'numeric');

 

Scott

You can either plot all the plots at the same time by entering the following code:

seq(assign(P || k, plot(x*log[10](x^k), x = -5 .. 5)), k = 1 .. 3);
plots:-display([seq(P || k, k = 1 .. 3)]);

 

You can then use the code above to have an animation by just adding insequence=true to the display command.  So the command would be as follows:

plots:-display([seq(P || k, k = 1 .. 3)], insequence = true);

A better animation would be to use the animate command from the plots package as follows:

plots:-animate(plot, [x*log[10](x^k), x = -5 .. 5], k = 1 .. 3);

This has the advantage of liksting the k values at the top of the animation.

 

Scott

The FLEXlm program would only complain if you had a timed copy of Maple.  If you had purchased a cheaper 1 year copy of Maple as a student, this would happen but any permanent copies of Maple should never use this feature of FLEXlm of checking dates.  According to the documentation on FLEXlm from Macrovision

"FLEXlm detects when systems have had their dates set more than 24 hours back, and prevents users from using expired licenses by setting the clock back."

Therefore going across the date line shouldn't cause any problems (although I haven't tested this out personally).

Scott

Can you verify that when you entered the function that you entered either exp(x), chose the exponential function from the palette or used command completion?  If I entered just the normal e (that isn't exp(x), but actually a variable e that isn't linked to anything) I get ex/ln(e).  I don't know why it is squared.  Maybe something else is happening and the worksheet would help us narrow down what went wrong.

Scott

The two solutions are as follows:

1) Do a search of your hard drive to find the offending files that have a creation date that is future compared to your current system time and date.

2) Contact Maplesoft Customer Service to get another license file.

 

Scott

For those who are looking for the post that Doug was refering to, I believe this is the link you would be looking for.

Using DEplot to plot a phase portrait

Doug also mentions in this post to see the following post which also deals with the phase portraits.

phase portrait

Scott

If you wanted to approximate the integral to check your answer, the function in Maple is Student[Calculus1][ApproximateInt](...).  This function will have the options for the methods you had mentioned.  But it appears from your question that you are being asked to create a function for each yourself.  This page gives those methods nicely and should be quite easy to convert to Maple.

 

One quick attempt at the Rectangle method (which is the left Riemann Sum) would be the following:

myRect := proc (f, n, lower, upper)
local width, newF;
newF := unapply(f, x);
width := (upper-lower)/n;
sum(newF(lower+i*width)*width, i = 0 .. n-1)
end proc;

 

Scott

If you had defined y as a function like the following:

y:=x->x^2;

 

Then you can create an Array the following way (assuming you wanted the integer values between 1 and 5)

Array(1 .. 5, 1 .. 1, (i) -> [i, y(i)]);

 

Or if you want a Matrix type instead of an Array you would enter:

Matrix(5, 1, (i) ->[i, y(i)]);

 

Scott

First, to be able to post pictures or Maple worksheets, you should be able to use the Green arrow in the editor on MaplePrimes to upload files to the File Manager here one MaplePrimes.  Also, are you sure about your equation?  You had change in change in # workers/change in # cups smoothies?  Looking at the Wikipedia page for this function shouldn't it be the change in output over the input and in this case the # of worksers should be considered input.

 

Below is a worksheet that does both and use a ScatterPlot command from the Statistics menu to do the plotting.

View 185_ECO.mw on MapleNet or Download 185_ECO.mw
View file details

 

Scott

Now that you have seen the two surfaces from the previous plot commands, if you would like to see that curve that is the intersection between those two surfaces you could try the following:

> with(plots, intersectplot);
> intersectplot(x^2-y+z^2 = 0, y+z^2 = 1, x = -1 .. 1, y = -1 .. 1, z = -1 .. 1, axes = boxed);

 

The above will only work for Maple 11 since the intersectplot is a new command for Maple 11.

 

Scott

Save the plots to variable names and then use the display command in the plots package to display them both.

 For example you could try something like the following:

> with(plottools);
> l1 := arrow([0, 0], [10, 10], .2, .4, .1, color = green);
> P1 := plot(sin(x), x = 0 .. 10);
> plots:-display(P1, l1);

 

Scott

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