I am not aware of any Maple commands to create a 3D convex hull. There are commands in the geometry package for a 2D convex hull, but not 3D. I found nothing useful - for Maple - in a quick search of the web. Doug -------------------------------------------------------------------- Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

I am not aware of any Maple commands to create a 3D convex hull. There are commands in the geometry package for a 2D convex hull, but not 3D. I found nothing useful - for Maple - in a quick search of the web. Doug -------------------------------------------------------------------- Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

I have had no problems using Maple on my HP/Compaq tablet. In fact, I find the pen and touchscreen UI much preferrable to the traditional mouse. Doug ------------------------------------------------------------------ Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

I, too, have had my MaplePrimes sessions terminated. I am using FireFox: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.7.12) Gecko/20050915 Firefox/1.0.7 I have to login every couple of hours (each time I check back during the work day). Another request that I have is to be able to "convert a worksheet" without losing what has been typed in a response. On MANY occasions I have started to respond to a post when I realized that I should make some changes to the worksheet to be attached to the post. But, if I click on "convert a worksheet" I lose all of my response unless I copy my partial text to another window. Thanks for listening. Doug ----------------------------------------------------------------- Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

The quick answer to your question is that it is impossible to find the solutions to a general transcendental equation. A more complete answer requires additional information from you -- in what form would you like to see the solution?

The example given in your post is not very interesting. It is immediately obvious that any solution to sin(x)=x must occur on [-1,1]. A quick plot of the functions y=sin(x) and y=x

> plot( [sin(x),x], x=-Pi..Pi );

Shows that there is one intersection of these two graphs:

> solve( sin(x)=x, x );

It is a little more interesting to look for solutions to cos(x)=x.

>

> plot( [cos(x),x], x=-Pi..Pi );

Again there is one intersection, but there is no explicit representation for this solution.

> solve( cos(x)=x, x );

We can force Maple to give a little more information about solution.

> allvalues( % );

> evalf( % );

>

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Another example to consider is tan(x)=x. Now there are an infinite number of solutions (plot omitted - remember to set the vertical viewing window and to use discont=true to eliminate the vertical asymptotes). The approach suggested above yields only x=0. To find other solutions (in intervals determined from a plot, or other analysis) you could use fsolve, e.g. fsolve( tan(x)=x, x=4..5 );.

I hope this is helpful.

In my initial post I neglected to include the fact that the license includes a maplet launcher for Macintosh computers. This application makes it possible to have a maplet launched directly from a webpage. Doug

A first curiosity is that when I copied and pasted your code into a Maple 10 worksheet (in worksheet mode), the left square brackets in the first and third lines were not copied. Strange! I have not looked at the code being used by dsolve, but I do not see any mention of maxmesh in the online help (and search turns up nothing either). I found maxstep and minstep (on ?dsolve[Error_Control]. This help page, and ?dsolve[numeric], both give information about abserr. While I wish these pages would provide some indication of the default settings of abserr, but the error message does gives useful information. Here are the results I find:

>

>

>

Error, (in dsolve/numeric/bvp) unable to achieve requested accuracy of 0.1e-5 with maximum 128 point mesh (was able to get 0.13e-4), consider increasing `maxmesh` or using larger `abserr`

> J:=dsolve(BVP,y(x), type=numeric,method=bvp[midrich], abserr=1e-4);

> plots[odeplot](J,[x,y(x)], 0..1,color=blue,style=line,symbol=circle,symbolsize=12);

>

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Note that the inconsistent colorings and fonts appear to be caused by some invisible settings in the worksheet. While all input regions APPEAR the same in my worksheet (attached) I believe you will find that there are some 2d Math Input characters embedded in the document. Very frustrating! I hope there is something you can use, and that the shortcomings mentioned can be addressed in future enhancements. Doug ------------------------------------------------------------------ Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

I remember posting similar comments about Re many years, and many releases of Maple, ago. The answer at that time, and what I have used without fail since that time is: always apply evalc BEFORE calling Re, Im, etc. My understanding is that evalc forces Maple to return an answer in standard form (re + I*im); then Re, Im, ... work as one would expect. In addition, I believe that judicious use of evalc can be very beneficial for the efficient evaluation and plotting of expressions. One must remember that Maple, by default, is working with the complex valued definitions of functions but that (most) plots require real values. One of the side effects of evalc is that names appearing within the expression are assumed to be real-valued, unless otherwise indicated. See the online help for evalc, Re, ... for more details. Doug ----------------------------------------------------------------- Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

Alasdair, I sympathize with your situation. I have struggled with the same resistence from my students. The new Maple 10 interface contains many new features that should make Maple a little more student-friendly. I, personlly, am still trying to learn how to make optimal use of the new interface. An altogether different approach is to develop maplets for special types of problems that students should practice. Phil Yasskin (Texas A&M) and I have created a collection of 40 maplets for the first two semesters of calculus (limits, derivatives, integrals, applications, differential equations, sequences, series). The Maplets for Calculus collection is available for purchase through the MapleConnect program. To see the full list of maplets, and to view selected demo videos, please visit www.math.sc.edu/calclab/MapletsForCalculus.html. The direct URL to Maplets for Calculus is www.maplesoft.com/thirdparty/maplets_calc/index.aspx. If you have any questions, please send e-mail to me or Phil Yasskin (yasskin@math.tamu.edu or post to this forum on MaplePrimes. I hope this contains some useful information for you. Doug ----------------------------------------------------------------- Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

The Klein Four Group has a nice collection of songs with mathematical topics. I highly recommend Finite Simple Group (of Order Two). I just listened to Three Body Problem for the first time - quite enjoyable. I have not yet viewed any of the videos. The lyrics are original and, often, humorous. Doug ----------------------------------------------------------------- Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

Here are my comments on the source code that has been posted. I have not had a chance to test this, but these comments should help get you closer to a resolution of your problem. 1. All references to local MapleTA "variables" in a question should include parentheses around the name. My best explanation for this is that these values are substituted directly into the expression. This means that while it seems acceptable to enter x^$a, this produces a syntax error if $a has a negative value (e.g., x^-1). As has already been suggested, parentheses avoid this problem (x^(-1)). *** GENERAL ADVISE: When working in MapleTA it is important to realize that Maple is used only on the expressions that appear inside an explicit call to Maple. AND, these expressions are formed using the substitution rules of TA (NOT Maple). *** SUGGESTION: Instead of requiring users to learn about and remember to use parentheses, wouldn't it be easier to revise MapleTA's substitution rules to automatically include the parentheses? 2. While RESPONSE has the value of the user's response, ANSWER is not defined by MapleTA. In your question the "correct answer" is assigned to maple_answer. My recommendation is to replace maple=evalb($ANSWER-$RESPONSE=0);@ maple_answer=$A/(($k)+s)^$alpha +($B)*s^$gamma/(($l)+s);@ with maple=evalb(simplify($ANSWER-$RESPONSE)=0);@ ANSWER=$A/(($k)+s)^$alpha +($B)*s^$gamma/(($l)+s);@ The use of simplify is frequently helpful. In this case, in particular, it might be helpful to first call normal: maple=evalb(simplify(normal($ANSWER-$RESPONSE))=0);@ I have had occasions where it was easier to write my own procedure to test if a response is correct. Here is an example of how this can be done: maple=test_eqn := proc( a, r ) local eqn; if type( {a,r}, set(numeric) ) then eqn := simplify( a-r ) = 0; elif member(a,{infinity,-infinity,undefined}) then eqn := member(r,{`dne`,a}); else eqn := a=r; end if; end proc: evalb( test_eqn( $ans, $RESPONSE ) );@ Note that in this example the "correct answer" is stored in ans. I hope these comments are useful. Doug ----------------------------------------------------------------- Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

Here are my comments on the source code that has been posted. I have not had a chance to test this, but these comments should help get you closer to a resolution of your problem. 1. All references to local MapleTA "variables" in a question should include parentheses around the name. My best explanation for this is that these values are substituted directly into the expression. This means that while it seems acceptable to enter x^$a, this produces a syntax error if $a has a negative value (e.g., x^-1). As has already been suggested, parentheses avoid this problem (x^(-1)). *** GENERAL ADVISE: When working in MapleTA it is important to realize that Maple is used only on the expressions that appear inside an explicit call to Maple. AND, these expressions are formed using the substitution rules of TA (NOT Maple). *** SUGGESTION: Instead of requiring users to learn about and remember to use parentheses, wouldn't it be easier to revise MapleTA's substitution rules to automatically include the parentheses? 2. While RESPONSE has the value of the user's response, ANSWER is not defined by MapleTA. In your question the "correct answer" is assigned to maple_answer. My recommendation is to replace maple=evalb($ANSWER-$RESPONSE=0);@ maple_answer=$A/(($k)+s)^$alpha +($B)*s^$gamma/(($l)+s);@ with maple=evalb(simplify($ANSWER-$RESPONSE)=0);@ ANSWER=$A/(($k)+s)^$alpha +($B)*s^$gamma/(($l)+s);@ The use of simplify is frequently helpful. In this case, in particular, it might be helpful to first call normal: maple=evalb(simplify(normal($ANSWER-$RESPONSE))=0);@ I have had occasions where it was easier to write my own procedure to test if a response is correct. Here is an example of how this can be done: maple=test_eqn := proc( a, r ) local eqn; if type( {a,r}, set(numeric) ) then eqn := simplify( a-r ) = 0; elif member(a,{infinity,-infinity,undefined}) then eqn := member(r,{`dne`,a}); else eqn := a=r; end if; end proc: evalb( test_eqn( $ans, $RESPONSE ) );@ Note that in this example the "correct answer" is stored in ans. I hope these comments are useful. Doug ----------------------------------------------------------------- Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

Another way to see only the points in the plot is to use plot with style=points. This is almost the same as using pointplot but provides better access to the full range of options available within plot. For example, you can specify two or more sets of points in plot but pointplot can accept only a single collection of data points (you need to use display to combine plots created with separate pointplot commands). Doug ---------------------------------------------------------------- Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu

Another way to see only the points in the plot is to use plot with style=points. This is almost the same as using pointplot but provides better access to the full range of options available within plot. For example, you can specify two or more sets of points in plot but pointplot can accept only a single collection of data points (you need to use display to combine plots created with separate pointplot commands). Doug ---------------------------------------------------------------- Prof. Douglas B. Meade Phone: (803) 777-6183 Department of Mathematics URL: http://www.math.sc.edu/~meade/ USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu