Alex Smith

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One organizational problem I encountered with the Question Repository structure in MapleTA 5 is this:

Authors of questions in previous versions tended to organize the content into question banks with topics. So for example, there might be a question bank titled "Foundations of Differential Calculus" with a topic named "average rates" and another topic named "Set up Difference Quotient" etc.  Each topic would then have 5-10 questions with their own individualized name.

Now when  you import this content into the new MapleTA 5 Question Repository structure, the old  Question Bank name is dropped along with the Topic, and all you are left with is a list of questions identified by their individualized name, sorted alphabetically! So the old organizational structure gets flattened, and  questions gets completely jumbled.

My "quick" fix was to open up each question bank with a text editor and append each question name with a sorter. So for example, a question named "foo" in the Question Bank named "Foundations of Differential Calculus" was renamed "A: foo". Then when question banks were imported into the new Question Repository, at least some order was restored.

 

Needless to say, I think there was not enough beta-testing before MapleTA 5 was rolled out. You wonder if developers actually tested the transition with real users. I was told last summer that a fix would be forthcoming. So far I have seen nothing.
 

Here is one idea to do the conversion.

ex:=ln(cosh(t));

diff(ex,t); convert(%,exp); int(%,t); ans:=simplify(%-ln(2),symbolic); combine(%,ln);

This seems to work:

expand(cos(3*theta));

 

The "curve" defined by the equation x*sin(x*y)=x consists of hyperbolas y=c/x, where c=(2*k+1)*Pi/2, along with the y-axis, from the solution x=0.

 

So when x=0, dy/dx is undefined.

Try

 plots[animate]( plot, [sin(c*x), x=0..10], c=1..5 );
 

 

It is transparent from the initial post that this is yet another problem that can be traced to 2D input, especially given the * after VectorCalculus.

But I figure Maplesoft is sick and tired of hearing about this. They know the problem, and they  have decided to ignore-- it for as long as possible.

with (VectorCalculus):

x:= (r,t) -> r*sin(t);
y:= (r,t) -> r*cos(t);
z:= (r,t) -> r^2*sin(t)*cos(t);

 R := (r,t)-><x(r, t), y(r, t), z(r, t)>;

R(r,t);


r1 := diff(R(r,t), r);
r2 := diff(R(r,t), t);


dS:=simplify(CrossProduct(r1,r2));
 

I really miss Matthias Kawski's intdraw3d. Either of these links give background:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.41.7387&rep=rep1&type=pdf

http://math.asu.edu/~kawski/preprints/97mapletech.ps

It worked great for situations exactly like this. You can still make it work in more recent versions of Maple, but it's a little bothersome.

 

 

If you look at the MathWorld web site under Steinmetz solid, you will see equation (11) which is a triple integral for the volume.

By thinking about the limits of integration, you can assemble parametric representations for the components of the bounding surface.

Then you plot such a component by the construction

plot3d([x(u,v),y(u,v),z(u,v)],u=a..b,v=c..d);

For example, I think one component is

plot3d([x,y,sqrt(1-y^2)],x=-1..1,y=-sqrt(1-x^2)..sqrt(1-x^2));

 

 

You might find this thread illuminating:

 

http://www.mapleprimes.com/forum/reproducibility

It is difficult to understand exactly what you are doing. Let me try to rephrase to see if we are on the same page:

You have the ode diff(y(x),x,x)-(x3^2+x^2*x4^2)*y(x)=0 with initial conditions
y(x2)=exp(-x2),D(y)(x2)=1/2.

You can now get a numerical solution as follows:

x0:=1/2;x2:=x0/3;x3:=10;x4:=1;

sys:={diff(y(x),x,x)-(x3^2+x^2*x4^2)*y(x)=0,y(x2)=exp(-x2),D(y)(x2)=1/2};

soln:=dsolve(sys,numeric,range=0..1/2);

soln(.3);

Now you want to think of soln as depending on the location x2 where you are prescribing the initial values, correct?


And so you have y=y(x,x2) and would like to have the partial derivative of y with respect to x2, but now what exactly you want starts to get fuzzy. 

If x=0 and a(r)=-1, then x-a=1,and polylog(3/2,-exp(1))=-1.576.


In this case, your integral

0.014*(Int(r^2*polylog(3/2,-exp(x-a(r))), r = 0 .. 2)) is clearly negative.

Why do think it should be positive?

You could replace the last line with

NextZero(D(sin), 0);

 

I suppose the problem is that in t->diff(sin(t),t), you are using t as both a dummy variable for the differentiation and as a "proper" variable for the function definition.

 

Perhaps what you want is polynomial interpolation.

You can get help by

?PolynomialInterpolation

The basic example given on this help screen is

with(CurveFitting);
PolynomialInterpolation([[0, 0], [1, 3], [2, 1], [3, 3]], z);

MapleTA and Maple each have their own random generator. Here $rA=range(1,100) and $rB=range(1,100) are calls to MapleTA's random generator, not Maple's. Evidently, MapleTA's seed is not reset to the same value every time you call MapleTA. This is how we expect life to progress.

However, as Jay explains, every time you call Maple from MapleTA, you invoke a new session of Maple, so you get the same seed, and this explains the surprise of getting identical random matrices.  

So to answer your question, my approach merely exploits the MapleTA random generator instead of invoking Maple.

In these cases, I am always reminded of the hypothesis that our human brains are built on top of some sort of "old lizard brain," and that many of our unexpected actions can be explained by this model. I garner that there was some sort of "primitive" online system that was developed  by Brownstone Learning. This is the analogue of the "old lizard brain." Then Maplesoft  built MapleTA on top of this system, and put a "new brain" on top of an old lizard brain. Much of the difficulty and confusion that happens when we use MapleTA can be explained by this "merger."

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