Alex Smith

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These are answers submitted by Alex Smith

I checked your algorithm in MapleTA 4, and it seems to work fine in equation editor mode.

Did you try replacing "sum" with "add" and putting an evalf out in front?

Rx := x -> evalf(add( ( ln(x) )^k / ( k * k! * evalf( Zeta( k+1 ) ) ) , k = 1..100 ));

It would be easier to help if you directly provided what you call "Zeroes".

In the examples you cite, the first is not Lebesgue integrable whereas the second is, having value infinity.

So the answer to your question is probably that Maple has been trained to give responses for these two specific integrals that are consistent with this context.

 

If you create an eps file with Classic, then you can touch it up with LaTeX using the psfrag package.

Your command seems to work fine for me:

solve( N=sum(  z^j / (1-exp(-c / x)) ,j=1..infinity), z);

gives a good result.

I do notice that if you use "Sum" instead of  "sum" then you get  "warning:solutions may have been lost".

For your first question, try this:

 

A:=series(sin(x),x=0,10);

B:=series(cos(x),x=0,10);

series(A*B,x=0,20);
 

For your second question, look at this example:

a:=diff(tan(x),x);

b:=sec(x)^2;

simplify(a-b);
 

And for your third:

seq(coeff(A,x^k),k=1..9);

This should get you going.

de:={diff(y(t),t) = - 3*y(t), y(0)=2};

soln:=dsolve(ode,numeric,type=foreuler,stepsize=0.2);

soln(.2);

plots[odeplot](soln,[t,y(t)],t=0..5);

 

Yes, I see what you mean. It looks like the second solution is dropped.

However the dropped solution is this:

(x^2-1)^(n/2)

 

 

In this case, you can solve your equation mm for t terms of S. This allows us to use plot instead of implicitplot. We can also nail thing tighter by using fsolve to find the value of the independent variable S that corresponds to t=0.

Note I replaced S(t) by S in your equation mm.

mm:=(101/100)*ln(10)-ln(S)+10-S = 5*t;

 solve(mm,t);

 fsolve(%);

 plot([101/500*ln(10)-1/5*ln(S)+2-1/5*S,S,S=0..10.02093458],labels=[t,S]);

For the second question, you could use

 

 F:=proc(u,v);
        proc(x);
        sin(u(x)*v(x));
       end;
     end;
  

The you invoke it like this:

F(cos,ln)(Pi);

For the first question, maybe something like this:

 G:=proc(y);
          proc(x)
          y(x)*D(y)(x);
          end;
       end;
   

Then invoke it as follows:

G(cos)(Pi/4);

 

Maybe you want listcontplot, which produces a 2d-contourplot from numerical data.

?listcontplot

If you click on the graph, in the upper left hand corner you will see values for theta and phi.

Use these values as an option to plot3d:

plot3d(x+y,x=0..1,y=0..1,orientation=[90,60]);

You could also go about it this way:

with(plots):
setoptions3d(orientation=[90,60]);

 

Sure, something like $a = maple("0") might be overkill.

But I find myself frequently going back to my MapleTA algorithms and modifying them to make new ones.  I've found by experience that if I just make a rule for myself to consistently use

$a=maple("var") instead of $a=var, then code is easier and faster to modify, and I prevent surprises like the -0 you encountered.

Try this:

with(LinearAlgebra):
C:=k->Matrix(2, 2, [9*(1-k), 4*k, -4*k, 2*(1-k)]);
C(k);
lambda:=k->Eigenvalues(C(k));
lambda(.1);
plot(lambda(k),k=0..1);
 

Note that linalg is "old" and LinearAlgebra is preferred.

Reparameterize so the new parameters u, v fit the geometry of the problem:

 

u:=(x,y)->(x+y)/2;
v:=(x,y)->(x-y)/2;

plot3d([u(x,y)+v(x,y),u(x,y)-v(x,y),-abs(2*u(x,y))],x=-1..1,y=-1..1,axes=boxed);

 

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