In classic Maple the only other way is to draw the axis manually, as in How to control the thickness of axes and tickmarks thread. __________ Alec Mihailovs http://mihailovs.com/Alec/

That depends if you need it in the input or in the output. If you need it in the output, then type as I wrote it (with, maybe, \^ instead of ^, if ^ can't be typed otherwise) - it will look as x hat in the output. If you need it in the input, then first also type and then select, click right mouse button and Convert - to 2d-math or 2d-math input, depending on what you want. The semicolon appearing after it can be deleted after that. The only problem with that is that if you do that and then execute it, the hat in the output will be too high. To avoid that, you can first execute it in the form it is, and then convert it in the input to 2d-math input. Then they will both look nice. Another possibility, if you need it many times in the output, is to define

xhat:=`#mover(mi(x),mo(^))`;

and then use it as xhat. Then you will have xhat in the input and 2-dimensional x-hat in the output. __________ Alec Mihailovs http://mihailovs.com/Alec/

That depends if you need it in the input or in the output. If you need it in the output, then type as I wrote it (with, maybe, \^ instead of ^, if ^ can't be typed otherwise) - it will look as x hat in the output. If you need it in the input, then first also type and then select, click right mouse button and Convert - to 2d-math or 2d-math input, depending on what you want. The semicolon appearing after it can be deleted after that. The only problem with that is that if you do that and then execute it, the hat in the output will be too high. To avoid that, you can first execute it in the form it is, and then convert it in the input to 2d-math input. Then they will both look nice. Another possibility, if you need it many times in the output, is to define

xhat:=`#mover(mi(x),mo(^))`;

and then use it as xhat. Then you will have xhat in the input and 2-dimensional x-hat in the output. __________ Alec Mihailovs http://mihailovs.com/Alec/

See Maple doesn't start thread. __________ Alec Mihailovs http://mihailovs.com/Alec/

Will, Thank you, _________ Alec Mihailovs http://mihailovs.com/Alec/

That's what I meant talking about a bug. You should be able to do that using assuming, but in this example that produces some erroneous expressions. eval means evaluate. If you have an expression F depending on x and want to find its value, say, at x=1, that can be done as eval(F,x=1). __________ Alec Mihailovs http://mihailovs.com/Alec/

That's what I meant talking about a bug. You should be able to do that using assuming, but in this example that produces some erroneous expressions. eval means evaluate. If you have an expression F depending on x and want to find its value, say, at x=1, that can be done as eval(F,x=1). __________ Alec Mihailovs http://mihailovs.com/Alec/

If you don't know the formula for the area in polar coordinates that I used, you can get it from your double integral. For example,

Student:-MultivariateCalculus:-MultiInt(
r,r=R*cos(alpha)/cos(theta)..R,theta=-alpha..alpha);

                 alpha
                /        2         2           2
               |        R         R  cos(alpha)
               |       ---- - 1/2 -------------- dtheta
               |        2                    2
              /                    cos(theta)
                -alpha

Now, Maple has problems with evaluating this integral, so it can be evaluated manually using Fundamental Theorem of Calculus, as I did in the previous post. Now, sin(2*alpha)=2*sin(alpha)*cos(alpha), so the answer is generally the same as in your textbook. Also, you could obtain the integral above as

int(int(r,r=R*cos(alpha)/cos(theta)..R),theta=-alpha..alpha);

or using old student package as

value(student[Doubleint](r,
r=R*cos(alpha)/cos(theta)..R,theta=-alpha..alpha));

I thought that you already did something like that, so I suggested a way to evaluate it. __________ Alec Mihailovs http://mihailovs.com/Alec/

If you don't know the formula for the area in polar coordinates that I used, you can get it from your double integral. For example,

Student:-MultivariateCalculus:-MultiInt(
r,r=R*cos(alpha)/cos(theta)..R,theta=-alpha..alpha);

                 alpha
                /        2         2           2
               |        R         R  cos(alpha)
               |       ---- - 1/2 -------------- dtheta
               |        2                    2
              /                    cos(theta)
                -alpha

Now, Maple has problems with evaluating this integral, so it can be evaluated manually using Fundamental Theorem of Calculus, as I did in the previous post. Now, sin(2*alpha)=2*sin(alpha)*cos(alpha), so the answer is generally the same as in your textbook. Also, you could obtain the integral above as

int(int(r,r=R*cos(alpha)/cos(theta)..R),theta=-alpha..alpha);

or using old student package as

value(student[Doubleint](r,
r=R*cos(alpha)/cos(theta)..R,theta=-alpha..alpha));

I thought that you already did something like that, so I suggested a way to evaluate it. __________ Alec Mihailovs http://mihailovs.com/Alec/

Yes, it seems as if all 3 attached worksheets, Thomas Richard's, Joe Riel's and mine has disappeared. Nevertheless, the procedures from my blog, Ponder This, can be used. __________ Alec Mihailovs http://mihailovs.com/Alec/

It seems to be a bug in definite integration. As a workaround, you could find indefinite integral first and then evaluate it at the boundary values,

int(1/2*R^2-1/2*R^2*cos(alpha)^2/cos(theta)^2,theta);

                2              2           2
               R  theta       R  cos(alpha)  sin(theta)
               -------- - 1/2 -------------------------
                  2                  cos(theta)

eval(%,theta=alpha)-eval(%,theta=-alpha);

                  2          2
                 R  alpha - R  cos(alpha) sin(alpha)

When you paste something from Maple here, it looks nice if you type <pre> before that and </pre> after. __________ Alec Mihailovs http://mihailovs.com/Alec/

It seems to be a bug in definite integration. As a workaround, you could find indefinite integral first and then evaluate it at the boundary values,

int(1/2*R^2-1/2*R^2*cos(alpha)^2/cos(theta)^2,theta);

                2              2           2
               R  theta       R  cos(alpha)  sin(theta)
               -------- - 1/2 -------------------------
                  2                  cos(theta)

eval(%,theta=alpha)-eval(%,theta=-alpha);

                  2          2
                 R  alpha - R  cos(alpha) sin(alpha)

When you paste something from Maple here, it looks nice if you type <pre> before that and </pre> after. __________ Alec Mihailovs http://mihailovs.com/Alec/

I just wonder what if somebody visited 5 countries? Does it count as 5-10 or 3-5? __________ Alec Mihailovs http://mihailovs.com/Alec/

Will, Thank you. It is always nice to feel privileged. Will we get a special title to come with that (such as curmudgeon)? Alec __________ Alec Mihailovs http://mihailovs.com/Alec/

Certainly, I didn't want to say anything bad about Rosen's text. I didn't use it in my Discrete Math courses, but I might use it in the future. I was commenting on the code in the texts (and supplements) that I used, in Numerical Analysis, Linear Algebra, Probability and Statistics etc. In some cases the code was written by students and in some cases I don't know who wrote the code. Perhaps, it worked in Maple V Rel. 3 or 4 - I don't have any experience with them. The first version of Maple that I knew was Maple V Release 5. Also, I know some texts with good Maple code - Robert Israel's Calculus the Maple Way, for instance. I just didn't have a chance to use it (Calculus texts should be the same in all sections, and in the places where I taught, Stewart's Calculus was used - a very good text, by the way.) I could write good Maple (or Mathematica, or any other CAS, or Matlab) supplements (or textbooks) if I get paid for that (including benefits.) That would be a good idea, since I don't have a job since May. Unfortunately, nobody offered me such kind (or any other kind) of work. __________ Alec Mihailovs http://mihailovs.com/Alec/