-1/2 is the real Bernoulli number. Maple is correct. //Georgios

Greetings. From the link above, the description of Post's formula states, "As can be seen from the formula, the need to evaluate derivatives of arbitrarily high orders renders this formula impractical for most purposes." With all of that said, using the Bromwich Integral might be a better method for higher orders of "s". > # Example 1 with small value of exponent(3): > restart: > L(s):=2/s^3; > ls:=exp(s*t)*L(s); > denominator:=factor(denom(ls)); > p:=solve(denom(ls)=0,s); > res:=px->residue(ls,s=p[px]); > res1:=res(1); > evalf(subs(t=10.0,res1)); The answer matches your procedure above. > # Example 2 with larger value of exponent(5): > restart: > L(s):=2/s^5; > ls:=exp(s*t)*L(s); > denominator:=factor(denom(ls)); > p:=solve(denom(ls)=0,s); > res:=px->residue(ls,s=p[px]); > res1:=res(1); > evalf(subs(t=10.0,res1)); Here we get an answer that matches what intrans(invlaplace) yields with the substitution of t=10. Because of the higher order of s, the procedure you have listed above does not return a numerical value. Regards, Georgios Kokovidis P.S. Welcome back to Maple. I missed your posts. Most of what I know in Maple I learned from studying examples like yours. Thanks.

Use another loop to create multiple plots structures, and then use "display" to show all of them on the same plots. As the number grows, the plot will start to look cluttered. > restart: with(plots): for j from 1 by 1 to 5 do grnumber:= x -> stats[random,normald](1): T:=1.0: n:=1000: dt:=T/n: t:=array(0..n): w:=array(0..n): g:=array(1..n): wt:=array(1..n+1,1..2): w[0]:=0: t[0]:=0: wt[1,1]:=0: wt[1,2]:=0: for i from 1 to n do t[i]:=i*dt: g[i]:=grnumber(): w[i]:=w[i-1]+g[i]*sqrt(dt): wt[i+1,1]:=i*dt: wt[i+1,2]:=w[i]: end do: a[j]:=pointplot(wt,connect=true): end do: > display(a[1],a[2],a[3],a[4],a[5]); Regards, Georgios Kokovidis

Use display multiple times: > with(plots): > a:=plot(sin(x),x=0..2*Pi,color=green): > b:=plot(2*sin(x),x=0..2*Pi,color=blue): > c:=display({a,b}): > d:=plot(3*sin(x),x=0..2*Pi,color=red): > e:=plot(1.5*sin(x),x=0..2*Pi,color=yellow): > f:=display({d,e}): > display(c,f); Regards, Georgios Kokovidis

Are you looking for the area under the curve over your range, or are you looking for the closed form solution. Be careful, because there is a square root in your function. The output of the closed form is in terms of Elliptic integrals of the second and first kind. The answer Maple gives you is accurate. For pure real, i.e. the area under the curve over your range, you can try the following: > with(Student[Calculus1]): > ApproximateInt(sqrt(1/x^4+1), x=1..2, method=midpoint, output=plot); You will get the answer that you are looking for (pure real). Regards, Georgios Kokovidis

I tried again with hardware accleration turned on. On my system, I do not see the problem. My only suggestion would be that your particular case is dependant on the graphics card that you are using. If turning off hardware acceleration fixes the problem, and you do not see a significant slow down in the ability to rotate your plot, then turn it off. The other suggestion would be to update your drivers for yourparticular graphics card and see if that helps. Regards, Georgios Kokovidis

It must be the version of Maple that you are using. I am using version 10.05 and I executed your code sample with the classic worksheet (cwmaple.exe) and the Maple 10 worksheet interface (maplew.exe). It works in both cases. I can rotate and then right click, and the program does not exit. I am also running Win XP Pro. What version of Maple are you trying to do this on (10.0x)? Regards, Georgios Kokovidis

Using a text editor, create a file called maple.ini and place it the the Maple sub directory called Users. There should already be an ini file there called maple10.ini. Do not confuse the two. You have to create the file yourself. On my machine I have the ini file installed at C:\EngineeringApps\Maple10\Users Your ini file could look like this: libname := libname,`c:/EngineeringApps/Maple9/lib`:with(plots); Regards, Georgios Kokovidis

Take a look at the word doc below, saved as Word 6.0/95 and see if the symbols look o.k. to you. http://www.mapleprimes.com/files/221_Infinity.doc Regards, Georgios Kokovidis

Differential Algebraic Equation - The index of a DAE is the number of differentiations needed to get a system consisting only of ordinary differential equations with no algebraic constraints. Regards, Georgios Kokovidis

Differential Algebraic Equation - The index of a DAE is the number of differentiations needed to get a system consisting only of ordinary differential equations with no algebraic constraints. Regards, Georgios Kokovidis

The code below is from a previous posting that I answered. You can cut and paste it into your worksheet, and then play with it to see what the different commands will do. ?plot, ?textplot, and ?display will give you more info as to why the code below does what you asked. > restart: > with(plots): > P1 :=plot (sin(x), x=-3*Pi/2..3*Pi/2, tickmarks=[0,0], title=`Plot of sin(x)`): > P2 :=textplot([[Pi,-0.05,`p`], [Pi/2,-0.05,`p/2`], [-Pi/2,-0.05,`-p/2`],[-Pi,-0.05,`-p`]], align={BELOW,CENTER}, font=[SYMBOL,10]): > P3:=textplot([[-0.1,1.0,`1.0`], [-0.1,0.5,`0.5`], [-0.1,-0.5,`-0.5`],[-0.1,-1.0,`-1.0`]], align={CENTER,LEFT}): > P4:=pointplot ([[-Pi,0], [-Pi/2,0], [Pi/2,0], [Pi,0],[0,1.0],[0,0.5],[0,-0.5],[0,-1.0]]): > display({P1,P2,P3,P4}); Regards, Georgios Kokovidis Dräger Medical

> with(plots): > ode:={1/100*diff(x(t),[t$2])+diff(x(t),t)^2=0,x(0)=1,x(1)=0}; > S:=dsolve(ode,x(t)); The above yields this as a solution: S := x(t) = 1/100*ln(t-t*exp(100)+exp(100)) > plot(1/100*ln(t-t*exp(100)+exp(100)),t=0..1); This shows the discontinuity near 1. Regards, Georgios Kokovidis Dräger Medical

> restart:assume(L>0): > dotpro := (psi,phi,L)->int(evalc(conjugate(psi)*phi),x=-L..L); > dotpro(exp(I/hbar*p*x)/sqrt(2*L), exp(I/hbar*q*x)/sqrt(2*L),L); > combine(%); > limit(%,L=infinity); 0 Is this what you are expecting? Regards, Georgios Kokovidis

I received an e-mail from Maplesoft. You have to have an extended maintenance plan active for your current license. If you do, you can go to the site below, login, and download. http://www.maplesoft.com/mapleemp Regards, Georgios Kokovidis