Hi, I have encountered a difficult question.

My answer is A=151,B = 47.

Could anyone tell me whether this answer is correct?

The question is as follow:

=∑((120n²+An+B)/(16ⁿ((512n⁴ + 1024n³ + 712n² + 194ⁿ + 15))  (n starts from 0 to infinity)

Thanks in advance.

Good morning sir.

I request your kind support to the above cited question.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Hi there..

I have a question on how to do a pointplot.

before plotting, I need to know the value of lambda[j] and  all the values of lambda already have.

so now I need to plot a graph with the values of lambda with different range and different colour,

Let say I have

> for j from 17 to 32 do k[j] := j+1;

x[j] := add(P[j, 1], j = j-1 .. j+2);

X[j] := add(P[j, 1]^2, j = j-1 .. j+2);

y[j] := add(P[j, 2], j = j-1 .. j+2);

Y[j] := add(P[j, 2]^2, j = j-1 .. j+2);

xy[j] := add(P[j, 1]*P[j, 2], j = j-1 .. j+2);

cx[j] := evalf(x[j]/k[j]);

cy[j] := evalf(y[j]/k[j]);

c11[j] := evalf(X[j]/k[j]-cx[j]^2);

c22[j] := evalf(Y[j]/k[j]-cy[j]^2);

c12[j] := evalf(xy[j]/k[j]-cx[j]*cy[j]);

C[j] := evalf(Matrix(2, 2, [[c11[j], c12[j]], [c12[j], c22[j]]]));

E[j] := simplify(fnormal(LinearAlgebra[Eigenvalues](C[j])));

if E[j][1] > E[j][2] then lambda[j] := E[j][2]/(E[j][1]+E[j][2]) else lambda[j] := E[j][1]/(E[j][1]+E[j][2])  end if;

lambda[j];

 end do;

the range of lambda [j] are as follows:

 0.02< lambda [j]<0.06

 0.06< lambda [j]<0.12

 0.12< lambda [j]<0.18

for i from 17 to 32, do if   0.02< lambda [j]<0.06 then green[i]:=P[i,j]; j:=i+1 elif

 0.06< lambda [j]<0.12 then red[i]:=P[i,j];j:=i+1 ; elif 0.12< lambda [j]<0.18 then blue[i]:=P[i,j];j:=i+1 end if;end do

how to do a point plot with the above situation so that in my plotting all the information are on the same graph.

All help is greatly appreciated.

Thanks

Im trying to plot the different values of shanks as points in this ] loop.

pp:=0.0:sumn:=0:sumnm1:=0:sumnp1:=0:

for i from 1 to 60 do

if(n>2) then sumnm1:=sumn fi;

if (n>1) then sumn:=sumnp1 fi; p:=1/evalf(2*beta*BesselJ(2,zeros[i])+epsilon*zeros[i]*BesselJ(0,zeros[i])+zeros[i]*BesselJ(1,zeros[i])); pp:=pp+p;

sumnp1:=pp;

if (n>2) then shanks:=(sumnp1*sumnm1-sumn*sumn)/(sumnp1-2*sumn+sumnm1) fi;

shanks;

od;

sumnp1: -2*sumn+sumnm1:

I have tried plotting it but it only plots the last value. 

Many thanks James

I have 2nd order nonlinear ode I try to solve with Runge Kutta 4th order method in maple but all I get from the out is 1 and 0.This is the equation: theta_ode.mw . How do I do it Or how do I write the code to solve it with maple using  Runge Kutta 4th order method?

Hello

I am not that good at english, but i will try to tell you what my problem is. 

I have a worksheet in maple where i can't find out to make the results appear. 

Maybe it is easiere for you guys to help me if i can send you the document. 

Looking forward to hear form you

Regards

Niclas 

Dear All,

please help me with my problem. i have quite a big program all parts of which are distributed in the several code edit regions and in the main text. i'd like to find all occurenses of gven text in all open documents including code edit regions. i know how to do it manually by openening each code edit regiong and pressing Ctrl-F. however it is very time consuming and defocuses me apart from my main tasks. i'd prefer to use some combinations of 'hot keys' on the keybord or one or two mouse clicks as for example in MS Visual Studio.  

I am creating a plot in Maple17 which will include many line segments and polygons.  I want the axes to be equally scaled, so that line segments that are perpendicular actually look perpendicular.  When I view what I have created so far, line segments that are perpendicular do not appear to be so in a plot, even though I used the "scaling=constrained" option several times.  I created a stripped-down file that isolates the problem.  Here it is:

Download perp.mw

An angle that should be a right angle looks obtuse in the plot.  I used "scaling=constrained" in both the "display" command and the "segp" procedure.  I am using "polygonplot" to plot line segments (degenerate polygons) because the final plot will contain genuine polygons and this seemed like the easiest way to do it.  If this is a bad idea for some reason I can change it.

GS

restart;
with(plots):
with(Optimization):
with(LinearAlgebra):
with(Statistics):
with(DEtools):
x11 := <0.208408965651696e-3, -0.157194487523421e-2, -0.294739401402979e-2, 0.788206708183853e-2, 0.499394753201753e-2, 0.191468321959759e-3, 0.504980449104750e-2, 0.222150494088535e-2, 0.132091821964287e-2, 0.161118434883258e-2, -0.281236534046873e-2, -0.398055875132037e-2, -0.111753680372819e-1, 0.588868146012489e-2, -0.354191562612469e-2, 0.984082837373291e-3, -0.116041186868374e-1, 0.603027845850267e-3, -0.448778128168742e-2, -0.127561485214862e-1, -0.412027655195339e-2, 0.379387381798949e-2, -0.602550446997765e-2, -0.605986284736216e-2, -0.751396992404410e-2, 0.633613424008655e-2, -0.677581832613623e-2>;
y11 := <-21321.9719565717, 231.709204951251, 1527.92905167191, -32.8508507060675, 54.9408176234139, -99.4222178124229, -675.771433486265, 42.0838668074923, -12559.3183308951, 5.21412214166344*10^5, 1110.50031772203, 3.67149699000155, -108.543878970269, -8.48861069398811, -521.810552387313, 26.4792411876883, -8.32240296737599, -1085.40982521906, -44.1390030597906, -203.891397612798, -56.3746416571417, -218.205643256096, -178.991498697065, -42.2468018350386, .328546922634921, -1883.18308996621, 111.747881085748>;
z11 := <1549.88755331800, -329.861725802688, 8.54200301129155, -283.381775745327, -54.5469129127573, 1875.94875597129, -16.2230517860850, 6084.82381954832, 1146.15489803104, -456.460512914647, 104.533252701641, 16.3998365630734, 11.5710907832054, -175.370276462696, 33.8045539958636, 2029.50029336951, 1387.92643570857, 9.54717543291120, -1999.09590358328, 29.7628085078953, 2.58210333216737*10^6, 57.7969622731082, -6.42551196941394, -8549.23677077892, -49.0081775323244, -72.5156360537114, 183.539911458475>;
ICS:=[x1(0)=x11[1],y1(0)=y11[1],z1(0)=z11[1]];
N := Dimension(x11)-1:
sys1 := [Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t), Diff(y1(t),t) = k5*x1(t)+ k6*y1(t)+ k7*z1(t), Diff(z1(t),t) = k9*x1(t)+ k10*y1(t)+ k11*z1(t)];
SS := proc(k1,k2,k3,k5,k6,k7,k9,k10,k11)
local F, V;
if not type([k1,k2,k3,k5,k6,k7,k9,k10,k11],[numeric,numeric,numeric,numeric,numeric,numeric,numeric,numeric,numeric]) then return 'SS'(k1,k2,k3,k5,k6,k7,k9,k10,k11);
elif k1<0 or k2<0 or k3<0 or k5<0 or k6<0 or k7<0 or k9<0 or k10<0 or k11<0 then return 1e100;
end if;
F := dsolve(eval({Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t), Diff(y1(t),t) = k5*x1(t)+ k6*y1(t)+ k7*z1(t), Diff(z1(t),t) = k9*x1(t)+ k10*y1(t)+ k11*z1(t),x1(0)=x11[1],y1(0)=y11[1],z1(0)=z11[1]},{:-k1=k1,:-k2=k2,:-k3=k3,:-k5=k5,:-k6=k6,:-k7=k7,:-k9=k9,:-k10=k10,:-k11=k11}), [x1(t),y1(t),z1(t)], numeric, output=Array([seq(k,k=0..N)]));
V := convert(Column(F[2,1],2),Vector);
Norm(V-x11,2);
Norm(V-y11,2);
Norm(V-z11,2);
end proc:
params := NLPSolve(SS(k1,k2,k3,k5,k6,k7,k9,k10,k11), method=nonlinearsimplex, initialpoint=[k1=.1, k2=.1, k3=.1, k5=.1, k6=.1, k7=.1, k9=.1, k10=.1, k11=.1],evaluationlimit=200):

Warning, limiting number of function evaluations reached

reference from 

http://www.maplesoft.com/applications/view.aspx?SID=1667

when debug

k1=.1; k2=.1; k3=.1; k5=.1; k6=.1; k7=.1; k9=.1; k10=.1; k11=.1;
F := dsolve({Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t), Diff(y1(t),t) = k5*x1(t)+ k6*y1(t)+ k7*z1(t), Diff(z1(t),t) = k9*x1(t)+ k10*y1(t)+ k11*z1(t),x1(0)=x11[1],y1(0)=y11[1],z1(0)=z11[1]}, [x1(t),y1(t),z1(t)], numeric, output=Array([seq(k,k=0..N)]));

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)
Error, (in dsolve/numeric) Array/array solutions cannot be obtained for ODE containing unassigned global variables {k1, k10, k11, k2, k3, k5, k6, k7, k9}

x11 := Vector([0.208408965651696e-3, -0.157194487523421e-2, -0.294739401402979e-2, 0.788206708183853e-2, 0.499394753201753e-2, 0.191468321959759e-3, 0.504980449104750e-2, 0.222150494088535e-2, 0.132091821964287e-2, 0.161118434883258e-2, -0.281236534046873e-2, -0.398055875132037e-2, -0.111753680372819e-1, 0.588868146012489e-2, -0.354191562612469e-2, 0.984082837373291e-3, -0.116041186868374e-1, 0.603027845850267e-3, -0.448778128168742e-2, -0.127561485214862e-1, -0.412027655195339e-2, 0.379387381798949e-2, -0.602550446997765e-2, -0.605986284736216e-2, -0.751396992404410e-2, 0.633613424008655e-2, -0.677581832613623e-2]):
y11 := Vector([ -21321.9719565717, 231.709204951251, 1527.92905167191, -32.8508507060675, 54.9408176234139, -99.4222178124229, -675.771433486265, 42.0838668074923, -12559.3183308951, 5.21412214166344*10^5, 1110.50031772203, 3.67149699000155, -108.543878970269, -8.48861069398811, -521.810552387313, 26.4792411876883, -8.32240296737599, -1085.40982521906, -44.1390030597906, -203.891397612798, -56.3746416571417, -218.205643256096, -178.991498697065, -42.2468018350386, .328546922634921, -1883.18308996621, 111.747881085748]):
z11 := Vector([ 1549.88755331800, -329.861725802688, 8.54200301129155, -283.381775745327, -54.5469129127573, 1875.94875597129, -16.2230517860850, 6084.82381954832, 1146.15489803104, -456.460512914647, 104.533252701641, 16.3998365630734, 11.5710907832054, -175.370276462696, 33.8045539958636, 2029.50029336951, 1387.92643570857, 9.54717543291120, -1999.09590358328, 29.7628085078953, 2.58210333216737*10^6, 57.7969622731082, -6.42551196941394, -8549.23677077892, -49.0081775323244, -72.5156360537114, 183.539911458475]):

a1 := Diff(x1(t),t) = k1*x1(t)+ k2*y1(t)+ k3*z1(t) + k4*u(t);
b1 := Diff(y1(t),t) = k5*x1(t)+ k6*y1(t)+ k7*z1(t) + k8*u(t);
c1 := Diff(z1(t),t) = k9*x1(t)+ k10*y1(t)+ k11*z1(t) + k12*u(t);
d1 := Diff(u(t), t) = 0;
ICS:=x1(0)=x11[1],y1(0)=y11[1],z1(0)=z11[1];
solL:=dsolve({a1,b1,c1,d1,ICS}, numeric, method=rkf45, parameters=[k1,k2,k3,k4,k5,k6,k7,k8,k9,k10,k11,k12]);
ans:=proc(p1,p2,p3) solL(parameters=[a1=p1,b1=p2,c1=p3]); end proc:
FitParams:=Statistics:-NonlinearFit(ans, x11, y11, z11, x1, y1, z1);

Error, (in Statistics:-NonlinearFit) unexpected parameters: Vector(27, {(1) = 1549.88755331800, (2) = -329.861725802688, (3) = 8.54200301129155, (4) = -283.381775745327, (5) = -54.5469129127573, (6) = 1875.94875597129, (7) = -16.2230517860850, (8) = 6084.82381954832, (9) = 1146.15489803104, (10) = -456.460512914647, (11) = 104.533252701641, (12) = 16.3998365630734, (13) = 11.5710907832054, (14) = -175.370276462696, (15) = 33.8045539958636, (16) = 2029.50029336951, (17) = 1387.92643570857, (18) = 9.54717543291120, (19) = -1999.09590358328, (20) = 29.7628085078953, (21) = 2582103.332, (22) = 57.7969622731082, (23) = -6.42551196941394, (24) = -...

So I am working on doing some trajectory simulations in Maple using standard Newton's Laws, some force expressions, and initial conditions.

Anyway, the numerical solution works fine if I let the initial conditions I specified (for z=-1) be actually for z=-0.9. To illustrate, when I give an initial condition like this:

x(-1) = x_0, D(x)(-1) = xd_0, Vz(-1) = v_0

the results don't make any sense. However, when using the same x_0, xd_0, and v_0 and I give initial conditions like this:

x(-.9) = x_0, D(x)(-.9) = xd_0, Vz(-0.9) = v_0,

the solutions at least make a bit of sense.

What's weird is that, when I let z -> 0.93 or so, the solution changes discontinuously. And this shouldn't happen. The initial conditions were calculated for and should work for z = -1. I don't understand why they aren't.

Here is my Maple document. ics1 are the problem.

dsolve_field_traject.mw

Do you guys have any idea what could be going on?

Hello, everyone!

Last week I’ve encountered problems with integration of Maple 17 in Microsoft Office Excel 2013. The Maplesoft note on the point (http://www.maplesoft.com/support/faqs/detail.aspx?sid=32651) offers some ways of fixing it up, though I’ve run all of them the problem is the same:

While the connection is established, after entering the formula “=Maple(“x+x”)”, the Excel returns “Critical Error in Formula”

Before contacting the Maplesoft Technical Support, I want to ask here whether someone had the same case and managed to solve it.

Many thanks in advance.

the question is as follow:

1)receive two integers p and q

2)declare two local p1 and q1 and give them intial values and q

3)check if p o q are equal or less to zero print works only with positive integers

4)while p1 not equal to q1 then p1-a1 otherwise q1-p1

5)whenever p1=q1 we have the GCD

note:must use procedure and call it for different values of p and q after the procedure is written

-by following the instruction above this is what i got

GCD:=proc(p,q)

local p1,q1;

p1:=p;

q1:=q;

if p<=0 OR Q<=0 then 'works only with positive integers'
else while p1<>q1 do if q1<p1 then p1-q1 else q1-p1

end if;

end do;

end if;

end proc;

but when I call two integers eg:p=2, q=6 -> GCD(2,6) maple just freeze...evaluating....forever. is it because i got the procedure wrong etc? it would be helpful if anyone can help me with this. thanks

Does N variables caylay table have N permutation group so that can generate N functions?

for exmaple 3 variables cayley table have 3 permutation group, for 1, it has a permutation group , for 2 has a permutation group etc.

then does it mean that it has 3 functions, do it need to composite 3 functions in order to get a function belong to this cayley table?

1 1 1

1 2 2

1 2 3

Hi, I am trying to plot these two curves:

I tried:

with(plots);  A := Array(1..2)  A[1] :=plot (0.199563349672261+0.0178636902277546 x^1.14406289706794-0.0182070811144750 x^(1.13867380551454),x=50..2050,  color=red);  A[2]  := plot(0.298910542599302+0.0117459591500434 x^1.00390277106937-0.0137065176395662 x^0.970667551759677, x = 50..2050, color = blue);  display (A);

and I got:

Error, (in plot) unexpected option: .298910542599302+0.117459591500434e-1*x^1.00390277106937-0.137065176395662e-1*x^.970667551759677

so I tried

so I am not sure how I would graph these two functions...