I have this expression; f(a,c,n)=64a²n-16a⁴n-256c²n+32c⁴n-96a²c²+ 8a²c⁴+24a⁴c²-64a²n²+256a²-124a⁴+ 15a⁶+256n²+64a²c²n

such as "a" is between 0 and 2, "c" between 0 and 2 and "n" between 0 and 4.

How do I plot f(a,c,n) so that I can study its sign?

I have computed the infinite multiplication using Maple, $\Pi_{k=3}^{\infty} ( \cos (\frac{\pi}{k} ))$, as follows, but it resulted in 0! I wonder why this happened, although maple was using exact arithmetic.

    P := Product(cos(Pi/k), k = 3 .. infinity)   

    value(P)

Note that if I use floating-point instead, it gives me the right answer, 0.1149420449.

    evalf(P)
By the way, I did not expect such a situation! Exact arithmetic should be exact! I am multiplying non-zero numbers to each other, starting from $1/2$ to $1$ as $n \rightarrow \infty$. So it should not be zero! Why such a thing happened?

Dear all;

Special thanks for all the member who help me in Maple.

My last question is:

Write a maple procedure that solves for y(1) in the initial value problem y'(x)=f(y), y(0)=1

using a Numerical stencil based on the n^{th] order taylor series expansion of y.

The procedure arguments include an arbitrary function f, an integrer n, representing the accuracy of the taylor series expansion, and N representing the number of steps between x=0 and x=1.

Given a 2x2 matrix I am struggling to write a function that would return a list (a,b, a1, a2) of 2 complex numbers followed by 2 vectors such that the set of the 2 vectors is a basis for CxC and also Ab1=ab1, Ab2=Bb2 if these exist

Any ideas would be greatly appreciated

how to convert decimal to fraction without simplify

for example

convert(0.25, fraction)

expect 25/100, but not 1/4

Hi,

Please help me in solving system consist the three differential equations with three unknowns. I did already a few attempts, but I can not finish. Once in the final result was got RootOf and do not know what to do. I tried also numerically. I very very ask for some suggestions: ( 

with the boundary condition

parameters A,B,C are constans

1)

qa1 := A1*(diff(Tg(x), x, x))+A2*(diff(Tg(x), x))+(A3+A4)*Tg+A3*Tz+A4*Tw = 0;

eqa2 := B1*(diff(Tw(x), x, x))+B2*(diff(Tw(x), x))+(B3+B4)*Tw+B3*Tz+B4*Tg = 0;

eqa3 := C1*(diff(Tz(x), x, x))+(C3+C4)*Tz+C3*Tg+C4*Tw = 0

2)

On paper, the system of three equations with three unknowns I changed to system of two equations with two unknowns but still nothing. 

A[1] := 2, 

eqa1 := A[1]*C[1]*(diff(z(x), x, x, x, x))/C[3]+A[2]*C[1]*(diff(z(x), x, x, x))/C[3]+(A[1]*C[3]+A[1]*C[4]+A[3]*C[1]+A[4]*C[1])*(diff(z(x), x, x))/C[3]+(A[1]*C[3]+A[1]*C[4])*(diff(z(x), x))/C[3]+(A[3]*C[3]+A[3]*C[4]+A[4]*C[3]+A[4]*C[4]+A[3]*C[3])*z(x)/C[3]+A[1]*C[4]*(diff(y(x), x, x))/C[3]+A[2]*C[4]*(diff(y(x), x))/C[3]+(A[3]*C[4]+A[4]*C[4]+A[4]*C[3])*y(x)/C[3] = 0;

eqa2 := B[4]*C[1]*(diff(z(x), x, x))/C[3]+(B[4]*C[3]+B[4]*C[4]+B[3]*C[3])*z(x)/C[3]+B[1]*(diff(y(x), x, x))+B[2]*(diff(y(x), x))+(B[4]*C[3]+B[4]*C[4]+B[3]*C[3])*y(x)/C[3] = 0;

row := eqa1, eqa2;

sol := dsolve({row}, {y(x), z(x)});

Thank you very much for your help.

Ewa.

Dear all,

I need to compute the error, How to define the error between the exact and approximation.

                               d              
                              --- y(x) = -y(x)
                               dx             
                               y(x) = exp(-x)

I have a problem in this code, my goal is to compute the error between the approximate solution obtained by RK3 and Exact  and E ( approximation by RK3).

How to definie the error and prouve that the error is O(h^4)  ( with one step) and the global error is O(h^3).

Thank you  for helping me.

Hi,

I have a problem with dsolve in the following code

restart;
>
n:=20;
m:=1;
cc:=-200;
zzeta:=0.1;
sefr1:=0.3;
sefr:=0.2;
MM:=0;
lambda:=0.1;
Br:=1;
nn:=3;
>
>
#u(tau):=tau;
u(tau):=421.7129935*tau-2217.587728*tau^2+8897.376593*tau^3-27612.59182*tau^4+64248.00336*tau^5-1.083977605*10^5*tau^6-10.57029600-1.080951714*10^6*tau^13+7.999517316*10^5*tau^14-4.788741005*10^5*tau^15+2.309563748*10^5*tau^16+26511.11102*tau^18-5959.001794*tau^19+1.148523882*10^5*tau^7-95.23809524*tau^21+4.545454545*tau^22-9435.563781*tau^8-2.587683745*10^5*tau^9+6.473880128*10^5*tau^10+948.0272727*tau^20-88660.41892*tau^17-1.008692404*10^6*tau^11+1.175504242*10^6*tau^12;
>
>
B := 1+(2*(1-zzeta))*Br*(int(tau*(diff(u(tau), tau))^2, tau = (1/2)*zzeta*(1-zzeta) .. 1/2*(1-zzeta)));
eq4 := 4*B*u(tau)-(1+zzeta)*(diff(tau*(diff(theta(tau), tau)), tau))/tau-(1+zzeta)*Br*(diff(u(tau), tau))^2;


theta(tau):=sum(p^ii*theta[ii](tau),ii=0..nn);
HH:= p*((4*(1+(2*(1-zzeta))*Br*(int(tau*(diff(u(tau), tau))^2, tau = (1/2)*zzeta*(1-zzeta) .. 1/2-(1/2)*zzeta))))*u(tau)-(1+zzeta)*(diff(theta(tau), tau)+tau*(diff(theta(tau), tau, tau)))/tau-(1+zzeta)*Br*(diff(u(tau), tau))^2)+(1-p)*(diff(theta(tau),tau$2)):
eq5:=simplify(HH):
eq6:=collect(expand(eq5),p);

eq7:=
convert(series(collect(expand(eq5), p), p, nn+1), 'polynom');


for ii to nn do
ss[ii] := (coeff(eq7, p^ii)) ;
print (ii);
end do;

ss[0]:=diff(theta[0](tau), tau, tau);

icss[0]:=theta[0](zzeta/(2*(1-zzeta)))=0, D(theta[0])(1/(2*(1-zzeta)))=1;

dsolve({ss[0], icss[0]});
theta[0](tau):= rhs(%);


for ii to nn do
ss[ii]:=evalf[5](ss[ii]);
icss[ii]:=theta[ii](zzeta/(2*(1-zzeta)))=0, D(theta[ii])(1/(2*(1-zzeta)))=0;
dsolve({ss[ii], icss[ii]});
theta[ii](tau):=rhs(%);
end do;

I would be most grateful if you help me to find this problem.

Thanks for your attention in advance

How to find the equation of the tangent line to f(x)=6x/squareroot(x^2+12) at the point (2,3) ?

Dear all,

Please someone gave an idea,

I write in maple this line but  I get an error,

> Butcher, map(x->if (x=0) then `` else x end if,Butcher);
Error, invalid arrow procedure

Is it possible to describe billiards in the unit square (see http://en.wikipedia.org/wiki/Dynamical_billiards for info) in terms of events and if? For example, let the dynamical system
{x''(t)=0,y''(t)=0, x(0)=0.5, x'(0)=0.2, y(0)=0.5, y'(0)= sqrt(3)/5}
be given, where the trajectory [x(t), y(t)] satisfies the usual laws of reflection http://en.wikipedia.org/wiki/Reflection_%28physics%29 when reaching the boundary {x=0}, {x=1}, {y=0}, {y=1}. The same question about billiards in the unit disk.

hi everybody

I want to solve this system of equations


t*((p-.764*z-2.194768)^2-1.170308549+.529948*(z-.382)^2)-(1-t)*p
t*((p+.382*z+.661624*y-1.907568)^2-1.018097144+.529984*(-.866*y-.5*z-.382)^2)+(1-t)*y
t*((p+.382*z-.661624*y-2.470348)^2-1.31636154+.529984*(.866*y-.5*z-.382)^2)+(1-t)*z


while t varies from 0 to 1 by 0.0001 interval. Using newton raphson method, the inital value for each step is the result of the previous step for y,z,p. the very initial values are y=1,z=1,p=1


please help me. Thanks

I'm having a weird memory leak problem when I use Compiler, and numerical NAG routines for integration - at least I think it's that combination that's causing it. To see it run this:

First define the functions to use:

F_:=Compiler:-Compile(codegen[prep2trans](codegen[optimize](codegen[makeproc](convert(sinh(x)*sin(x),float),[x]))),optimize=true);

F:=proc(k)
if not (k::numeric) then return 'procname'(args) fi;
F_(k);
end proc;

INT:=proc(X) if not X::numeric then return 'procname'(x) fi; int(F(x),x=0..X,numeric,method=_d01ajc); end proc;

Then evaluate lots of times:

for i to 10^6 do a:=rand()/1e12; INT(a);  od:

And watch your computer memory go wild. I'm using Maple 17 on a new mac with 8Gig RAM, using Mavericks. It doesn't take more than a few minutes to grind the system to a halt. A restart command does not release the memory in the mserver process. [I've noticed similar problems in the past, so it's not locallised to this OS I think.]

On a related note, there's a problem with nested NAG integrals - in the do loop try this:

int('INT'(XX),XX=0..a,numeric,method=_d01akc)-int('INT'(XX),XX=0..a,numeric,method=_d01ajc);

it never gives zero! The problem lies in using the same NAG routine twice [here _d01ajc] for a nested integral. I've never found a way around this bug!

Any help would be much appreciated!

Good afternoon sir.

I am working on problems related to functions which require dynamic geometry program or

the Geometers sketch pad. I request to you to kindly suggest me with regard to the above cited query.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

I am trying to graph the cube root of x, but when I do as

plot(x^1/3,thickness=5)

I get a graph with domain of non negative reals.  I need the entire graph, across all reals and I'm not sure how to handle it.  Thanks