Any tips on how to solve fixed endpoint problems in the calculus of variations?

For instance,

Find the extremal for:

int(diff(x(t),t)^2/(t^3),t=1..2) with x(1)=2 and x(2)=17.

The correct answer is x(t) = t^4 + 1.

hello, first post here.

i'm attempting to solve the 1 d heat equation using a finite difference scheme, with continous boundaries eg.

Where I can get right and complete instructions for read .txt files from Maple 7 ? 

I follow the instructions like:

L := ImportMatrix( "data.txt", delimiter=" " );

for read a deta.txt file, or others like fopen, etc, and do not get the data.

How do I plot in the simplex with Maple [11]?

I am working with variables x1,x2,x3, each non-negative, and summing to one.  Thus, the triangular 2-simplex is an easier environment to work in.

Thank you in advance,

Colin Rowat, Department of Economics, University of Birmingham

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Hello All,

Can I get maple to give me a hint as to what test for convergence to use with infinite series?

Thanks!

HI to all!

I've a math question about the Hessian Matrix. I know that it's used for clasify critical points of a 3-D function, but what happens if the Hessian is undefined (Hessian = 0) in a point?... How i can analyze the critical point?...

A particular sample is:  f(x,y) = (y-x)^2*(y+x).

The gradient vector of this function is: grad(f)= [ 3x^2 - 2xy - y^2 , -x^2 - 2xy + 3y^2 ]. To find critical points we have to do grad(f)=0 (vector). And in this case it's easy to verify that the critical points lie in the Y=X line.

hi

i have to calculate a extreme value for a box that is open on one side that should have a volume of 32.

V = x * y*z

For the surface ob the box-sides i used this function:

O = 2xz + xy + 2yz

my idea was to solve this in maple using lagrange because i ve a side condition

with(RealDomain):
L:=(x,y,lambda)->x*y + 2*x*z * 2*y*z +lambda*(x*y*z-32);
solve({diff(L(x,y,lambda),x)=0, diff(L(x,y,lambda),y)=0, diff(L(x,y,lambda),lambda)=0});
evalf(%);

it gives me for my values x = 32/x*y; y = y; z =z

I would use the chain rule twice:

f(s,t) = e^u

u = sin(s*t);

u = sin(v);

v = s*t

v' = s;

u' = cos(s*t*)*s

f' = e^cos(s*t)*s

Maple adds *ln(exp), what's wrong with my way?

complete maple output: exp^sin(s*t)*cos(s*t)*t*ln(exp)

I want to create a list of the first 100 prime numbers.  I remember vaguely the use of seq and type but I can find it in the differents forums.  Could someone state it again for me.  thanks!

Hi,

I have a matrix

A:=<<1,-3,2>|<-2,6,-4>|<2,-1,5>|<3,1,8>|<-1,-7,-4>>;

how do I find a basis of im(A)?

Thanks

Chen

Hello everybody,

I am using the GF package from Maple to solve an equation with elements of a given galois field. It looks like that:

field := GF(7, 1):

eq1 := x = y^2:
eq2 := x^2 = y^4:
equationToUse := eq1:

isSolving := false:
use field in  
    isSolving := is(eval(equationToUse, [x=field:-random(), y=field:-random()]));
end use:

if isSolving then
    print(`Equation solved`);
end if:
 

The Maple Manual says to use a parametric plot to graph a circle.  I've been fiddling with the syntax  but can't seem to get it right.  I want to plot

x^2 - 2x + y^2 = 0,           which can be written as

(x-1)^2 + y^2 = 1

Can someone please give me the PLOT command to plot this circle?

Allan