## 205 Reputation

16 years, 17 days

## how to integrate on irregular area?...

Maple 2015

hello,my friends.I got a problem in using maple.

I want project a cuboid on a plane, and integrate function on that area.

for example, a cuboid which have a spatial diagonal between (0,0,0) and (1,2,1).
Then it was projected to a plane defined by three points (-1,0,0), (0,-1,0) and (0,0,-1).
Finally, a function x^2+y^2 was integrated on that projected area.

I found the cuboid can be defined with plottools:-cuboid and projected with plottools:-project in maple.
but how to integration next?
I can't find any commands in maple can do the integration with that irregular area.

I need some help.Thank you very much in advance.

## how to use dchange command with new=old?...

Maple

for example,transform diff(u(x,y),x) with xi=xi(x,y) and eta=eta(x,y);

it should be

diff(u(x,y),x)=diff(u(xi,eta),xi)*diff(xi(x,y),x)+diff(u(xi,eta),eta)*diff(eta(x,y),x)

## how to plot this function?...

plots:-implicitplot((-2.0)^x-y,x=-sqrt(2)..-exp(-1),y=-1.5..1.5);

I tried surd, but there is a limitation (integer order).

## Difficult implicit odes...

Maple

restart;
odes:=diff(x1(t),t)*diff(x2(t),t\$2)*sin(x1(t)*x2(t))+5*diff(x1(t),t\$2)*diff(x2(t),t)*cos(x1(t)^2)+t^2*x1(t)*x2(t)^2=exp(-x2(t)^2),diff(x1(t),t\$2)*x2(t)+diff(x2(t),t\$2)*diff(x1(t),t)*sin(x1(t)^2)+cos(diff(x2(t),t\$2)*x2(t))=sin(t);
ics:=x1(0)=1,D(x1)(0)=1,x2(0)=2,D(x2)(0)=2;
subs(diff(x1(t),t\$2)=yp2,diff(x2(t),t\$2)=yp4,diff(x1(t),t)=Y[2],diff(x2(t),t)=Y[4],x1(t)=Y[1],x2(t)=Y[3],{odes});
p:=proc(N,t,Y,YP)
local eqs,yp2,yp4;
YP[1]=Y[2];
YP[3]=Y[4];
eqs:=[yp2*Y[3]+yp4*Y[2]*sin(Y[1]^2)+cos(yp4*Y[3]) = sin(t), Y[2]*yp4*sin(Y[1]*Y[3])+5*yp2*Y[4]*cos(Y[1]^2)+t^2*Y[1]*Y[3]^2 = exp(-Y[3]^2)];
YP[2],YP[4]:=op(subs(fsolve(eqs,{yp2=1,yp4=2}),[yp2,yp4]));
end proc:
res:=dsolve(numeric,procedure=p,initial=array([1,1,2,2]),number=4,procvars=[x1(t),diff(x1(t),t),x2(t),diff(x2(t),t)],start=0,maxfun=0);
plots:-odeplot(res,[t,x1(t)],0..5,gridlines=true);

It's a long time to wait for the odeplot.

## Is this output right??...

Maple

DEtools[DEplot](diff(x(t),t)=-abs(x(t)),x(t),t=0..40,[x(0)=1],numpoints=1000,dirgrid=[30,30],linecolor=blue)

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