MaplePrimes Questions

I wonder if it is possible to automatically obtain the well-known  binomial theorem  for an arbitrary integer and a positive exponent  n  in Maple. The expansion  (1)  below  I want to get in Maple automatically. But all my attempts were unsuccessful:
 

restart;

(a+b)^n=Sum(binomial(n,k)*a^(n-k)*b^k, k=0..n);  # The binomial theorem

(a+b)^n = Sum(binomial(n, k)*a^(n-k)*b^k, k = 0 .. n)

(1)

expand((a+b)^n) assuming n::posint;
convert((a+b)^n, Sum) assuming n::posint;
convert((a+b)^n, polynom) assuming n::posint;
convert((a+b)^n, binomial) assuming n::posint;

 

(a+b)^n

 

(a+b)^n

 

(a+b)^n

 

(a+b)^n

(2)

 


 

Download binomial_theorem.mw

I am trying to price an option with the explicit fnite difference method. The code works up until   but does not run after that. Any help would be greatly appreicated 


I tried to solve this double integral in Maple but didn't get the solution so how can I solve this?

Please help

restart

a := .5

.5

(1)

b := .6

.6

(2)

R := 0.1e-1

0.1e-1

(3)

E := 210000000000/(1-.3^2)

0.2307692308e12

(4)

h := a/(2*sqrt(-2*y^2+1))

.2500000000/(-2*y^2+1)^(1/2)

(5)

F1 := sqrt(tan((1/2)*Pi*h)/((1/2)*Pi*h))*[.752+2.02*h+.37*(1-sin((1/2)*Pi*h))^3]/cos((1/2)*Pi*h)

2.828427125*(tan(.1250000000*Pi/(-2*y^2+1)^(1/2))*(-2*y^2+1)^(1/2)/Pi)^(1/2)*[.752+.5050000000/(-2*y^2+1)^(1/2)+.37*(1-sin(.1250000000*Pi/(-2*y^2+1)^(1/2)))^3]/cos(.1250000000*Pi/(-2*y^2+1)^(1/2))

(6)

F4 := sqrt(tan((1/2)*Pi*h)/((1/2)*Pi*h))

2.828427125*(tan(.1250000000*Pi/(-2*y^2+1)^(1/2))*(-2*y^2+1)^(1/2)/Pi)^(1/2)

(7)

C1 := (1/2)*u*(F1^2+1.3*F4^2)/(Pi*E*R)

0.2166666666e-9*u*(8.000000001*tan(.1250000000*Pi/(-2*y^2+1)^(1/2))*(-2*y^2+1)^(1/2)*[.752+.5050000000/(-2*y^2+1)^(1/2)+.37*(1-sin(.1250000000*Pi/(-2*y^2+1)^(1/2)))^3]^2/(Pi*cos(.1250000000*Pi/(-2*y^2+1)^(1/2))^2)+10.40000000*tan(.1250000000*Pi/(-2*y^2+1)^(1/2))*(-2*y^2+1)^(1/2)/Pi)/Pi

(8)

B := int(int(C1, u = 0 .. a), y = -b .. b)

int(0.2195292312e-10*tan(.3926990817/(-2.*y^2+1.)^(1/2))*(-2.*y^2+1.)^(1/2)*[.7520000000+.5050000000/(-2.*y^2+1.)^(1/2)+.3700000000*(1.-1.*sin(.3926990817/(-2.*y^2+1.)^(1/2)))^3]^2/cos(.3926990817/(-2.*y^2+1.)^(1/2))^2+0.2853880005e-10*tan(.3926990817/(-2.*y^2+1.)^(1/2))*(-2.*y^2+1.)^(1/2), y = -.6 .. .6)

(9)

evalf(B)

int(0.2195292312e-10*tan(.3926990817/(-2.*y^2+1.)^(1/2))*(-2.*y^2+1.)^(1/2)*[.7520000000+.5050000000/(-2.*y^2+1.)^(1/2)+.3700000000*(1.-1.*sin(.3926990817/(-2.*y^2+1.)^(1/2)))^3]^2/cos(.3926990817/(-2.*y^2+1.)^(1/2))^2+0.2853880005e-10*tan(.3926990817/(-2.*y^2+1.)^(1/2))*(-2.*y^2+1.)^(1/2), y = -.6 .. .6)

(10)

 

(11)

``


 

Download mapleprime.mw

Can Maple perform huge calculations via parallel-pooling (i.e working on multiple or all CPUs) similar to Matlab?

verify(2*cos(phi)^2-1, cos(2*phi), equal); returns FAIL even though is a trig identify. Any ideas why?
 

Maple currently can't integrate things like sin(x)^n or cos(x)^n. These have antiderivative in terms of  hypergeometric functions.

Is there a technical reason why Maple at version 18 still can't integrate these? Will it be able to in next version?

int(cos(x)^k, x) 
int(sin(x)^k, x) 

fyi, These are the antiderivatives

Same problem for tan(x)^n....  I am asking because Maple is able to solve many ODE's but some results contains unevaluated integrals such as the above. 

 

When making this call to dsolve

 

restart;
ode:=diff(y(x),x)=1:
stopat(dsolve);
dsolve(ode,y(x));

Then in the debugger, I see that dsolve signature is

dsolve := proc(ODEs::{anything} := NULL, 
                {atomizenames::truefalse := true, build::truefalse := false, type::name := 'none'})

When typing print(ODEs) inside the debugger, it gives "diff(y(x),x)=1" which is correct.

But where is the second argument I passed to dsolve in the above call, which is "y(x)" gone?  I also do print(_nparams) inside the debugger and Maple returns 1 and not 2.

I expected to see 2 since I passed in two arguments to dsolve.

dsolve actually works without passing y(x), as follows

dsolve(ode);

And it seems Maple figure inside what is the dependent variable.

But my question is, is the second argument being thrown away before calling dsolve? If not, why it does not show in the debugger?   Is there some other pre-processing being done between the time the user calls dsolve() and the time the debugger is called?

 

 

 

So i have beeing working with finite elements and i have the stifness matrix that i came with Maple as you can see here:

Ke := Matrix(4, 4, {(1, 1) = (12*I)*E/l^3, (1, 2) = (6*I)*E/l^2, (1, 3) = -(12*I)*E/l^3, (1, 4) = (6*I)*E/l^2, (2, 1) = (6*I)*E/l^2, (2, 2) = (4*I)*E/l, (2, 3) = -(6*I)*E/l^2, (2, 4) = (2*I)*E/l, (3, 1) = -(12*I)*E/l^3, (3, 2) = -(6*I)*E/l^2, (3, 3) = (12*I)*E/l^3, (3, 4) = -(6*I)*E/l^2, (4, 1) = (6*I)*E/l^2, (4, 2) = (2*I)*E/l, (4, 3) = -(6*I)*E/l^2, (4, 4) = (4*I)*E/l})

How can i re-write this matrix to put in this form:


Thanks

Hi, everybody.

Is there a command or a way to assign an initial value to animate plot?

Trivial example:

animate(plot,[m*x,x=-10..10],m=-10..10)

but initial value for m would be m=1 so the initial render will present the line with slope 1.

As always, thank you all in advanced.

 

i have two ode equations, when try to solve, i face this error
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system
any comment or help to solve this? ( or any simplifying comments to solve) . thnx in advance

 

restart

A := 4263736263.736263:B := 11868131.86813187:C := 600146.5201465202:hr := 0.3e7:muz := 0.2632654643708247e-5:P:=1000:

1000

(1)

ode1 := diff(u(r), r, r)+(diff(u(r), r))/r-u(r)/r^2-B*(diff(w(r), r, r, r)+(diff(w(r), r, r))/r-(diff(w(r), r))/r^2)/A = 0;

diff(diff(u(r), r), r)+(diff(u(r), r))/r-u(r)/r^2-0.2783505155e-2*(diff(diff(diff(w(r), r), r), r))-0.2783505155e-2*(diff(diff(w(r), r), r))/r+0.2783505155e-2*(diff(w(r), r))/r^2 = 0

(2)

ode2 := C*(diff(w(r), r, r, r, r))+2*C*(diff(w(r), r, r, r))/r-(C/r^2+muz*hr^2)*(diff(w(r), r, r))+(C/r^3-muz*hr^2/r)*(diff(w(r), r))+muz*hr^2*w(r)/r^2-B*(diff(u(r), r, r, r))-2*B*(diff(u(r), r, r))/r+B*(diff(u(r), r))/r^2-B*u(r)/r^3 = P;

600146.5201465202*(diff(diff(diff(diff(w(r), r), r), r), r))+1200293.040*(diff(diff(diff(w(r), r), r), r))/r-(600146.5201465202/r^2+23693891.80)*(diff(diff(w(r), r), r))+(600146.5201465202/r^3-23693891.80/r)*(diff(w(r), r))+23693891.80*w(r)/r^2-11868131.86813187*(diff(diff(diff(u(r), r), r), r))-23736263.74*(diff(diff(u(r), r), r))/r+11868131.86813187*(diff(u(r), r))/r^2-11868131.86813187*u(r)/r^3 = 1000

(3)

ics := w(.2) = 0, (D(w))(.2) = 0, w(1) = 0, (D(w))(1) = 0, u(.2) = 0, u(1) = 0;

w(.2) = 0, (D(w))(.2) = 0, w(1) = 0, (D(w))(1) = 0, u(.2) = 0, u(1) = 0

(4)

dsolve({ode1,ode2} union {ics},{w(r),u(r)},numeric)

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

 

 

Download zzv.mw

Hi!

I want to plot the approximation of a surface by polynomials. The surface is given by (x,y,f(x,y)) where f(x,y) is given by the following expression

proc (x) options operator, arrow; (sum(i*cos((i+1)*(-2+4*x[1])+i), i = 1 .. 5))*(sum(i*cos((i+1)*(-2+4*x[2])+i), i = 1 .. 5)) end proc

with both variables varying in the interval [0,1]. Then, by using the Bernstein polynomials of two variables (see, for instance, this paper for details  https://www.sciencedirect.com/science/article/pii/0021904589900956), the graph of the resulting (plot3d) surface (x,y,p(x,y))  it is not even like to the original surfaces.

Please, see this PDF of what I have done:  plots.pdf

Some idea or suggestion?

Thanks!

numeric.mws

 

Dear Colleagues,
Please give advice - How correct in Maple can be solve the heat nonlinear equation system with perfect thermal contact conditions?

Using procedure dsolve (numeric) Maple cannot determine type of problem (initial or boundary).

****
initial/boundary conditions specified at too many points 1
Error, (in dsolve/numeric/type_check) cannot determine type of problem (initial or boundary), as conditions are given at 4 points
****
 

In attachment Maple file - numeric.

Maybe anyone can get a simple exaple of the maple code for numeric solution of this  task?

 

 


 

restart;

k1:=5; k2:=7;k3:=8; Q:=4;p:=0.001;l:=0.1; d:=0.6;

k1 := 5

k2 := 7

k3 := 8

Q := 4

p := 0.1e-2

l := .1

d := .6

(1)

Eq1:=(k1^2)*diff(T1(x),x$2)=0;

 

Eq1 := 25*(diff(T1(x), `$`(x, 2))) = 0

(2)

Eq2:=(k2^2)*diff(T2(x),x$2)=-Q*Dirac(x)+T2(x)^4;

Eq2 := 49*(diff(T2(x), `$`(x, 2))) = -4*Dirac(x)+T2(x)^4

(3)

Eq3:=(k3^2)*diff(T3(x),x$2)=0;

Eq3 := 64*(diff(T3(x), `$`(x, 2))) = 0

(4)

con1:=T1(0)=T2(0);con2:=T3(p)=T2(p); con3:=k1*(D(T1)(0))=Q-k2*(D(T2)(0)); con4:=k2*(D(T2)(p))=k3*(D(T3)(p)); con5:= T3(l)=300; con6:=T1(-d)=300;

con1 := T1(0) = T2(0)

con2 := T3(0.1e-2) = T2(0.1e-2)

con3 := 5*(D(T1))(0) = 4-7*(D(T2))(0)

con4 := 7*(D(T2))(0.1e-2) = 8*(D(T3))(0.1e-2)

con5 := T3(.1) = 300

con6 := T1(-.6) = 300

(5)

nsol:=dsolve({Eq1, Eq2, Eq3,con1,con2,con3,con4,con5,con6},{T1(x),T2(x),T3(x)}, numeric,bvp);

 

 

initial/boundary conditions specified at too many points 1

Error, (in dsolve/numeric/type_check) cannot determine type of problem (initial or boundary), as conditions are given at 4 points

 

 

 

 


 

Download numeric.mws

I am brand new to Maple Cloud and Maple Player.

I have uploaded two worksheets to the cloud, and my wife has just installed Maple Player on her laptop.

In Maple Player, the second worksheet shows the shareable symbol but the first doesn't even thought I uploaded both in the same way by clicking on the upload symbol in the Maple Cloud palette. Why is the first worksheet not shareable?

When my wife displays the second worksheet she is able to move its sliders but they do not change the display as they do when I move the sliders within Maple2016. How can she change the display?

Here is a link to the second worksheet:

Cassinian_oval.mw

Say I have 2 matrices, in which the elements themselves are vectors.

I'm looking for a way to perform matrix multiplication on these so that rather than having the first element as x11y11+x12y21+x13y31

It would be x11.y11+x12.y21+x13.y31 where . is the dot product on the elements of each matrix.

I know I could write a procedure to do this manually but I was wondering if there's any pre-made operations (or modifiers on the Multiply operation) to do this.

How do I plot the optimal control functions in an optimal control problem ?

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