I have a set of around 60 linear equations with symbolic coefficients. ie

a*x₁ + b*x₂ + ... + c*x₆₀ = 1

x₁ + (c-a)*x₂ + ... + d*x₆₀ = 0

...

c*x₁ + d*x₂ + ... + b*x₆₀ = a

The coefficients a,b,c,d are functions of x₁...x₆₀. I am trying to find the values of these coefficients. When I had a smaller set of equations I was solving them symbolically to find x₁...x₆₀ in terms of a,b,c,d and then using this solution to solve for a,b,c,d. I can no longer solve the set of equations symbolically as it is too large. How do I find the coefficients? I had some sort of optimization routine in mind.

Bonjour

Comment se calcul le résidue d'une fonction f(x,y) ?

Si par exemple f(x,y)=1/x+1/y+5/(x*y), alors le residue de f en (0,0) est défini comme étant (1/2*Pi)^2*int(f(x,y)) avec intégrale est sur une sphère qui contient l'origine.

Est ce qu'il est égal au coefficient 5 de 1/(x*y) dans le developpement de laurent en deux variables ??

Merci d'avance,

Gérard.

Solve the following initial value problem for y(t), z(t).

dy/dt + dz/dt =t

dy/dt-2 dz/dt=t^2

with initial condition y(0)=1, z(0)=2.

Thanks.

with(LinearAlgebra):

n := 31;

h := 0;

c1 := Array(1 .. 100);

c2 := Array(1 .. 100);

c3 := Array(1 .. 100);

for tt from 0 to n-4 do

c1[tt+1] := ...

c2[tt+1] := ...

c3[tt+1] := ...

od;

plot3d([c1[x],c2[x],c3[x]], x=1..27, y=1..27);

Here is the question:

Consider f(x)=x³ over [a,b] and a partition P of [a,b] into n equal subintervals. Find the length of this subinterval and assign it to dxj.

a) Assign the rightmost point of the jth subinterval to xj. Set up an expression corresponding to the Riemann sum for this partition with  as the rightmost point xj in each subinterval.

b) Find the limit of this expression as n->∞. Integrate f(x) between a and b and comment on your evaluation of the integral and the value of the limit.

 d) Show that the limit of the Riemann sum remain unchanged if

xj = the left most point in the jth interval

or if

xj = the midpoint in the jth interval

anyone know how to go about this question? thanks

I am trying to find what values of x f(x) is increasing without estimating from the graph

Hi,
     I'm comparing a numerical (asymptotic series solution) to a analytical one in Maple 14, 16 and17 (I have many different machines). I make a substitution S(r) = r^(l+1) R(r) to remove singularities and ask maple to solve for S(r) numerically. Then simply

R(r) = S(r)/ r^(l+1) where S(r) is a numeric procedure
and
diff(R(r), r) = diff(S(r),r)/ r^(l+1) - (l+1) S(r)/ r^(l+2) by the  chain rule, and diff(S(r),r) is another numeric procedure returned by maples dsolve.


Now |
S(r)_numeric agrees with S(r)_analytic,
R(r)_numeric agrees with R(r)_analytic,
diff(S(r),r)_numeric agrees with diff(S(r),r)_analytic
BUT diff(R(r),r)_numeric DOES NTO AGREE WITH  diff(R(r),r)_analytic
 
To me this seems that the formula from the chain rule most be wrong. Does anyone have any ideas? I've attached a .msw file too

Thanks,
Matt
testingDRoutside.mw

Dear Experts,

Analytical integration is not a choice for the integrals listed here. Hence, Maple is not able to find the numerical integration for the following oscillatory functions. However mathematica can. However, before I take the mathematica results, just need to check with you.

Following link shows that for a diverging series, the (Numerical) integral is finite.

http://books.google.com.sg/books?id=vntDnyh0gacC&pg=PA664&lpg=PA664&dq=nintegrate++seqlim&source=bl&ots=iNYR1o6kVd&sig=VuiQuiUMDEEGOBnguSwfcPPSHQA&hl=en&sa=X&ei=k_J4UofXJYjNkwW79IDYBw&ved=0CE4Q6AEwBA#v=onepage&q=nintegrate%20%20seqlim&f=false

1)

 Maple: 

eval(int(r^2 BesselJ(1,r)* BesselJ(0,r), r = 0..infinity)) 

Float(undefined)

Mathematica: 

NumberForm[ NIntegrate[BesselJ[0, x]*BesselJ[1, x]*x^2, {x, 0, Infinity},   AccuracyGoal -> 20], 15]

SequenceLimit::seqlim: The general form of the sequence could not be determined, and the result may be incorrect. >>

-95982.37707206068

2)  Maple:
       eval(int(r* BesselJ(0,r), r = 10..infinity)) 

                         Float(undefined)

Mathematica: 

NumberForm[ NIntegrate[BesselJ[0, x]*x, {x, 10, Infinity},   AccuracyGoal -> 20], 15]

SequenceLimit::seqlim: The general form of the sequence could not be determined, and the result may be incorrect. >>

-0.434727

Any conclusions on the result.

a) Why maple not able to evaluate the integrals.  b) Are the result of the Mathematica can be considered as appropriate.

Attached is the maple file for your consideration.

Integrations.mw 

Lookinf forward to your reply.

Thanks.

Hello!

Im a regular student and Math is a really difficult topic for me, and every once in a while i run into a problen that i am unable to solve. This time i would like to ask this commmunity for some help. Many thanks in advance.

The function itself is: y = sqrt((x^2-5*x+6)/log[10]((x+10)^2))

I was able to determine the domain (X), but i am having very big trouble with finding the range (Y). Also i should be able to do it with pen on paper, but so far i have wasted 2 days and many papers on pointless scribblig.

Could anyone please explain how could i find the range of that function and provide a step by step solution? 

Suppose I broadcast a game show where every episode there is 5 randomly chosen topics from 8 possible topics (A,B,C….). how can I get maple to do this automatically?

 I thought I could use

  > with(combinat):

> choose([A,B,C,D,E,F,G,H], 5);

of course the output comes out ordered. is there some way to randomize it? or another way? rgds

Hi, 

I have the following six equations that I need to solve:

eq1 := A^5*f6+A^4*f5+A^3*f4+A^2*f3+A*f2+f1 = ln(V1);
print(??); # input placeholder
eq2 := B^5*f6+B^4*f5+B^3*f4+B^2*f3+B*f2+f1 = ln(V2);

eq3 := 5*A^4*f6+4*A^3*f5+3*A^2*f4+2*A*f3+f2 = F1/V1;
eq4 := 5*B^4*f6+4*B^3*f5+3*B^2*f4+2*B*f3+f2 = F2/V2;
eq5 := 20*A^3*f6+12*A^2*f5+6*A*f4+2*f3 = G1/V1-[F1/V1]^2;
eq6 := 20*B^3*f6+12*B^2*f5+6*B*f4+2*f3 = G2/V2-[F2/V2]^2;

 where V1, V2, F1 & F2 have previously been found/defined in the worksheet (document).

When I use the solve command, more often than not I get the expression for the numerical calculation for each variable f1-f6, rather than an actual value:

solutionset := solve({eq1, eq2, eq3, eq4, eq5, eq6}, {f1, f2, f3, f4, f5, f6})

{f1 = 0.4096495220755576e-2*[-1.328181534188746]^2-0.3072371415566682e-1*[-9.408269235937702]^2+12.64287210303000, f2 = .3686845698680018*[-9.408269235937702]^2-49.98313436120349-0.6690942193900774e-1*[-1.328181534188746]^2, f3 = -1.423532089212563*[-9.408269235937702]^2+150.6490386090756+.3909877105143377*[-1.328181534188746]^2, f4 = -.9490213928083751*[-1.328181534188746]^2+1.954938552571689*[-9.408269235937702]^2-190.3706247009334, f5 = .8192990441511152*[-1.328181534188746]^2-1.115157032316796*[-9.408269235937702]^2+103.8844069311055, f6 = .2275830678197542*[-9.408269235937702]^2-20.57204700597870-.2275830678197542*[-1.328181534188746]^2}

Why is Maple not giving me the actual value for the variables, and how do I get it to do so, everytime? [In fact it did output the actual values once – but I have no idea what I did differently: it seems to be very random….]

i.e. how do I output the following:

solutionset := {f1 = 9.930572749191651, f2 = -17.46685689954139, f3 = 25.33406943774393, f4 = -19.00233912206421, f5 = 6.620988906086421, f6 = -.8288827301180226}

thanks

hi

is there any way that i run my maplet output in  systems that havnt any maple install on them?

(i wanna run maple program without maple)

Reza²⁹⁶¹

Bonjour,

Comment se calcule avec maple le développement de laurent d'une fonction de deux variables ?

Maple n'autorise pas la commande laurent(1/x/y, [x=0,y=0]).

Merci d'avance.

Gérard.

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

Compute integral In(X)/(X-A)(X-1)    0<x<∞ for positive a.

                         ∞

Compute the sum∑(k^2+k-1)/(k+2)! 

                        k=1