## Problem with characteristic equation...

Hi fellow Maple users,

I'm trying to solve an eigenvalue problem of Ax=wx, where A is a 6 by 6 Hermitian matrix with two parameters x and y. I want to solve it for w and then plot3d it with x and y as unknowns. The way I have been doing is first find the characteristic equation Determinant(A-wI)=0 and then solve it for w, and then plot3d the solutions within a range for x and y. My problem is sometimes solve(Determinant(A-wI)=0,w) would give me the 6 solutions expressed in x and y, but sometimes when the numbers in A are changed it will only give me a Rootof solution with which I cannot plot. I'm wondering if there is a better way to do this. I'm actually not very interested in the symbolic solution of w expressed in x and y, just the plot, so if there is a numerical alternative it's good too.

## How to show chain rule when diff?...

how to show chain rules result when diff this

Eq1 := f(x,g(x,t)) + f(x,y);
diff(Eq1, x);

http://math.stackexchange.com/questions/372093/chain-rule-definition-f-fx-gx-y

## How to plot two vectors of data?...

Hoe do you plot two vectors of data as a bar plot or historygram. I tried the statistics package but could not plot a bar plot that shows the proper relation of numbers in vector x to numbers in relation to vector y. Vector x contained years as data, and vector y contained for example crime data per year.

## 'tord' error in Basis and Normal Form ...

with(Groebner):
T := lexdeg([x,y,z],[e1,e2]);
intermsof1 := y;
intermsof2 := -z;
GB := Basis([e1-intermsof1, e2-intermsof2], 'tord',T);
result := NormalForm(y^2-x*z, GB,'tord', T);
result := NormalForm(y^2-x*z, GB, T);

originally Basis do not have error when without parameter 'tord'

after it has argument error, it has to be added extra parameter tord

NormalForm has the same error too.

i do not understand why it has error, how to solve?

i just want to express y^2-x*z in terms of y and -z

## Warning, solutions may have been lost...

hi everyone,
I wanna to solve this equation using maple 12 but I receive this warning message

cos(x)*cosh(x)=1

cos(x)*cosh(x)=-1

tan(x)=tanh(x)

## How to solve Cauchy sequences...

(a) Show that if {an} ∞ n=1 is Cauchy then {a 2 n} ∞ n=1 is also Cauchy. (b) Give an example of a Cauchy sequence {a 2 n} ∞ n=1 such that {an} ∞ n=1 is not Cauchy

## how to solve an exercise with Maple involving the ...

Show that 2^3 + x ^2 − 3x + 2 is O(x ^3 ).

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## How to solve infinite series...

If a dosage Q units of a certain drug is administrated to an individual, then the amount remaining in the bloodstream at the end of t minutes is given by Q*exp^-ct, where c>0. Suppose this same dosage is given at successive T-minute intervals.

a) Show that the amount A(k) of the drug is given by A(k) = ∑n=0k-1 Q*exp(^-ncT).

b) Find an upper bound for the amount of the drug in the bloodsteam after any number of doses.

c) Find the smallest time between doses that will ensure that A(k) does not exceed a certain level M for M>Q.

## Gerschorin's theorem Linear Algebra...

worksheet/expressions/copypasteMaple

Gerschgorin := proc (A::Matrix) local Delta, m, n, AA, R, C, i, c, eig, P, Plt; Delta := proc (i, j) if i = j then 0 else 1 end if end proc; m, n := LinearAlgebra[Dimension](A); AA := Matrix(m, n, proc (i, j) options operator, arrow; Delta(i, j)*abs(A[i, j]) end proc); R := evalm(`&*`(AA, Vector(m, 1))); C := {seq(('plottools[circle]')([Re(A[i, i]), Im(A[i, i])], R[i], color = violet), i = 1 .. m)}; c := {seq(('plottools[point]')([Re(A[i, i]), Im(A[i, i])], color = blue, symbol = diamond), i = 1 .. m)}; eig := evalf(LinearAlgebra[Eigenvalues](A)); P := {seq(('plottools[point]')([Re(eig[i]), Im(eig[i])], color = red, symbol = box), i = 1 .. m)}; Plt := `union`(`union`(C, c), P); plots[display](eval(Plt), scaling = constrained) end proc

A := Matrix([[5, 8, 4, -3], [8, -9, 7, 5], [0, 4, 4, 2], [5, -5, 9, -9]]); evalf(LinearAlgebra[Eigenvalues](A), 3); Gerschgorin(A)

worksheet/expressions/pasteMathML

F := Matrix([[2, -1/2, -1/3, 0], [0, 6, 1, 0], [1/3, -1/3, 5, 1/3], [-1/2, 1/4, -1/4, 4]]); evalf(LinearAlgebra[Eigenvalues](F)); Gerschgorin(F)

Could you print A & F ?

regards

## how to copy and paste from maple 12 a quite big qu...

Hi, as I can't manage to copy and paste on mapleprimes, I would be glad to get a hint ...

## sequence convergence and limit...

Determine wether the sequence below converges or diverges, and if it converges, find the limit.

and,

Thanks

## discontinue in piecewise function...

how can you graph when piecewise function is not continuous?

example:

BB := piecewise (-1.57 < c and c < -1.56, h, -0.06< c and  c < -0.05, aa, -0.5< c and c < 0.04, bb);

## piecewise function...

how to graph in maple

for example

-2 < x < -3, h

-1 < x < -2, b

why do I get the error Error, (in rtable/Sum) invalid arguments

In positive numbers, I get it ok

## something wrong with implicitplot?...

code:

restart;
convert([92*x/790+18*x*(1-y)/1000=0.125,ln(46.59/x)=1/1.5*(ln(0.553/y)+2.5*ln((1-y)/(1-0.553)))],rational);
fsolve(%);
plots:-implicitplot(%%,x=0..2,y=0..1,numpoints=1000,thickness=2,gridlines,color=[blue,red]);

question:

there is something missing with the red line. I can't find the intersect point on the figure.

Is there something wrong with implicitplot?

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