maple2015

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Hi

I need to express some discrete functions with domain in the natural numbers.

Is there a command like the 'AllSolutions' which is used for int?

As an example, how we can express all possible values of first derivative of chebyshev polynomial for various orders in terms of a piecewise function at origin ?

The following commands do not return a suitable answer, in this case!

f:=diff(ChebyshevT(n, r), r):

g:=simplify(eval(f, r = 0), symbolic) assuming(n::integer);

`assuming`([convert(g, piecewise, n)], [n::integer]);

Hi

Assume a linear second order ode with constant coefficients as follows:

M*u''+C*u'+K*u=0

where the symbol (') denotes derivative with respect to time and M, C and K are positive real constants.

The initial conditions are u(0)=u0 and u'(0)=u'0.

Substituting u=exp(a*t) in the ODE to calculate characteristic equation, one has

M*a^2+C*a+K=0  ---> If 0<C<2sqrt(M*K) then u=exp(-C/(2M)*t)*(c1*sin(w*t)+c2*cos(W*t))

in which c1 and c2 can be obtained from initial conditions and W=sqrt(C^2-4*M*K)/2M.

For the case that C is imaginary number, assuming C=i*c yields

{a1,a2} ={ -(c/(2M) +sqrt(c^2+4*M*K)/2M)*i,(-c/(2M) +sqrt(c^2+4*M*K)/2M)*i }

where i is one of the square roots of -1.

Is it true to write u=c1*(sin(a1*t)+cos(a1*t))+c2*(sin(a2*t)+cos(a2*t)) ?

I solve two examples by Maple,

dsolve({diff(u(t), t, t)+0.1*(diff(u(t), t))+2*u(t)} union {u(0) = 1, (D(u))(0) =0.1});

dsolve({diff(u(t), t, t)+0.1*I*(diff(u(t), t))+2*u(t)} union {u(0) = 1, (D(u))(0) = 0.1});

Second example gives complex answer. Is it possible to get trigonometric answer with real constants c1 and c2?

Hi

I need to find a relation between delta [m,k] in terms of m and k

delta[m,k]=f(m,k), where k=0,1,2,...,m

A code is written (delta.mw) to find delta[m,k] for a certain amoun of m.

Is there a way or a code to find a general form of f(m,k)?

Thanks

 

 

Hi

For the data presented below, assuming a linear model yields to observe the great amounts of standard errors.

Is there a way (an appropriate command) to find the best statistical model?

 

Y := `<,>`(.2, .2, .2, .2, .2, .3, .3, .3, .3, .3, .3, .35, .35, .35, .35, .35, .35);

X := `<,>`(2, 2.2, 2.4, 2.6, 2.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 2, 2.2, 2.4, 2.6, 2.8, 3);

Z := `<,>`(15, 33.7, 62.8, 188, 394, 5.47, 5.82, 6.21, 8.3, 11.5, 24.1, .372, .485, .675, 1.11, 1.27, 1.35);

Statistics:-Fit(add(add(a[k, n-k]*x^k*y^(n-k), k = 0 .. n), n = 0 .. 2), `<|>`(X, Y), Z, [x, y], summarize = embed)

 

 

I want to know about some algorithms used by Maple, if there is a way to dig through the code.

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