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H-R

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These are questions asked by H-R

Showing Oriented Parametric Curve...

H-R 155 Maple 18
circle parametric
December 23 2015
3 21

Suppose I have the parametric equations of a circle

x=cost

y=sint

where t runs from 0 to 2*pi. How can I show the orientation of this parametric curve on a plot?

How to Transform Relation?...

H-R 155 Maple 18
December 22 2015
2 4

Suppose that I have the equation x=1. I want to manipluate it. For example, I want to multiply by 2. Then, Take the power of two. Next, take a cubic root. How can I do this in Maple?

Simplifying multivariate polynomial ...

H-R 155 Maple 2015
algebra polynomial linearalgebra
December 12 2015
1 0

I have a multivariate polynomial in x and y. How can I firstly collect the terms with respect to the powers of x and y and then simplifying their coefficients.

> 

restart
> 

with(RealDomain):
> 

with(LinearAlgebra):
> 

A := Matrix(5, 5, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 1, (1, 4) = 1, (1, 5) = 1, (2, 1) = 1, (2, 2) = 0, (2, 3) = c__1, (2, 4) = y, (2, 5) = c__2, (3, 1) = 1, (3, 2) = c__1, (3, 3) = 0, (3, 4) = c__3, (3, 5) = x, (4, 1) = 1, (4, 2) = y, (4, 3) = c__3, (4, 4) = 0, (4, 5) = c__4, (5, 1) = 1, (5, 2) = c__2, (5, 3) = x, (5, 4) = c__4, (5, 5) = 0})

Matrix(%id = 4510803138)

 (1)
> 

B := Determinant(A)

-2*c__1^2*c__4+2*c__1*c__2*c__3+2*c__1*c__2*c__4-2*c__1*c__2*x+2*c__1*c__3*c__4-2*c__1*c__3*y-2*c__1*c__4^2+2*c__1*c__4*x+2*c__1*c__4*y+2*c__1*x*y-2*c__2^2*c__3-2*c__2*c__3^2+2*c__2*c__3*c__4+2*c__2*c__3*x+2*c__2*c__3*y-2*c__2*c__4*y+2*c__2*x*y-2*c__3*c__4*x+2*c__3*x*y+2*c__4*x*y-2*x^2*y-2*x*y^2

 (2)
> 

``

 

Download A.mw

Series solution to an ODE?...

H-R 155 Maple 18
ode powseries
December 09 2015
1 4

I don't know what is the problem with this. Please take a look at it. Any help is appreciated. Thanks.

> 

restart
> 

with(RealDomain)

[Im, Re, `^`, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, cos, cosh, cot, coth, csc, csch, eval, exp, expand, limit, ln, log, sec, sech, signum, simplify, sin, sinh, solve, sqrt, surd, tan, tanh]

 (1)
> 

with(Slode)

[DEdetermine, FPseries, FTseries, candidate_mpoints, candidate_points, dAlembertian_formal_sol, dAlembertian_series_sol, hypergeom_formal_sol, hypergeom_series_sol, mhypergeom_formal_sol, mhypergeom_series_sol, msparse_series_sol, polynomial_series_sol, rational_series_sol, series_by_leastsquare]

 (2)
> 

ODE := x*(diff(y(x), x, x))-(diff(y(x), x))-x*y(x)

x*(diff(diff(y(x), x), x))-(diff(y(x), x))-x*y(x)

 (3)
> 

SS := convert(sin(x), FormalPowerSeries)

Sum((-1)^k*x^(2*k+1)/factorial(2*k+1), k = 0 .. infinity)

 (4)
> 

FPseries(ODE = SS, y(x), v(n))

Error, the right-hand side of the differential equation must be a polynomial or a series in x

  
> 

``

 

Download AA.mw

How to obtain the Maclaurin series of a ...

H-R 155 Maple 18
infinity series
December 09 2015
2 3

I want to obtain the taylor series of a function say sin(x) at x=0 up to infinity. I mean that I don't want a trauncated series. I tried using "series" and "taylor" but they just give the truncated series.

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