rrbaldino

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6 years, 98 days

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These are questions asked by rrbaldino

restart;
with(inttrans);
[addtable, fourier, fouriercos, fouriersin, hankel, hilbert, 

  invfourier, invhilbert, invlaplace, invmellin, laplace, mellin, 

  savetable]
laplace((diff(Dirac(t), t))*cos(t), t, s);
                               0
int((diff(Dirac(t), t))*exp(-s*t)*cos(t), t = 0 .. infinity);
                              1  
                              - s
                              2  
 

 

Why do I get different answers for the same command?

 different_answers.mw


 

``

restart

x := proc (n) options operator, arrow; cos(n*Pi) end proc;

proc (n) options operator, arrow; cos(n*Pi) end proc

(1)

"f:=k->"sum(k*x(n), n = 2 .. 3);f(1);

0

 

f(1)

(2)

f := proc (k) options operator, arrow; sum(k*x(n), n = 2 .. 3) end proc;

proc (k) options operator, arrow; sum(k*x(n), n = 2 .. 3) end proc

 

0

(3)

``


 

Download different_answers.mw


 

restart

eq := diff(y(t), t, t)+9*y(t) = Dirac(t)

diff(diff(y(t), t), t)+9*y(t) = Dirac(t)

(1)

with(inttrans):

icon := y(0) = 0, (D(y))(0) = 0;

y(0) = 0, (D(y))(0) = 0

(2)

dsolve({eq, icon}, y(t), method = laplace);

y(t) = (1/3)*sin(3*t)

(3)

dsolve({eq, icon}, y(t));

y(t) = (1/3)*(Heaviside(t)-1/2)*sin(3*t)

(4)

``


 

Download Dirac_for_Primes.mw

I want to use the solutuion of a DE as a function, including the possibility to plot it.

I have found out that the following comands work, but I cannot undesrtand why. Is there a simpler way?

Truly, Roberto R. Baldino

sol := dsolve({eq, icon}, i(t));
i := unapply(eval(i(t), sol), t);
plot(i(t), t = 0 .. 20, view = [-1 .. 20, -3 .. 3], gridlines);

How to change the numer of hatchings in a 3d plot?

 

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