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shashi598

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These are questions asked by shashi598

Why does simple differenciation using pa...

shashi598 30 Maple 2022
differentiation step-by-step fractional-derivative
July 13 2022
1 0

I recently got introduced to fractional calculus, I saw this image on the internet and went to verify the 3rd block of image i.e fractional differentiation on Maple 2022. But Maple returned answer which does not match the result claimed in the image i.e x. I want to know what I am missing here. But when used fracdiff() the answer matches.I also wanted to know how its done by using showSolution command but didn't get the answer. Can I get the steps? meme.mw


> 

f := diff(x, [`$`(x, 1/2)])

x

 (1)
> 

``
> 

evalb(diff(x, [`$`(x, 1/2)]) = x)

true

 (2)
> 

evalb(diff(x, [`$`(x, 1/2)]) = 2*sqrt(x/Pi))

false

 (3)
> 

ShowSolution(diff(x, x^(1/2)))

Error, invalid input: diff received x^(1/2), which is not valid for its 2nd argument

  
> 

fracdiff(x, x, 1/2)

2*x^(1/2)/Pi^(1/2)

 (4)
> 

ShowSolution(fracdiff(x, x, 1/2))

Error, (in Student:-Calculus1:-ShowSolution) input expression does not have any incomplete calculus operations

  
> 

NULL

Download meme.mw

 

What is the reason for unable to compute...

shashi598 30 Maple 2022
integration step-by-step
July 12 2022
1 0

I am curious to know steps of integration for e^(t^3)*(cos(t))^3 as Maple found the answer correctly. So I wanted to know how it got to that solution. I applied the commands shown in document but unable to get steps. I want to know the reason for this and is it possible to get it work.
 

> 

``
> 

exp(t^2)*cos(t)^3
> 

int(exp(t^2)*cos(t)^3, t)

-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t+3/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t+1/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t-1/2)-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t-3/2)

 (1)
> 

Student[Calculus1][IntTutor]()
> 

eval(-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t+3/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t+1/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t-1/2)-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t-3/2), [t = 1])

-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2+I)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2+I)+((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2-I)+((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2-I)

 (2)
> 

evalf[10](-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2+I)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2+I)+((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2-I)+((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2-I))

.8154967124+0.*I

 (3)
> 

        
with(Student:-Calculus1):

 

 
> 

Understand(Int, constant, constantmultiple, sum, difference)
> 

ShowSolution(Int(exp(t^2)*cos(t)^3, t), maxsteps = 1000)

Error, (in Student:-Calculus1:-ShowSolution) unable to compute solution steps

  
> 

NULL


 

Download e.mwe.mw

 

Why adding noise mu(t) to y_a not workin...

shashi598 30 Maple
statistics integration plotting
June 29 2022
2 1

5_6190449716501677775.pdf

I ahve a signal y_a to which adding mu(t) doesn't seem to give any plot but error , what is missing here?.

And also in second k(x,t) pdf file I want the value of k(x,t) after I did the integration. When I type k(x,t) and hit enter it's not giving me the value of k(x,t) but returns k(x,t) as it is.K(x_t).pdf

Expecting numerical value from Integrate...

shashi598 30 Maple
integration distribution numeric
June 29 2022
2 0

pdf.mw
 

> 

with(stats)
> 

"f(x):=statevalf[pdf,normald[0,2*4.47]] "

proc (x) options operator, arrow, function_assign; statevalf[pdf, normald[0, 2*4.47]] end proc

 (1)
> 

plot(f(x), -20 .. 20)

 
> 

int(x*f(x), x)

.5000000000*x^2*statevalf[pdf, normald[0, 8.94]]

 (2)
> 

NULL


 

Download pdf.mw

Want to integrate x*f(x) where x is from -20..20, I am expecting a pure float number but getting symbols like statevalf_pdf in answer.

 

Getting error too many levels of recursi...

shashi598 30 Maple 2022
integration pde differential-equations
June 23 2022
1 0

recurssion.mw

> 

NULL
> 

"f(x,t) :=(|Psi|)^(2)"

proc (x, t) options operator, arrow, function_assign; abs(Psi)^2 end proc

 (1)
> 

" a(t):=piecewise(0<= t<=1,1.5*t,1<= t<=2,1.5*(2-t))"

proc (t) options operator, arrow, function_assign; piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 1.5*(2-t)) end proc

 (2)
> 

" y[a](t):=piecewise(0<= t<=0.1,a(t),0.1<= t<=0.2,-a(t))"

proc (t) options operator, arrow, function_assign; piecewise(0 <= t and t <= .1, a(t), .1 <= t and t <= .2, -a(t)) end proc

 (3)
> 

"y(t):=y[a](t)+mu(t)"

proc (t) options operator, arrow, function_assign; y[a](t)+mu(t) end proc

 (4)
> 

"w(t):=&int;x(t)*f(x,t) &DifferentialD;x"

proc (t) options operator, arrow, function_assign; int(x(t)*f(x, t), x) end proc

 (5)
> 

" v(t):=y(t)-w(t)*w(t)"

proc (t) options operator, arrow, function_assign; y(t)-w(t)^2 end proc

 (6)
> 

NULL
> 

diff(K(x, t), t) = beta*v(t)*f(x, t)

Error, (in y[a]) too many levels of recursion

  
> 

"map(int, , t)"

Error, invalid function arguments

"map(int,,t)"

  
> 

NULL

Here psi is a general wave function from schrodinger wave equation.

Download recurssion.mw

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