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These are questions asked by janhardo

Contour integration notation

" (∫)[+infinity]^(+infinity)((-x)^(z))/((e)^(x)-1). (ⅆx)/(x)"


The limits of integration are intented to indicate a path of integration which begins at + ∞, moves to th e left down the positive real axis, circles the orign once in positive ( counterclockwise) direction, and returns up to the positive real axis to  +∞

-How does this contour look like  in a  graph ?
- the "(ⅆx)/(x)" notation  ?
- calculating this complexe contour integral?

Seems that the concept of the contour integration is similar wit a line integral in real calculus ?


Download contourintegraal_vraag1.mw

I following a example of products multiplication like this one


Calculating with  this with maple 1d input is correct, but when i convert a maple 1d input  to 2D input ( i did somewhere) and use this then there is difference with the maple 1d calculation

Seems to be not a advisable to use converted maple 1d to 2 D input for calculation : ( for a mixed calculation(maple input/2D input)  or solely 2d input) , but only for purpose of seeing what the expression in maple input is standing for.   

Note: i did the calculation again with mixed input and now the correct sequenze of answers shows up ?

The prime notation as used default on my keyboard is not the same as used in Maple.




interface(typesetting = extended);



Typesetting:-Settings(typesetprime = true);



diff(y(x), x)

diff(y(x), x)


y*`\`   `and  diff(y(x), x)are not working on my keyboard as prime?

 prime symbols (not showed)  not as (3)




`Maple 2021.1, X86 64 LINUX, May 19 2021, Build ID 1539851`


interface(typesetting = extended)

diff(y(x), x)

diff(y(x), x)


Typesetting:-Settings(typesetprime = true)

diff(y(x), x)

diff(y(x), x)



diff(diff(diff(y(x), x), x), x)



y(x)*`will now be displayed as`*y


diff(y(x), x)

diff(y(x), x)



diff(diff(diff(y(x), x), x), x)


PDEtools:-declare(f(x, y))

f(x, y)*`will now be displayed as`*f


diff(f(x, y), y, x, y)

diff(diff(diff(f(x, y), x), y), y)



Application Differential equation :  

int((10000*k/(100*k*P(t) - 1) - 100/P(t))*diff(P(t), t), t = 0 .. t) = t;

int((10000*k/(100*k*P(t)-1)-100/P(t))*(diff(P(t), t)), t = 0 .. t) = t



Error, (in solve) cannot solve expressions with diff(P(t), t) for P(t)


This error .. see  Applications to Differential Equations

Applications to Differential Equations




Download vraag_over_dv_in_harald_pleym_-error_.mw

Also a error in old studymaterial : how to be fixed ? ...or obselote now this calculation and must be replaced for a modern calculation in Maple ?

Thought always that the round d is reserved for function of two variables x,y , but  that seems to be not the case here ?


Comparing Different Answers


Een antwoord ergens gegeven is

Int(sqrt(x^2+1), x) = (1/2)*x*sqrt(x^2+1)+(1/2)*ln(x+sqrt(x^2+1)) + C                                                             (vb)


Mple geeft



Int((x^2+1)^(1/2), x) = (1/2)*x*(x^2+1)^(1/2)+(1/2)*arcsinh(x)+C[1]



De twee antwoorden lijken nog niet opelkaar !
In het gegeven antwoord staat er een ln en in Maple kan een expressie omgezet worden in ln termen


Int((x^2+1)^(1/2), x) = (1/2)*x*(x^2+1)^(1/2)+(1/2)*ln(x+(x^2+1)^(1/2))+C[1]


(2)  is hetzelfde (vb)

Dezelfde integraal i sook gegeven als


Int((x^2+1)^(1/2), x) = (1/8)*(x+(x^2+1)^(1/2))^2+(1/2)*ln(x+(x^2+1)^(1/2))-(1/8)/(x+(x^2+1)^(1/2))^2+C[2]



een effectieve manier om twe antwoorden t evergelijken voor hetzelfde probleem is het verschil te berekenen van een vergelijking met de twee integralen








(x^2+1)^(1/2)-(1/4)*(x+(x^2+1)^(1/2))*(1+x/(x^2+1)^(1/2))-(1/2)*(1+x/(x^2+1)^(1/2))/(x+(x^2+1)^(1/2))-(1/4)*(1+x/(x^2+1)^(1/2))/(x+(x^2+1)^(1/2))^3 = 0



0 = 0


Strange that  diff(lhs(%)-rhs(%)=0,x);  is translated by 2 d input with round d notation for functions with two variables ?
The two integrals are functions of one variable
diff(f, x)

Download Controleren_dezelfde_antwoord_voo_expressies.mw

Sometimes its easier when doing math in maple input mode to use first the 2d maple input mode and convert this to maple input
Is there a hotkey assigned in Maple to do this toggling from 1d input to 2d input ( also from 1d output to 2d output  )

Now it must be done by mouse

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