210 Reputation

7 years, 210 days

How calculating this contour integral...

Maple
 Contour integration notation   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  notation  ? - calculating this complexe contour integral? Seems that the concept of the contour integration is similar wit a line integral in real calculus ?

Is 2D input reliable versus 1d maple inp...

Maple

I following a example of products multiplication like this one

u:=n->Product(2*k-1,k=1..n)/Product(3*k-1,k=1..n)*x^n;

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 is not working on my...

Maple

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

 > restart;
 > with(student):
 > interface(typesetting = extended);
 (1)
 > Typesetting:-Settings(typesetprime = true);
 (2)
 >
 (3)
 > and  are not working on my keyboard as prime?
prime symbols (not showed)  not as (3)

========================================

 >
 >
 (4)
 >
 >
 (5)
 >
 >
 (6)
 >
 (7)
 >
 (8)
 >
 (9)
 >
 (10)
 >
 (11)
 >
 (12)

=================================================

Application Differential equation :

 > int((10000*k/(100*k*P(t) - 1) - 100/P(t))*diff(P(t), t), t = 0 .. t) = t;
 (13)
 > P(t)=solve(%,P(t));

This error .. see  Applications to Differential Equations

 Applications to Differential Equations
 >

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 ?

Transforming to 2d input from a derative...

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 ?

 > restart;

Een antwoord ergens gegeven is

+ C                                                             (vb)

Mple geeft

 > Int(sqrt(x^2+1),x)=int(sqrt(x^2+1),x)+C[1];
 (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

 > convert(%,ln);
 (2)

(2)  is hetzelfde (vb)

Dezelfde integraal i sook gegeven als

 > Int(sqrt(x^2+1),x)=((x+sqrt(x^2+1))^2+4*ln(x+sqrt(x^2+1))-(x+sqrt(x^2+1))^(-2))/8+C[2];
 (3)

Controle

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

 > #lhs(%);
 > #rhs(%%);
 >
 > #diff(lhs(%)-rhs(%)=0,x);
 >
 > #diff(f,x);
 > diff(lhs(%)-rhs(%)=0,x);
 (4)
 > simplify(%);
 (5)

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