Alfred_F

Mr. Alfred Flaßhaar

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1 years, 197 days
Brandenburg, Germany
As a retired individual with degrees from German universities in mathematics/analysis and structural engineering, I spent my professional life in responsible positions in research, teaching, and practical application, working on the mathematical modeling of states and processes in real-world systems. Now I have the time to explore interesting mathematical problems using Maple. It is my professional curiosity that drives me.

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These are questions asked by Alfred_F

On my journey of discovery through the Maple world, I now want to try out Maple's convenient features in the complex plane, something that used to be laboriously worked out and demonstrated on the blackboard with chalk. I couldn't find a suitable introduction in the help text. I'm interested in whether a package needs to be loaded and how to handle polynomials, series, and line integrals (I have a reasonable understanding only of the theory).

In the attached file, I want to calculate the integral Q1. Numerically, this is easy to do in Maple. For theoretical reasons, the exact result pi/e is known. However, a contradiction arises between command lines (4) and (5). Command (6) is also unsuccessful, as its exact result is unknown. What am I doing wrong?

restart

Q1 := int(sin(Pi*x)/(x^x*(1-x)^(1-x)), x = 0 .. 1)

int(sin(Pi*x)/(x^x*(1-x)^(1-x)), x = 0 .. 1)

(1)

evalf[100](Q1)

1.155727349790921717910093183312696299120851023164415820499706535327288631840916939440188434235673559

(2)

evalf[100](Pi/exp(1))

1.155727349790921717910093183312696299120851023164415820499706535327288631840916939440188434235673559

(3)

is(Q1 = Pi/exp(1))

false

(4)

identify(evalf[100](Q1))

Pi*exp(-1)

(5)

identify(.2340257795502385151002175791580229871350403567739388325733228478980460706709848394726222465477567339)

.2340257795502385151002175791580229871350403567739388325733228478980460706709848394726222465477567339

(6)

NULL

Download test.mw

The plot in the attached file only works if the complete function expression is entered. If only the function name is entered, no plot appears. What am I doing wrong?test.mw

restart;

c(x)dsum(sin(10^k*x)/10^k, k = 1 .. 10^2)

plot(c(x), x = -(1/4)*Pi .. (1/4)*Pi)

 

``

c(x)dsum(sin(10^k*x)/10^k, k = 1 .. 10^2)

plot(sum(sin(10^k*x)/10^k, k = 1 .. 10^2), x = -(1/4)*Pi .. (1/4)*Pi)

 

 

NULL

Download test.mw

I'm looking for the general solution to the attached differential equation. Maple doesn't provide it. What am I doing wrong?

restart

ode5 := diff(y(x), x) = (8*y(x)*b-32*b^2*x/y(x)-64*b^2*x^2*y(x))/(3*y(x)^2+8*b*x-16*b^2*x^2/y(x)^2)

diff(y(x), x) = (8*y(x)*b-32*b^2*x/y(x)-64*b^2*x^2*y(x))/(3*y(x)^2+8*b*x-16*b^2*x^2/y(x)^2)

(1)

simplify(ode5)

diff(y(x), x) = ((64*b^2*x^2-8*b)*y(x)^3+32*b^2*x*y(x))/(-3*y(x)^4-8*b*x*y(x)^2+16*b^2*x^2)

(2)

dsolve(ode5, y(x))

NULLNULL

Download testdgl5.mw

In the attached file, I want to transform (1) into (3) and back again (3) into (1). Attempts using CompleteSquare and expand in combination with other commands have failed. I would appreciate any advice.

dio1.mw

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