Advanced Search

Alfred_F

Mr. Alfred Flaßhaar

605 Reputation

11 Badges

1 years, 358 days
Brandenburg, Germany
Contact Alfred Flaßhaar
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.

MaplePrimes Activity


These are questions asked by Alfred_F

An unruly integral...

Alfred_F 605 Maple
integration
10 hours ago
1 0

As an exercise to further familiarize myself with Maple, I would like to calculate the definite integral specified in the attached file. The integrand has an antiderivative, and a source lists the value of the integral as approximately 0.57... Based on the plot, this value is plausible according to a simple estimate (Pi/2 * 0.8 / 2). Following standard practice taught in school, I therefore calculated the difference between the values ​​of the antiderivative at the limits of integration. Surprisingly, the result is a complex number. What am I doing wrong? Did the internal Maple calculation switch to complex principal values?

testint5.mw

Local curve distance sought...

Alfred_F 605 Maple
integration numeric plotting
August 10 2026
2 6

For the purpose of practicing with Maple, I have worked on a definite integral in the attached file. I found it on the Internet. According to a side calculation, it can only be calculated using famous special functions or series expansions. That is why I am only interested in the numerical evaluation here. According to auxiliary calculations, it can only be computed using famous special functions or a series expansion. It is known that the series expansion of the antiderivative converges very rapidly. Therefore, for comparison purposes, I calculated the values ​​for integration limits of 10 and 100 instead of infinity. In the first graph, the two result curves appear to coincide perfectly. Is there a way to zoom in locally - like using a magnifying glass - to make the difference in the ordinate values ​​visible?

restart

int(sinh((Pi-a)*x)/(cosh(Pi*x)*sinh(a*x)), x = -100 .. 100)

int(sinh((Pi-a)*x)/(cosh(Pi*x)*sinh(a*x)), x = -100 .. 100)

 (1)

plot([int(sinh((Pi-a)*x)/(cosh(Pi*x)*sinh(a*x)), x = -100 .. 100), int(sinh((Pi-a)*x)/(cosh(Pi*x)*sinh(a*x)), x = -10 .. 10)], a = 0 .. 3.2, y = 0 .. 100)

  

plot(int(sinh((Pi-a)*x)/(cosh(Pi*x)*sinh(a*x)), x = -10 .. 10), a = 0 .. 3.2, y = 0 .. 100)

  

NULL

Download testint3.mw

Recalcitrant differential equation...

Alfred_F 605 Maple 2026
ode dsolve differential-equations
July 29 2026
3 2

In the attached file, I'd like to solve an ODE as an exercise. Only the "series" option yielded a solution. How can the length of the result series be controlled? Is there a package that leads to a "closed" solution – even using well-known transcendental functions?

restart

ode := (1+f(x))*(diff(f(x), x, x)) = 1+x

(1+f(x))*(diff(diff(f(x), x), x)) = 1+x

 (1)

ics := f(0) = 1, (D(f))(0) = 0

f(0) = 1, (D(f))(0) = 0

 (2)

dsolve({ics, ode}, f(x), series)

f(x) = series(1+(1/4)*x^2+(1/12)*x^3-(1/192)*x^4-(1/240)*x^5+O(x^6),x,6)

 (3)

``

Download test.mw

How is a cyclic command sequence program...

Alfred_F 605 Maple
programming recursion
July 25 2026
3 2

In the attached file, I would like to calculate the expressions for the function f(n,x) using a recursion for a given index range, e.g., n=3..15. I would appreciate any advice on this.
 

> 

NULL
> 

restart;
> 

kernelopts(version);

`Maple 2026.1, X86 64 WINDOWS, Jun 04 2026, Build ID 2018217`

 (1)
> 

f(1,x):=x;

x

 (2)
> 

f(2,x):=2*x + 2*sin(x);

2*x+2*sin(x)

 (3)
> 

f(n,x):=2*f(n-1,x)-f(n-2,x)+2*sin((n-1)*x)/(n-1);

2*f(n-1, x)-f(n-2, x)+2*sin((n-1)*x)/(n-1)

 (4)
> 

f(3,x):=eval(f(n,x),n=3);

3*x+4*sin(x)+sin(2*x)

 (5)
> 

f(4,x):=eval(f(n,x),n=4);

4*x+6*sin(x)+2*sin(2*x)+(2/3)*sin(3*x)

 (6)
> 

NULL
> 

NULL


 

Download test24c.mw

 

How to solve the equation?...

Alfred_F 605 Maple
solve
July 07 2026
2 1

I would like to solve an equation in the attached file as an exercise. I am looking for all solutions - including the complex ones. This is easily done using "derive". There are six solutions:

restart

solve(2^x*(2+sqrt(3))^x-2*(1+sqrt(3))^x = 2, x)

RootOf(2^_Z*(2+3^(1/2))^_Z-2*(1+3^(1/2))^_Z-2)

 (1)

NULL

edited "test":

test.mw

Five are complex, and the single real solution can be guessed simply by taking a close look. I am unable to obtain the complete solution in Maple; I cannot find my mistake and would appreciate some advice.

1 2 3 4 5 6 7 Last Page 1 of 19