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Paras31

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1 years, 91 days
Hellenic Open University
Mathematician

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Teacher of Mathematics with a proven track record of working in education management. Proficient in Ease of Adaptation, Course Design, and Instructional Technology. Holds a Bachelor's degree in Mathematics from the University of the Aegean and a Master's in Applied Mathematics at the Hellenic Open University, focusing on Ordinary and Partial Differential Equations. His enthusiasm lies in the application of mathematical models to real-world contexts, such as epidemiology and population growth. Aside from his passion for teaching, Athanasios enjoys football, basketball, and spending time with his dogs.

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These are questions asked by Paras31

Trouble Plotting Solution in Maple Using...

Paras31 245 Maple 2025
integration pde numeric
16 hours ago
1 2

Hello,

I’m trying to solve a problem from Modern Mathematical Methods for Scientists and Engineers using Maple, specifically applying the Fokas method (Unified Transform) to the heat equation on the half-line. The problem setup matches Example 9.1 from the book.

Everything runs fine until I try to plot the solution using plot3d.
 

> 

restart; with(plots); with(LinearAlgebra); with(Student[VectorCalculus]); V := proc (k, x, t) options operator, arrow; -((1/2)*I)*exp(I*k*x-k^2*t)*(1/(k-I)+1/(k+I)-k*(1/(k^2+1)+1/(k^2-1)))/(Pi*k) end proc

proc (k, x, t) options operator, arrow; Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(I, Student:-VectorCalculus:-`*`(2, Pi)^Student:-VectorCalculus:-`-`(1)), Student:-VectorCalculus:-`*`(exp(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(I, k), x), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(k^2, t)))), k^Student:-VectorCalculus:-`-`(1))), Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(k, Student:-VectorCalculus:-`-`(I))^Student:-VectorCalculus:-`-`(1), Student:-VectorCalculus:-`+`(k, I)^Student:-VectorCalculus:-`-`(1)), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(k, Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(k^2, 1)^Student:-VectorCalculus:-`-`(1), Student:-VectorCalculus:-`+`(k^2, -1)^Student:-VectorCalculus:-`-`(1))))))) end proc

 (1)
> 

phi1 := (1/8)*Pi; phi2 := 7*Pi*(1/8); k1 := proc (r) options operator, arrow; r*exp(I*phi1) end proc; k2 := proc (r) options operator, arrow; r*exp(I*phi2) end proc; dk1 := proc (r) options operator, arrow; diff(k1(r), r) end proc; dk2 := proc (r) options operator, arrow; diff(k2(r), r) end proc
> 

u1 := proc (x, t) options operator, arrow; evalf(int(Re(V(k1(r), x, t)*dk1(r)-V(k2(r), x, t)*dk2(r)), r = 0 .. 80)) end proc

proc (x, t) options operator, arrow; evalf(Student:-VectorCalculus:-int(Re(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`*`(V(k1(r), x, t), dk1(r)), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(V(k2(r), x, t), dk2(r))))), r = 0 .. 80)) end proc

 (2)
> 

u := proc (x, t) options operator, arrow; exp(-x/sqrt(2))*cos(t-x/sqrt(2))+u1(x, t) end proc

proc (x, t) options operator, arrow; Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`*`(exp(Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(x, sqrt(2)^Student:-VectorCalculus:-`-`(1)))), cos(Student:-VectorCalculus:-`+`(t, Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(x, sqrt(2)^Student:-VectorCalculus:-`-`(1)))))), u1(x, t)) end proc

 (3)
> 

plot3d(u(x, t), x = 0 .. 3, t = 0 .. 2*Pi, axes = boxed, shading = zhue, style = surface, labels = ["x", "t", "u(x,t)"])
> 

NULL


 

Download fokas_method.mw

Has anyone successfully handled similar integrals inside plot3d? Is there a better way to numerically evaluate the Fokas integral so Maple can plot it efficiently?

 

Why does plot3d take much longer with pd...

Paras31 245 Maple 2025
fourier plotting inttrans
July 01 2025
2 1

I'm solving the 1D heat equation using two different approaches, both involving Fourier transforms.

  1. First Attempt: Using pdsolve the Fourier method. This code either takes a very long time or doesn't produce a plot at all.

  2. Second Attempt: Manual Fourier transform. This one works fine and quickly plots the result.

Why does the first version using pdsolve(..., method = Fourier) result in slow or non-responsive behaviorplot3d, while the second version (manual transform) runs efficiently? Is the pdsolve result too symbolic or unevaluated for plotting? How can I make the first approach plot correctly?

Thanks for any insights!

ft1.mw

Plotting contour integral diagrams...

Paras31 245 Maple 2025
integration contour plotting
April 27 2025
3 4

 I am writing notes on complex analysis, I need to use figures of contour paths to integrate on them, i want to create something like this

I tried to plot the contour for 
\oint_{|z|=2} \frac{1}{z^2+1}\,dz
I need to have connecting lines all around because the poles can not be isolated

> 

with(plots); circle1 := plot([2*cos(t), 2*sin(t), t = 0 .. 2*Pi], color = blue, thickness = 2); circle2 := plot([(1/2)*cos(t), 1+(1/2)*sin(t), t = 0 .. 2*Pi], color = "Green", thickness = 2); circle3 := plot([(1/2)*cos(t), -1+(1/2)*sin(t), t = 0 .. 2*Pi], color = "Red", thickness = 2); sing1 := plottools[disk]([0, 1], 0.2e-1, color = white); sing2 := plottools[disk]([0, -1], 0.2e-1, color = white); label1 := textplot([.1, 1.1, "z = i"], font = [Arial, Bold, 12]); label2 := textplot([.1, -1.1, "z = -i"], font = [Arial, Bold, 12])
> 

display(circle1, circle2, circle3, sing1, sing2, label1, label2, scaling = constrained, labels = ["Re", "Im"])

 
 
> 

restart; f := proc (z) options operator, arrow; 1/(z^2+1) end proc; z := 2*exp(I*t); dz := diff(z, t); integrand := f(z)*dz; simplify(integrand); value(Int(integrand, t = 0 .. 2*Pi))

0

 (1)

Download CIF.mw

Plotting a simply connected domain and ...

Paras31 245 Maple 2025
plotting incomplete-question connected
April 22 2025
2 6

I am trying to create a diagram in Maple using its plotting tools and simulate a simply connected domain and multiple paths between two points.

My first try is the following

> 

with(plots); with(plottools)

 

 
> 

curveDomainPts := [[-1, 0], [-.7, 1.2], [0, 1.5], [.7, 1.2], [1.2, 0], [.7, -1.2], [0, -1.4], [-.7, -1.2], [-1, 0]]; domain := polygon(curveDomainPts, color = "LightBlue", transparency = .4); z0 := [-.8, .6]; z := [.9, -.4]; curve1_pts := [[-.8, .6], [-.3, 1.0], [.4, .5], [.9, -.4]]; curve2_pts := [[-.8, .6], [-.7, 0.], [.2, -.6], [.9, -.4]]; curve1 := pointplot(curve1_pts, color = red, linestyle = dot, thickness = 2, connect = true); curve2 := pointplot(curve2_pts, color = green, linestyle = dot, thickness = 2, connect = true); pt1 := pointplot([z0], symbol = solidcircle, symbolsize = 15, color = black); pt2 := pointplot([z], symbol = solidcircle, symbolsize = 15, color = black); label1 := textplot([z0[1], z0[2]-.1, z__0], font = [Helvetica, Bold, 14]); label2 := textplot([z[1], z[2]-.1, "z"], font = [Helvetica, Bold, 14]); display(domain, curve1, curve2, pt1, pt2, label1, label2, scaling = constrained, axes = none, title = "Curved Domain with Arbitrary Paths")

 
 

NULL

I would like to ask if I could create something like that in Maple or should I use another software to draw it?

Download curved_domain.mw

Exploring the Mapping of Vertical Lines ...

Paras31 245 Maple 2025
complex plotting conformal
April 10 2025
2 0

In the transformation w = e^z, vertical lines in the complex z-plane of the form Re(z)=a are mapped to circles of radius e^a in the w-plane.

Can I create a Maple visualization that does the following:

  1. Displays the result side by side, showing each vertical line in the z-plane and its corresponding mapped circle in the w-plane.

  2. Does it use a different color and style for each line and its image (e.g., dashed, dotted, solid, or different colors)?

> 

restart; interface(imaginaryunit = 'i')
> 

z := 2+2*I

2+2*I

 (1)
> 

with(plots); point1 := pointplot([[Re(z), Im(z)]], symbol = solidcircle, color = blue, axes = normal, labels = ["Re(z)", "Im(z)"], title = "Complex Number Plot")

 
> 

mod_z := abs(z)

2*2^(1/2)

 (2)
> 

vector1 := arrow([0, 0], [Re(z), Im(z)], color = red, shape = double_arrow, width = 0.5e-1, border = false, head_width = .1, head_length = .1); vector2 := arrow([0, 0], [0, Im(z)], color = green, shape = double_arrow, width = 0.5e-1, border = false, head_width = .1, head_length = .1); vector3 := arrow([0, 0], [Re(z), 0], color = yellow, shape = double_arrow, width = 0.5e-1, border = false, head_width = .1, head_length = .1)
> 

display([vector1, point1, vector2, vector3], axes = normal, labels = ["Re(z)", "Im(z)"], view = [0 .. 3, -1 .. 4], scaling = constrained, title = "Modulus of complex number")

 
> 

w := 2+3*I

2+3*I

 (3)
> 

z+w

4+5*I

 (4)
> 

z-w

-I

 (5)
> 

z.w

-2+10*I

 (6)
> 

z/w

10/13-(2/13)*I

 (7)
> 

restart
> 

with(plots); a := 2; complexplot(a+I*t, t = -Pi .. Pi, title = "Vertical Line Re(z)=2")

 
> 

A := [-3, -1, 0, 1, 2]; P := [seq(complexplot(x+I*y, y = -10 .. 10, color = red), `in`(x, A))]; display(P, title = "Multiple Vertical Lines in Complex Plane")

 
> 

with(plots); B := [-3, -1, 0, 1, 2]; H := [seq(complexplot(x+I*y, x = -10 .. 10, color = blue), `in`(y, B))]; display(H, title = "Multiple Horizontal Lines in Complex Plane")

 
 

NULL

Download operations.mw

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