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Paras31

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1 years, 94 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 replies submitted by Paras31

@Rouben Rostamian, I created a func...

Paras31 245
July 22 2025
0 0


@Rouben Rostamian, I created a function, so the solution is given faster now, but when I try to replicate the two panels from the textbook, as you can see they are a bit different


 

> 

restart; with(plots); with(ColorTools); 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+I)+1/(k^2-I)))/Pi end proc; k1 := proc (r) options operator, arrow; r*exp(((1/8)*I)*Pi) end proc; k2 := proc (r) options operator, arrow; r*exp(((7/8)*I)*Pi) end proc; dk1 := proc (r) options operator, arrow; exp(((1/8)*I)*Pi) end proc; dk2 := proc (r) options operator, arrow; exp(((7/8)*I)*Pi) end proc; u1 := proc (x::numeric, t::numeric) try evalf(Int(Re(V(k1(r), x, t)*dk1(r)-V(k2(r), x, t)*dk2(r)), r = 0 .. infinity)) catch: 0 end try end proc; approx_u := proc (x::numeric, t::numeric) Re(evalf(exp(-x/sqrt(2))*cos(t-x/sqrt(2))+u1(x, t))) end proc; surf := plot3d(proc (x, t) options operator, arrow; approx_u(x, t) end proc, 0 .. 3, 0 .. Student[VectorCalculus]:-`*`(2, Pi), grid = [40, 40], axes = boxed, labels = ["x", "t", "u(x,t)"], title = "Fokas Method Solution of Half-Line Heat Equation", shading = zhue)

 
> 

``

 

 
> 

p1 := plot(proc (x) options operator, arrow; approx_u(x, .1) end proc, 0 .. 2, color = red); p2 := plot(proc (x) options operator, arrow; approx_u(x, .2) end proc, 0 .. 2, color = green); p3 := plot(proc (x) options operator, arrow; approx_u(x, .3) end proc, 0 .. 2, color = blue); p4 := plot(proc (x) options operator, arrow; approx_u(x, .4) end proc, 0 .. 2, color = magenta); p5 := plot(proc (x) options operator, arrow; approx_u(x, .5) end proc, 0 .. 2, color = RGB(1.0, .5, 0.)); p6 := plot(proc (x) options operator, arrow; approx_u(x, .6) end proc, 0 .. 2, color = cyan); p0 := plot(exp(-x), x = 0 .. 2, linestyle = dash, color = black); display([p0, p1, p2, p3, p4, p5, p6], legend = ["u(x,0)", "t=0.1", "t=0.2", "t=0.3", "t=0.4", "t=0.5", "t=0.6"], legendstyle = [location = right, font = [Helvetica, 12]], view = [0 .. 2, 0 .. 1.2], labels = ["x", "u(x,t)"], labelfont = [Helvetica, 12], axes = boxed, title = "Short-Time Behavior of u(x,t)")

 
> 

q1 := plot(proc (x) options operator, arrow; approx_u(x, .5) end proc, 0 .. 2, color = red); q2 := plot(proc (x) options operator, arrow; approx_u(x, 1.0) end proc, 0 .. 2, color = green); q3 := plot(proc (x) options operator, arrow; approx_u(x, 1.5) end proc, 0 .. 2, color = blue); q4 := plot(proc (x) options operator, arrow; approx_u(x, 2.0) end proc, 0 .. 2, color = magenta); q5 := plot(proc (x) options operator, arrow; approx_u(x, 2.5) end proc, 0 .. 2, color = RGB(1.0, .5, 0.)); q6 := plot(proc (x) options operator, arrow; approx_u(x, 3.0) end proc, 0 .. 2, color = cyan); q0 := plot(exp(-x), x = 0 .. 2, linestyle = dash, color = black); long_plot := display([q0, q1, q2, q3, q4, q5, q6], title = "Long-Time Behavior of u(x,t)", labels = ["x", "u(x,t)"], labelfont = [Helvetica, 12], legend = ["u(x,0)", "t=0.5", "t=1.0", "t=1.5", "t=2.0", "t=2.5", "t=3.0"], legendstyle = [location = right, font = [Helvetica, 10]], axes = boxed, view = [0 .. 2, -1.2 .. 1.2])

 

 

 
> 

``


 

Download fokas_method_new.mw

@dharr Thank you for your answer an...

Paras31 245
July 22 2025
0 0

@dharr Thank you for your answer and the time you spent looking at my question. I will try to find a faster way. 

@dharr oh!! Thank you this info is ...

Paras31 245
July 01 2025
0 0

@dharr oh!! Thank you this info is very usefyl.

  > ....

Paras31 245
May 07 2025
0 0
> 

restart; with(plots); with(plottools); TR := proc (col) options operator, arrow; cat(`#mo("►",mathcolor="`, col, `")`) end proc; TL := proc (col) options operator, arrow; cat(`#mo("◄",mathcolor="`, col, `")`) end proc; TU := proc (col) options operator, arrow; cat(`#mo("▲",mathcolor="`, col, `")`) end proc; TD := proc (col) options operator, arrow; cat(`#mo("▼",mathcolor="`, col, `")`) end proc; `print/slash` := proc (x, y) Typesetting:-mrow(Typesetting:-Typeset(x), Typesetting:-mo(), Typesetting:-mo("/", fontweight = "bold"), Typesetting:-mo(), Typesetting:-Typeset(y)) end proc; h := .2; Rint := 1/4; Rout := 2; aint := arcsin(h/Rint); aout := arcsin(h/Rout); opt := color = red, thickness = 2; theta1 := 0-(1/3)*Pi-.1; theta2 := Pi+(1/4)*Pi+.3; phi1 := 3*Pi*(1/4)-.3; phi2 := 2*Pi+(1/4)*Pi+.3; x1 := Rint*cos(theta1); y1 := 1+Rint*sin(theta1); x2 := Rint*cos(theta2); y2 := 1+Rint*sin(theta2); x3 := Rint*cos(phi1); y3 := -1+Rint*sin(phi1); x4 := Rint*cos(phi2); y4 := -1+Rint*sin(phi2); t := .5; x_arrow1 := (1-t)*x1+t*x4; y_arrow1 := (1-t)*y1+t*y4; x_arrow2 := (1-t)*x2+t*x3; y_arrow2 := (1-t)*y2+t*y3; display(arc([0, 0], Rout, aout .. 3*Pi-aout, opt), arc([0, 1], Rint, theta1 .. theta2, opt), arc([0, -1], Rint, phi1 .. phi2, opt), line([x1, y1], [x4, y4], opt), line([x2, y2], [x3, y3], opt), textplot([x_arrow1, y_arrow1, TU("red")], font = [Times, 20]), textplot([x_arrow2, y_arrow2, TD("red")], font = [Times, 20]), textplot([0, Rout, TL("red")], font = [Times, 20]), textplot([0, -Rout, TR("red")], font = [Times, 20]), textplot([0, -1.25, TR("red")], font = [Times, 20]), textplot([0, 1.25, TL("red")], font = [Times, 20]), textplot([.2, -1., z = -i], align = {above, left}), textplot([.2, 1., z = i], align = {above, left}), axis[1] = [tickmarks = []], axis[2] = [tickmarks = []], view = [-1.2*Rout .. 1.2*Rout, -1.2*Rout .. 1.2*Rout], scaling = constrained)

proc (col) options operator, arrow; cat(`#mo("►",mathcolor="`, col, `")`) end proc

  

proc (col) options operator, arrow; cat(`#mo("◄",mathcolor="`, col, `")`) end proc

  

proc (col) options operator, arrow; cat(`#mo("▲",mathcolor="`, col, `")`) end proc

  

proc (col) options operator, arrow; cat(`#mo("▼",mathcolor="`, col, `")`) end proc

  

proc (x, y) Typesetting:-mrow(Typesetting:-Typeset(x), Typesetting:-mo(), Typesetting:-mo("/", fontweight = "bold"), Typesetting:-mo(), Typesetting:-Typeset(y)) end proc

  

 
 

Download Plotting_contour_integrals.mw

@mmcdara  I played a bit with the code you gave me, and now I have the desired results. Thanks

@Rouben Rostamian  I thought about ...

Paras31 245
April 27 2025
0 0

@Rouben Rostamian  I thought about that, and sure, it's handy. However, I would like to know if I can do the same with Maple. I searched on Google for a tutorial, but I did not find anything.

@mmcdara, sorry for my English!! Th...

Paras31 245
April 25 2025
0 0

@mmcdara, sorry for my English!! This is exactly what I was trying to do

@janhardo I think this is what I am...

Paras31 245
April 24 2025
0 0

@janhardo I think this is what I am looking for! Thank you

@mmcdara First of all, thank you fo...

Paras31 245
April 24 2025
0 0

@mmcdara First of all, thank you for your answer. Your worksheet is handy, and I will play with the paths. My question is, if there is a way to create random curves on Maple

@Scot Gould ok! I clearly understoo...

Paras31 245
March 21 2025
0 0

@Scot Gould ok! I clearly understood your point

@nm This explanation it is very hel...

Paras31 245
March 21 2025
0 0

@nm This explanation it is very helpful. Thank you!

@Scot Gould oh ok understood, I am ...

Paras31 245
March 21 2025
0 0

@Scot Gould oh ok understood, I am trying to find other ways to write my code. Thank you!!

When I am trying to upload the content o...

Paras31 245
March 20 2025

When I am trying to upload the content of my worksheet on MaplePrimes, it just appears the link

@gkokovidis Thank you very much for...

Paras31 245
March 19 2025

@gkokovidis Thank you very much for the comment, I fixed it and uploaded it again

Linear Differential Equations IVP...

Paras31 245
December 09 2024

 Solve the following IVP.

du/dt = 9.8-.196*u, u(0) = 48

> 

with(plots); with(DEtools); ode1 := diff(u(t), t) = 9.8-.196*u(t)

diff(u(t), t) = 9.8-.196*u(t)

 (1)
> 

ic := u(0) = 20

u(0) = 20

 (2)
> 

dsolve(ode1, u(t))

u(t) = 50+exp(-(49/250)*t)*c__1

 (3)
> 

gsol := dsolve({ic, ode1}, u(t))

u(t) = 50-30*exp(-(49/250)*t)

 (4)
> 

soln := dsolve({ic, ode1}, u(t), numeric)
> 

p1 := odeplot(soln, [t, u(t)], t = 0 .. 5, labels = ["t", "u(t)"], color = red)

 
> 

DEplot(ode1, u(t), t = 0 .. 5, u = 0 .. 50, [[u(0) = 20]], color = blue, arrows = slim, scaling = unconstrained, axes = boxed)

 

Find the solution to the following IVP.

t*dy/dt-2*y = t^5*sin(2*t)-t^3+4*t^4, y(Pi) = (3/2)*Pi^4

> 

ode2 := t*(diff(y(t), t))-2*y(t) = t^5*sin(2*t)-t^3+4*t^4

t*(diff(y(t), t))-2*y(t) = t^5*sin(2*t)-t^3+4*t^4

 (5)
> 

ics := y(Pi) = (3/2)*Pi^4

y(Pi) = (3/2)*Pi^4

 (6)
> 

dsolve(ode2, y(t))

y(t) = (-t-(1/2)*cos(2*t)*t^2+(1/4)*cos(2*t)+(1/2)*sin(2*t)*t+2*t^2+c__1)*t^2

 (7)
> 

gsoln := dsolve({ics, ode2}, y(t))

y(t) = (1/4)*(-2*cos(2*t)*t^2+2*sin(2*t)*t+8*t^2+4*Pi+cos(2*t)-4*t-1)*t^2

 (8)
> 

soln1 := dsolve({ics, ode2}, y(t), numeric)
> 

p1 := odeplot(soln1, [t, y(t)], t = 0 .. 7, labels = ["t", "y(t)"], color = red)

 
> 

DEplot(ode2, y(t), t = 0 .. 7, y = 0 .. 5000, [[y(Pi) = (3/2)*Pi^4]], color = blue, arrows = slim, scaling = unconstrained, axes = boxed)

 
 

NULL

Download Linear_Differential_Equations_IVP.mw

Newton’s Law of Cooling Example...

Paras31 245
November 30 2024
0 0

@Scot Gould @Carl Love I was trying to solve on Maple Example 8.3.4: https://math.libretexts.org/Courses/Monroe_Community_College/MTH_211_Calculus_II/Chapter_8%3A_Introduction_to_Differential_Equations/8.3%3A_Separable_Differential_Equations. 

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