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Paras31

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1 years, 362 days
Agricultural University of Athens
PhD Candidate

Social Networks and Content at Maplesoft.com

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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

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

Paras31 240
July 01 2025
0 0

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

  > ....

Paras31 240
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 240
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 240
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 240
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 240
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 240
March 21 2025
0 0

@Scot Gould ok! I clearly understood your point

@nm This explanation it is very hel...

Paras31 240
March 21 2025
0 0

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

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

Paras31 240
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 240
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 240
March 19 2025

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

Linear Differential Equations IVP...

Paras31 240
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 240
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. 

Separable Differential Equations and Exp...

Paras31 240
November 21 2024


 

Solve the initial value problems

• 

dy/dx = -4*xy^2, y(0) = 1
• 

diff(y(x), x) = cos(x)^2, y(0) = 0
> 

``
> 

ode1 := diff(y(x), x) = -4*x*y(x)^2

diff(y(x), x) = -4*x*y(x)^2

 (1)
> 

ic := y(0) = 1

y(0) = 1

 (2)
> 

dsolve(ode1, y(x))

y(x) = 1/(2*x^2+c__1)

 (3)
> 

gsol := dsolve({ic, ode1}, y(x))

y(x) = 1/(2*x^2+1)

 (4)
> 

soln := dsolve({ic, ode1}, y(x), numeric)
> 

with(plots); p1 := odeplot(soln, [x, y(x)], x = -5 .. 5, labels = ["x", "y(x)"], color = red)
> 

with(DEtools)
> 

directionfield := dfieldplot(ode1, [y(x)], x = -5 .. 5, y = -5 .. 5, color = blue, arrows = slim, scaling = constrained, axes = boxed)
> 

display([p1, directionfield], view = [-5 .. 5, -5 .. 5])

 
> 

ode2 := diff(y(x), x) = cos(y(x))^2

diff(y(x), x) = cos(y(x))^2

 (5)
> 

inc := y(0) = 0

y(0) = 0

 (6)
> 

dsolve(ode2, y(x))

y(x) = arctan(x+c__1)

 (7)
> 

gen_sol := dsolve({ic, ode2}, y(x))

y(x) = arctan(x+tan(1))

 (8)
> 

soln1 := dsolve({ic, ode2}, y(x), numeric)
> 

p2 := odeplot(soln1, [x, y(x)], x = -5 .. 5, labels = ["x", "y(x)"], color = red)
> 

dfield := dfieldplot(ode2, [y(x)], x = -5 .. 5, y = -5 .. 5, color = blue, arrows = slim, scaling = constrained, axes = boxed)
> 

display([p2, dfield], view = [-5 .. 5, -5 .. 5])

 

The population of  Duckburg has a constant growth rate of 3.5% per year. The current population is 3200. Write an initial value problem and a correspong function to model the population of Duckburg x years from now.NULL

> 

k := 0.35e-1

0.35e-1

 (9)

The rate of change of the population with respect to time is

dP/dt = kPand the initial population is P(0)=3200.

NULL

> 

ode := diff(P(t), t) = k*P(t)

diff(P(t), t) = 0.35e-1*P(t)

 (10)
> 

dsolve(ode, P(t))

P(t) = c__1*exp((7/200)*t)

 (11)
> 

IC := P(0) = 3200

P(0) = 3200

 (12)
> 

solution := dsolve({IC, ode}, P(t), numeric)
> 

p := odeplot(solution, [t, P(t)], t = 0 .. 1000, labels = ["x", "y(x)"], color = red)

 
> 

dirfield := dfieldplot(ode, [P(t)], t = 0 .. 1000, P = 0 .. 5000, color = blue, arrows = slim, scaling = unconstrained, axes = boxed)
> 

display([p, dirfield], view = [0 .. 1000, 3200 .. 5000])

 
> 

DEplot(ode, P(t), t = 0 .. 1000, P = 3200 .. 5000, [[P(0) = 3200]], color = blue, arrows = slim, scaling = unconstrained, axes = boxed)

 
> 

NULL


 

Download exponential_change_diff_eq.mw

Thanks...

Paras31 240
November 21 2024

@Rouben Rostamian  Thank you for the advice. I didn't know that

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