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piecewise function and integral ...

Asked by: Zeineb 540
integration piecewise plotting
March 07 2022
1  4

Dear all 
I have a function defined over the closed interval [ x[k], x[k+2] ] and zero elsewhere 
I would like to plot this sequence of function and compute an integral. 

I need your help to finish the attahced code, something is wrong. I can't  use piecewise funciton in loop and plot all functions in the same graph

piecewise_funciton_and_integral.mw

thanks for your remaks and help

Simple isolate fails...

Asked by: opus64 110
isolate
March 07 2022
4  6

Hello, can someone explain why something like this fails? The help page for 'isolate' says the second argument can be 'any algebraic expression'. Thanks.

How do I solve systems of second order differentia...

Asked by: mmsV 25
ode dsolve differential-equations
March 07 2022
3  2

I have the following systems of ODE in hand and would like to solve them. It would be great if somebody could help me with it.

> 

dudx := -415; dudy := 3901; dudz := -3365; dvdx := 23; dvdy := -1270; dvdz := 994; dwdx := 57; dwdy := -1665; dwdz := 1683; taup := 0.5390603100674905e-5

-415

  

3901

  

-3365

  

23

  

-1270

  

994

  

57

  

-1665

  

1683

  

0.5390603100674905e-5

 (1)
> 

u := .387; v := -.205; w := -.286; x0 := -0.979849e-2; y0 := -0.14583e-2; z0 := 0.623749e-1

.387

  

-.205

  

-.286

  

-0.979849e-2

  

-0.14583e-2

  

0.623749e-1

 (2)
> 

a__1 := dudx/taup; a__2 := dudy/taup; a__3 := dudz/taup; a__4 := 1/taup; a__5 := u/taup; b__1 := dvdx/taup; b__2 := dvdy/taup; b__3 := dvdz/taup; b__4 := 1/taup; b__5 := v/taup; c__1 := dwdx/taup; c__2 := dwdy/taup; c__3 := dwdz/taup; c__4 := 1/taup; c__5 := w/taup

-76985820.00

  

723666708.0

  

-624234420.0

  

185508.0000

  

71791.59600

  

4266684.000

  

-235595160.0

  

184394952.0

  

185508.0000

  

-38029.14000

  

10573956.00

  

-308870820.0

  

312209964.0

  

185508.0000

  

-53055.28800

 (3)
> 

sys := diff(x(t), t, t) = a__1*x(t)+a__2*y(t)+a__3*z(t)-a__4*(diff(x(t), t))+a__5, diff(y(t), t, t) = b__1*x(t)+b__2*y(t)+b__3*z(t)-b__4*(diff(y(t), t))+b__5, diff(z(t), t, t) = c__1*x(t)+c__2*y(t)+c__3*z(t)-c__4*(diff(z(t), t))+c__5

diff(diff(x(t), t), t) = -76985820.00*x(t)+723666708.0*y(t)-624234420.0*z(t)-185508.0000*(diff(x(t), t))+71791.59600, diff(diff(y(t), t), t) = 4266684.000*x(t)-235595160.0*y(t)+184394952.0*z(t)-185508.0000*(diff(y(t), t))-38029.14000, diff(diff(z(t), t), t) = 10573956.00*x(t)-308870820.0*y(t)+312209964.0*z(t)-185508.0000*(diff(z(t), t))-53055.28800

 (4)
> 

ics := x(0) = x0, y(0) = y0, z(0) = z0, (D(x))(0) = 0, (D(y))(0) = 0, (D(z))(0) = 0

x(0) = -0.979849e-2, y(0) = -0.14583e-2, z(0) = 0.623749e-1, (D(x))(0) = 0, (D(y))(0) = 0, (D(z))(0) = 0

 (5)


Thank you very much!

Download m_solution.mw

How to solve this type of equations...

Asked by: Madhukesh J K 140
homework numeric differential-equations
March 07 2022
2  2

Hi 

Warm greetings.

Is it possible to solve the numerical scheme present in the below paper.

Anita Chaturvedi, Kokila Ramesh, and Vatsala G A. (2017). “A MATHEMATICAL APPROACH TO STUDY THE EFFECT OF POLLUTANTS/TOXICANTS IN AQUATIC ENVIRONMENT.” International Journal of Research - Granthaalayah, 5(4) RAST, 33-38.

https://doi.org/10.5281/zenodo.803418

Thank you.

Calculating Implicit Integral with Maple...

Asked by: bstuan 90
calculus integration homework
March 07 2022
1  6

Could please help me solving the following problem?
Thank you a lot.

Question disappeared...

Asked by: Axel Vogt 5936
March 06 2022
5  1

The question https://www.mapleprimes.com/questions/233780-Plot-Absolute-Advantage-Of-Option-A disappeared (I know since I answered today).

Why?

Simplify with Side Relations and then eval...

Asked by: Ronan 1361
eval simplify
March 06 2022
3  1

I simplified a vector column using side relations. Then I wanted to evaluate using

eval( equation,  [x1=3,  x2=5......})

But side relations uses the reverse order i.e. after evaluation

[3=x1, 5=x2......]

So then the internals of the list need to be swaped tto work with eval.That is easy. I am just wondering is there a neater way to achieve this?

restart

NULL

P1 := Vector(3, {(1) = -(y[1]-y[3])*(y[2]-y[3])*((x[2]^2-x[2]*x[3]+x[3]^2)*x[1]^2-x[2]*x[3]*(x[2]+x[3])*x[1]+x[2]^2*x[3]^2)*(y[1]-y[2]), (2) = -(x[1]-x[3])*(x[2]-x[3])*(x[1]-x[2])*((y[2]^2-y[2]*y[3]+y[3]^2)*y[1]^2-y[2]*y[3]*(y[2]+y[3])*y[1]+y[2]^2*y[3]^2), (3) = ((-y[1]^2*y[2]+(3*y[2]*y[3]-y[3]^2)*y[1]-y[2]^2*y[3])*x[2]+x[3]*(y[1]^2*y[3]+y[2]*(y[2]-3*y[3])*y[1]+y[2]*y[3]^2))*x[1]^2+((y[1]^2*y[3]+y[2]*(y[2]-3*y[3])*y[1]+y[2]*y[3]^2)*x[2]^2+3*x[3]*(y[2]-y[3])*(y[1]-y[3])*(y[1]-y[2])*x[2]-x[3]^2*(y[1]^2*y[2]+(-3*y[2]*y[3]+y[3]^2)*y[1]+y[2]^2*y[3]))*x[1]-x[3]*((y[1]^2*y[2]+(-3*y[2]*y[3]+y[3]^2)*y[1]+y[2]^2*y[3])*x[2]-x[3]*(y[1]^2*y[3]+y[2]*(y[2]-3*y[3])*y[1]+y[2]*y[3]^2))*x[2]})

eqns := {(x[1]-x[2])*(x[2]-x[3])*(x[3]-x[1]) = R, (y[1]-y[2])*(y[2]-y[3])*(y[3]-y[1]) = S, x[1]^2*x[2]^2-x[1]^2*x[2]*x[3]+x[1]^2*x[3]^2-x[1]*x[2]^2*x[3]-x[1]*x[2]*x[3]^2+x[2]^2*x[3]^2 = Y, y[1]^2*y[2]^2-y[1]^2*y[2]*y[3]+y[1]^2*y[3]^2-y[1]*y[2]^2*y[3]-y[1]*y[2]*y[3]^2+y[2]^2*y[3]^2 = X, x[1]^2*x[2]+x[1]^2*x[3]+x[1]*x[2]^2-6*x[1]*x[2]*x[3]+x[1]*x[3]^2+x[2]^2*x[3]+x[2]*x[3]^2 = Z, y[1]^2*y[2]+y[1]^2*y[3]+y[1]*y[2]^2-6*y[1]*y[2]*y[3]+y[1]*y[3]^2+y[2]^2*y[3]+y[2]*y[3]^2 = W}

P1new := simplify(P1, eqns)

Vector[column](%id = 36893490132854572084)

 (1)

values := {x[1] = 3, x[2] = 5, x[3] = 7, y[1] = 2, y[2] = -11, y[3] = 13}

{x[1] = 3, x[2] = 5, x[3] = 7, y[1] = 2, y[2] = -11, y[3] = 13}

 (2)

vals1 := eval(eqns, values)

{-3432 = S, 16 = R, 120 = Z, 316 = Y, 2018 = W, 22753 = X}

 (3)

eval(P1new, vals1)

Vector[column](%id = 36893490132854572084)

 (4)

vals1swap := [seq(rhs(vals1[i]) = lhs(vals1[i]), i = 1 .. nops(vals1))]

[S = -3432, R = 16, Z = 120, Y = 316, W = 2018, X = 22753]

 (5)

eval(P1new, vals1swap)

Vector[column](%id = 36893490132849052116)

 (6)

eval(P1, values)

Vector[column](%id = 36893490132871267020)

 (7)

``

NULL

``

Download Q_6-03-2022_side_rels_and_eval.mw

Need help on graph...

Asked by: AHSAN 160
plotting
March 06 2022
2  1

Need help to plot a graph along x-axis  in attached worksheet. 

help_graph.mw

Pythagorean Puzzle...

Asked by: Tokoro 115
graphtheory circuit
March 05 2022
1  8

NULL

> 

restart;
> 

with(plots):with(plottools):

Solve diagonal resistance of nodes (0,0,0)-(3,4,5), (Edge length = ohm).(156/47 ohm)

   

plots[display]([nodes, node2, plotlinesx], scaling = constrained, style = wireframe, axes = boxed, orientation = [-50, 70, 0])

  

Solve minimum diagonal surface distance of nodes (0,0,0)-(3,4,5).(sqrt(74))
NULL

NULL

Download Resistance-345.mw

Solve diagonal resistance of nodes (0,0,0)-(3,4,5),

Edge length = ohm, therefore, each edge has 3, 4 and 5 ohm, respectivery. (156/47 ohm)

Solve minimum diagonal surface distance of nodes (0,0,0)-(3,4,5). (sqrt(74))

Electric circuit study.

Tokoro.

Loading times(when saving and after pauses in writ...

Asked by: Kalledude 5
osx macosx incomplete-question
March 05 2022
1  1

A have som problems when i Will save a project. It Will take 2-5 Minutes where my other freinds never Experince this? Also i have some problems when i pauses writing, when i take notes in class, it Will give me the loading circle on mac( iam using a MacBook Air 2018) 

i hope you Can help:)

thx

How to optimize with a constraint ...

Asked by: Magnus Berg 20
optimization
March 05 2022
2  4

Hi, im trying to optimize a function with a constraint. 

I've tried the Optimize package but I can't seem to make it work. 

I've attached  an image to my question, witht the function and the constraint. I want to find the optimal "t_x"

Function: rho*ln((-beta*tau + rho)/(1 + t__x)) + sigma*ln(sigma/(1 + t__y)) + beta*tau + B - rho - sigma - beta*tau*ln((-beta*tau + rho)/(1 + t__x))

Constaint: -t__x*(-beta*tau + rho)/(1 + t__x) + t__y*sigma/(1 + t__y) = R

Hope you can help 

How do I get explict answer to system of ODEs...

Asked by: soneye 20
March 04 2022
4  3

Dear Colleagues,

I am trying to solve the following system of ode

odeSystem := {diff(y1(x), x) = -x*y2(x)-(1+x)*y3(x), diff(y2(x), x) = -x*y1(x)-(1+x)*y4(x), diff(y3(x), x) = -x*y1(x)-(1+x)*y4(x)-5*x*cos((1/2)*x^2), diff(y4(x), x) = -x*y2(x)-(1+x)*y3(x)+5*x*sin((1/2)*x^2), y1(0) = 5, y2(0) = 1, y3(0) = -1, y4(0) = 0};
systemSol := dsolve(odeSystem);

However, the result displayed is not explicit and contains integral sign. Please, I need help to obtain explicit result.

Thank you.

Why square roots are not simplifying in a fraction...

Asked by: mskalsi 290
radical substitution simplification
March 04 2022
1  6

Please see the attached file; I'm attempting to do some calculations with the 'PDETools' package; notice the first term in equation (4), where sqrt(x2+y2) is not canceling in the fraction, despite using the 'simplify' command; why is this happening, and how can I achieve complete simplification?

Ques_Mapleprime.mw

> 

with(PDEtools):
> 

DepVars := [u(x, y, t), U(xi, eta)]; 1; alias(u = u(x, y, t))

[u(x, y, t), U(xi, eta)]

  

u

 (1)
> 

xi[1] := 1/2*(x^2+y^2); 1; xi[2] := t; 1; u := (h(t)+(x^2+y^2)*(1/2))*arccos(x/sqrt(x^2+y^2))/t+U(xi[1], xi[2])

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

  

t

  

(h(t)+(1/2)*x^2+(1/2)*y^2)*arccos(x/(x^2+y^2)^(1/2))/t+U((1/2)*x^2+(1/2)*y^2, t)

 (2)
> 

(diff(u, x))*(diff(u, y))

(x*arccos(x/(x^2+y^2)^(1/2))/t-(h(t)+(1/2)*x^2+(1/2)*y^2)*(1/(x^2+y^2)^(1/2)-x^2/(x^2+y^2)^(3/2))/((1-x^2/(x^2+y^2))^(1/2)*t)+(D[1](U))((1/2)*x^2+(1/2)*y^2, t)*x)*(y*arccos(x/(x^2+y^2)^(1/2))/t+(h(t)+(1/2)*x^2+(1/2)*y^2)*x*y/((x^2+y^2)^(3/2)*(1-x^2/(x^2+y^2))^(1/2)*t)+(D[1](U))((1/2)*x^2+(1/2)*y^2, t)*y)

 (3)
> 

collect(simplify(subs(1/2*(x^2+y^2) = xi, t = eta, (x*arccos(x/(x^2+y^2)^(1/2))/t-(h(t)+(1/2)*x^2+(1/2)*y^2)*(1/(x^2+y^2)^(1/2)-x^2/(x^2+y^2)^(3/2))/((1-x^2/(x^2+y^2))^(1/2)*t)+(D[1](U))((1/2)*x^2+(1/2)*y^2, t)*x)*(y*arccos(x/(x^2+y^2)^(1/2))/t+(h(t)+(1/2)*x^2+(1/2)*y^2)*x*y/((x^2+y^2)^(3/2)*(1-x^2/(x^2+y^2))^(1/2)*t)+(D[1](U))((1/2)*x^2+(1/2)*y^2, t)*y))), D, 'distributed')

(1/4)*(2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x^3+2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x*y^2)*(2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x^2+2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*y^2)*(D[1](U))(xi, eta)^2/(y*(x^2+y^2)^2*eta^2)+(1/4)*((2*arccos(x/(x^2+y^2)^(1/2))*x^3*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)+2*arccos(x/(x^2+y^2)^(1/2))*x*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)*y^2-x^2*y^2-y^4-2*h(eta)*y^2)*(2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x^2+2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*y^2)+(2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x^3+2*(y^2/(x^2+y^2))^(1/2)*(x^2+y^2)^(1/2)*eta*x*y^2)*(2*arccos(x/(x^2+y^2)^(1/2))*x^2*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)+2*arccos(x/(x^2+y^2)^(1/2))*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)*y^2+x^3+x*y^2+2*h(eta)*x))*(D[1](U))(xi, eta)/(y*(x^2+y^2)^2*eta^2)+(1/4)*(2*arccos(x/(x^2+y^2)^(1/2))*x^3*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)+2*arccos(x/(x^2+y^2)^(1/2))*x*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)*y^2-x^2*y^2-y^4-2*h(eta)*y^2)*(2*arccos(x/(x^2+y^2)^(1/2))*x^2*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)+2*arccos(x/(x^2+y^2)^(1/2))*(x^2+y^2)^(1/2)*(y^2/(x^2+y^2))^(1/2)*y^2+x^3+x*y^2+2*h(eta)*x)/(y*(x^2+y^2)^2*eta^2)

 (4)
> 

``

Download Ques_Mapleprime.mw

Conversion of files?...

Asked by: AHSAN 160
March 03 2022
1  7

Hi, is it possible to convert mathematica files into maple. i was trying to upload mathematica file here but got failed, so uploading mathematica file into pdf. could anyone can help me to convert these file into maple.

Conversion.pdf

Converting a function expressed by the hypergeom f...

Asked by: Najibeh Borhani 50
hypergeom legendrep
March 03 2022
2  5

Could you help me to convert the following maple solution expressed by the hypergeom function to the LegendreP and Q function?

> 

diff(T[3](t), t, t)+3*(diff(a(t), t))*(diff(T[3](t), t))/a(t)+(2*(diff(a(t), t, t))/a(t)+6*(diff(a(t), t))^2/a(t)^2+(-Omega^2+6)/a(t)^2)*T[3](t)

diff(diff(T[3](t), t), t)+3*(diff(a(t), t))*(diff(T[3](t), t))/a(t)+(2*(diff(diff(a(t), t), t))/a(t)+6*(diff(a(t), t))^2/a(t)^2+(-Omega^2+6)/a(t)^2)*T[3](t)

 (1)
> 

"a(t) :=Zeta*(1-(1-t/(Zeta^()))^(2))^(1/(2)) "

proc (t) options operator, arrow, function_assign; Zeta*(1-(1-t/Zeta)^2)^(1/2) end proc

 (2)
> 

ODE2 := diff(T[3](t), t, t)+3*(diff(a(t), t))*(diff(T[3](t), t))/a(t)+(2*(diff(a(t), t, t))/a(t)+6*(diff(a(t), t))^2/a(t)^2+(-Omega^2+6)/a(t)^2)*T[3](t)

diff(diff(T[3](t), t), t)+3*(1-t/Zeta)*(diff(T[3](t), t))/((1-(1-t/Zeta)^2)*Zeta)+(2*(-(1-t/Zeta)^2/((1-(1-t/Zeta)^2)^(3/2)*Zeta)-1/((1-(1-t/Zeta)^2)^(1/2)*Zeta))/(Zeta*(1-(1-t/Zeta)^2)^(1/2))+6*(1-t/Zeta)^2/((1-(1-t/Zeta)^2)^2*Zeta^2)+(-Omega^2+6)/(Zeta^2*(1-(1-t/Zeta)^2)))*T[3](t)

 (3)
> 

generalsol := dsolve(ODE2, T[3](t))

T[3](t) = _C1*hypergeom([1/2+(-Omega^2+1)^(1/2), 1/2-(-Omega^2+1)^(1/2)], [1-((1/2)*I)*15^(1/2)], (1/2)*t/Zeta)*t^(-((1/4)*I)*15^(1/2)-1/4)*(2*Zeta-t)^(((1/4)*I)*15^(1/2)-1/4)+_C2*(-(-2*Zeta+t)*t)^(((1/4)*I)*15^(1/2)-1/4)*hypergeom([((1/2)*I)*15^(1/2)+1/2+(-Omega^2+1)^(1/2), ((1/2)*I)*15^(1/2)+1/2-(-Omega^2+1)^(1/2)], [1+((1/2)*I)*15^(1/2)], (1/2)*t/Zeta)

 (4)
> 

convert(_C1*hypergeom([1/2+sqrt(-Omega^2+1), 1/2-sqrt(-Omega^2+1)], [1-I*sqrt(15)*(1/2)], t/(2*Zeta))*t^(-I*sqrt(15)*(1/4)-1/4)*(2*Zeta-t)^(I*sqrt(15)*(1/4)-1/4), LegendreP)

_C1*GAMMA(1-((1/2)*I)*15^(1/2))*(-t/Zeta)^(((1/4)*I)*15^(1/2))*LegendreP(-1/2+(-Omega^2+1)^(1/2), ((1/2)*I)*15^(1/2), 1-t/Zeta)*t^(-((1/4)*I)*15^(1/2)-1/4)*(2*Zeta-t)^(((1/4)*I)*15^(1/2)-1/4)/((2*Zeta-t)/Zeta)^(((1/4)*I)*15^(1/2))

 (5)
> 

convert(_C2*(-t*(t-2*Zeta))^(I*sqrt(15)*(1/4)-1/4)*hypergeom([I*sqrt(15)*(1/2)+1/2+sqrt(-Omega^2+1), I*sqrt(15)*(1/2)+1/2-sqrt(-Omega^2+1)], [1+I*sqrt(15)*(1/2)], t/(2*Zeta)), LegendreQ)

_C2*(-t*(-2*Zeta+t))^(((1/4)*I)*15^(1/2)-1/4)*hypergeom([((1/2)*I)*15^(1/2)+1/2+(-Omega^2+1)^(1/2), ((1/2)*I)*15^(1/2)+1/2-(-Omega^2+1)^(1/2)], [1+((1/2)*I)*15^(1/2)], (1/2)*t/Zeta)

 (6)
> 

NULL

Download solve3.mw

Like this

Thank you.

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