## 145 Reputation

7 years, 266 days

## @Carl Love thanks for the correctio...

@Carl Love thanks for the correction!

I forgot the proper word for describing what I meant.

## @Thomas Richard    OK, indee...

OK, indeed you are correct.

I checked again and it seems I mistyped in the equation:

(a^2*sin(theta)^2 - Delta^2)*((a^2 + r^2)^2 - a^2*Delta*sin(theta)^2)*sin(theta)^2/rho^4 - 4*a^2*M^2*r^2*sin(theta)^4/rho^4;

the first appearance of Delta in this expression should be without the square... :-)

Now, it seems to be working: 1=1.

BTW, how do you suggest me to let maple showing all the steps of the this expansion?

## @Thomas Richard  You can check the...

You can check the post that I posted in PF here:

There are screenshots of the textbook's pages where this expression appears in.

## @Mac Dude   I know that the expre...

@Mac Dude

I know that the expression I typed should be expanded to -\Delta*\sin^2(\theta) in the end since it's written in the textbook I got this expression from. Schutz's A First Course in GR second edition on pages 309-313.

## @acer I tried using the plots:display co...

@acer I tried using the plots:display command by reading the help in maple, here's what I wrote:

HH := 5*log[10]((c/H_0)*Int(1/(A*(1+zp)^4+B*(1+z)^3+C)^(1/2)/10,                              zp=0..z,                              method=_d01ajc, epsilon=1e-5)):    F:=plot(eval(HH,[A=0, B=0.31, C=0.69, H_0=1,c=1]), z=1e-7 .. 1.0,       thickness=3, color=red, smartview=false); G:=plot(eval(HH,[A=0.7, B=0.3, C=0 H_0=1,c=1]), z=1e-7 .. 1.0,       thickness=3, color=blue, smartview=false);  H:=plot(eval(HH,[A=0.6, B=0.1, C=0.3, H_0=1,c=1]), z=1e-7 .. 1.0,       thickness=3, color=green,smartview=false);   display({F,G,H},axes=boxed,,scaling=constrained,title='3 comsological models')

But I get an error message:

Error, invalid function arguments
Typesetting:-mambiguous(HH Assign 5astlog(10)ApplyFunction((csol

H_0)astIntApplyFunction(1sol(Aast(1 + zp)circ4 + Bast(1 + z)

circ3 + C)circ(1sol2)sol10comma   zpequals0period;&periodzcomma

methodequals_d01ajccomma epsilonequals1e-5))colon    FAssign

plotApplyFunction(evalApplyFunction(HHcomma(Aequals0comma B

equals0.31comma Cequals0.69comma H_0equals1commacequals1))comma

zequals1e-7 period;&period 1.0comma   thicknessequals3comma

colorequalsredcomma smartviewequalsfalse)semi GAssignplotApply\

Function(evalApplyFunction(HHcomma(Aequals0.7comma Bequals0.3

comma Cequals0 H_0equals1commacequals1))comma zequals1e-7

period;&period 1.0comma  thicknessequals3comma colorequalsblue

comma smartviewequalsfalse)semi  HAssignplotApplyFunction(eval

ApplyFunction(HHcomma(Aequals0.6comma Bequals0.1comma Cequals

0.3comma H_0equals1commacequals1))comma zequals1e-7

period;&period 1.0comma  thicknessequals3comma colorequalsgreen

commasmartviewequalsfalse)semi  displayApplyFunction

Typesetting:-mambiguous(((FcommaGcommaH)commaaxesequalsboxed

commacommascalingequalsconstrainedcommatitleequals(3

comsological model)),

Typesetting:-merror("invalid function arguments"))   )

How to fix this?

Thnaks!

## @acer I still don't understand how t...

@acer I still don't understand how to plot three plots in one graph, can you please write an example to me?

Thanks!

## @acer How can I plot all the three plots...

@acer How can I plot all the three plots with 3 different A,B,C parameters in each graph?

All three different plots in the same graph.

Thnanks!

## @Mariusz Iwaniuk I am a member of so man...

@Mariusz Iwaniuk I am a member of so many forums, that if I do'nt use something frequently I am bound to forget.

## @Kitonum I meant that I want to plot two...

@Kitonum I meant that I want to plot two functions:

1.

f(x):=a*x*(1-x)+(x/4)*ln(x)+(1-x)*ln(1-x)

which satisfies f'(x1)=f'(x2)=b=(f(x1)-f(x2))/(x1-x2)

in the interval [x1,x2].

2. f(x):=a*x*(1-x)+(x/4)*ln(x)+(1-x)*ln(1-x)

where in order to find the parameter a one needs to solve f'(x0)=0 find x0 with respect to a and then find a with the condition f''(x0)=0.

Is this better understood?

Can you implement this for me?

## A follow-up question....

@Kitonum I have the following follow-up question to the original opening question.

I have the function f(x):=a*x*(1-x)+(x/4)*ln(x)+(1-x)*ln(1-x)

which satisfies f'(x1)=f'(x2)=b=(f(x1)-f(x2))/(x1-x2)

I want to find the graph of f above in the interval [x1,x2] or [x2,x1] alongside the same function f but which also satisfies at the point of intersection with the above graph f''(x)=0.

How to implement this in maple code?

## @Preben Alsholm  Well I am trying ...

Well I am trying to solve the following problem from Murdock's Perturbations: Theory and Methods.

"Exercise 2.6.1 (a)

Letting f(y)=y^3, investigate the correct and incorrect perturbation problems as follows.

Attempt to solve (2.6.3)-(2.6.4) for y1. Obtain the differential equation for y1, find its general solution, and show that the constants of integration cannot be chosen to satisfy the boundary conditions."

where (2.6.3) y''+n^2 \pi^2 y = epsilon*f(y) , y(0)=0 , y(1)=0;

(2.6.4)y ~ A sin(n\pi *x) + epsilon*y1(x)+epsilon^2*y2(x)+...

So I plugged the first-order in epsilon ansatz of A sin(n\pi*x)+epsilon*y1(x); so I get the following ode:

y1''+n^2 pi^2 * y1 = A^3 sin^3(n*pi*x), y1(0)=y1(1)=0.

So it seems both of you solved my problem.

I need to remember this option of assuming n::integer

Thanks.

## @Kitonum how to find those values algebr...

@Kitonum how to find those values algebraically?

I mean I have: epsilon = sqrt((x-2)^2(3-x))

and then I plug the values x=0, x=2 or 3 and get:

+-2*sqrt(3), 0.

Are those the values I am looking for?

I am not sure understand why?

## @Carl Love thanks. Perhaps you know how...

@Carl Love thanks.

Perhaps you know how to answer my following question from Murdock's text which I asked on stackexchange and didn't get an answer.

"Using the graph of y=(x-2)^2(x-3), sketch the bifurcation diagram of (x-2)^2(x-3)+epsilon^2=0 for all real epsilon.

Notice that this diagram is symmetrical about the x axis. Find the values of epsilon at the two pair pair bifurcation points".

My question is about the last sentence how to find these values?

## @Carl Love Well the equation is epsilon ...

@Carl Love Well the equation is epsilon = -(x-2)^2(x-3), in that case how to use the Bifurcation command here, I've only seen an example for the logisitc equation.

## @Rouben Rostamian  I know there'...

@Rouben Rostamian  I know there's a feature in maple where you can use iterativemaps, I looked at it in the help and also the web when searching bifurcation with maple.

Do you know perhaps know how to use this feature here?

Thanks!

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