MaplePrimes Questions

hi,

   here are  equations like this

 sol := [abs(r)^2+abs(t)^2 = 1, r*conjugate(t)+t*conjugate(r), abs(r) = abs(t)]

when i solve this equations using command solve,the result  is none. and i used r=x+I*y,t=u+I*v in the equations,

sol:=[u^2+v^2+x^2+y^2 = 1, 2*u*x+2*v*y, sqrt(x^2+y^2) = sqrt(u^2+v^2)]

i still can't get a result.why,can you help me.

thanks.

 

Hi there

I am stuck with the expression

 

> e := (3+2*sinh(x)^2)/(sinh(x)^2*tanh(x));
                                            2
                               3 + 2 sinh(x)  
                              ----------------
                                     2        
                              sinh(x)  tanh(x)

its simplified way, which i cannot find, is


> f := 3*coth(x)^3-coth(x);
                                     3          
                            3 coth(x)  - coth(x)
> simplify(e-f);
                                      0

I would appreciate immensely if someone could give me some pointers on how to solve it.

 

best regards

 

nvc

 

Hi:

I will a write program in maple for plot the function f(x),while asked value n from user at first,then plot function f(x) for each value of n and finally all plots show in one figure only for different value of n,how to do it?

f(x)=1+2*(1+x)^n,x=0..5

Dear Maple Users,

I'm beginner in Maple.

I have this system of Pde:

with lambda experimental parameter and n,c,v dependent variables. I write this on Maple but I read on internet that the solution "float(undefined)" is an error.

I will insert this initial condition: c(x,0)=0,n(x,0)=0.4

Thanks everybody

Hallo,

how can I  construct a Permutationgroup with given GroupOrder and Degree.

for instance: GroupOrder 12 and Degree 5, I found by accident

G:=<(1,2,3),(1,5,2)>

Best Regards

 

Kurt Ewald

Hi:

how i can plot the function in terms of different values of n in a figure:

f(x)=1+2*(1+x)^n

n=1,2,3,4

x-axis->x

y-axis->f(x)

 

The toggle button in the embedded components has a default image which points up and down. Is there any way to rotate this image so that it points left and right?  I though I might actually just rotate the default image gif(?) directly, but the properties window does not give the location of the gif(?) used for this image. I also can't locate the image file simply looking at the Maple program folder. Otherwise, I have to go find or create an image of my own.

Good Afternoon Everyone,

Would anybody be kind to help me with the interpolation of two variables in a table to obtain a value for f18.1 (Stiffness) and f18.2 (Damping) given SR_ratio and Lamda_ratio.

 

Regards

Moses


 

NULL

restart

with(CurveFitting)

with(ExcelTools):

``

Slenderness Ratio (Variable 1):

SR__ratio := 84.01

``

Ratio of modulus of elasticity of Pile vs shear modulus of soil (Variable 2):

`&lambda;__ratio` := 229.58

``

Slenderness ratio of pile from stiffness of pile table:

SR__stiff := [10.8696, 21.7391, 32.6087, 43.4783, 46.7391, 54.3478, 65.2174, 76.0870, 86.9565, 100.0]

``

Ratio of Young's Modulus of Pile to Shear modulus of soil:

EG__ratio := [250.0, 500.0, 1000.0, 2500.0, 5000.0, 10000.0]

``

Vertical stiffness coefficient for floating pile as per Novak (1983) f18.1.250:

`f__18.1.250` := [0.332e-1, 0.509e-1, 0.571e-1, 0.582e-1, 0.582e-1, 0.582e-1, 0.582e-1, 0.582e-1, 0.582e-1, 0.582e-1]

``

Vertical stiffness coefficient for floating pile as per Novak (1983) f18.1.500:

`f__18.1.500` := [0.187e-1, 0.301e-1, 0.364e-1, 0.405e-1, 0.416e-1, 0.416e-1, 0.416e-1, 0.416e-1, 0.416e-1, 0.416e-1]

``

Vertical stiffness coefficient for floating pile as per Novak (1983) f18.1.1000:

`f__18.1.1000` := [0.104e-1, 0.166e-1, 0.218e-1, 0.26e-1, 0.27e-1, 0.281e-1, 0.291e-1, 0.301e-1, 0.301e-1, 0.301e-1]

``

Vertical stiffness coefficient for floating pile as per Novak (1983) f18.1.2500:

`f__18.1.2500` := [0.52e-2, 0.83e-2, 0.104e-1, 0.125e-1, 0.135e-1, 0.145e-1, 0.166e-1, 0.177e-1, 0.187e-1, 0.197e-1]

``

Vertical stiffness coefficient for floating pile as per Novak (1983) f18.1.10000:

`f__18.1.10000` := [0.21e-2, 0.31e-2, 0.42e-2, 0.42e-2, 0.52e-2, 0.52e-2, 0.62e-2, 0.62e-2, 0.73e-2, 0.83e-2]

``

Slenderness ratio of pile from damping of pile table:

SR__damp := [10.8696, 16.3043, 21.7391, 27.1739, 32.6087, 38.0435, 43.4783, 48.913, 54.3478, 59.7826, 65.2174, 70.6522, 76.0870, 81.5217, 86.9565, 92.3913, 100.0]

``

Vertical damping coefficient for floating pile as per Novak (1983) f18.2.250:

`f__18.2.250` := [.1032, .1137, .1126, .1095, .1053, .1021, 0.989e-1, 0.979e-1, 0.979e-1, 0.979e-1, 0.979e-1, 0.979e-1, 0.979e-1, 0.979e-1, 0.979e-1, 0.989e-1, 0.989e-1]

``

Vertical damping coefficient for floating pile as per Novak (1983) f18.2.500:

`f__18.2.500` := [0.558e-1, 0.695e-1, 0.811e-1, 0.832e-1, 0.811e-1, 0.789e-1, 0.758e-1, 0.737e-1, 0.726e-1, 0.716e-1, 0.705e-1, 0.695e-1, 0.695e-1, 0.695e-1, 0.695e-1, 0.705e-1, 0.705e-1]

``

 Vertical damping coefficient for floating pile as per Novak (1983) f18.2.1000:

`f__18.2.1000` := [0.295e-1, 0.421e-1, 0.495e-1, 0.537e-1, 0.568e-1, 0.589e-1, 0.579e-1, 0.568e-1, 0.558e-1, 0.537e-1, 0.526e-1, 0.516e-1, 0.516e-1, 0.505e-1, 0.505e-1, 0.505e-1, 0.495e-1]

``

 Vertical damping coefficient for floating pile as per Novak (1983) f18.2.2500:

`f__18.2.2500` := [0.126e-1, 0.179e-1, 0.232e-1, 0.263e-1, 0.305e-1, 0.326e-1, 0.347e-1, 0.368e-1, 0.379e-1, 0.379e-1, 0.379e-1, 0.379e-1, 0.379e-1, 0.368e-1, 0.358e-1, 0.358e-1, 0.337e-1]

``

   Vertical damping coefficient for floating pile as per Novak (1983) f18.2.10000:

`f__18.2.10000` := [0.32e-2, 0.53e-2, 0.74e-2, 0.84e-2, 0.105e-1, 0.116e-1, 0.137e-1, 0.147e-1, 0.147e-1, 0.168e-1, 0.168e-1, 0.179e-1, 0.189e-1, 0.189e-1, 0.200e-1, 0.211e-1, 0.211e-1]

``

 

NULL

``

``

`f__18.1` := ArrayInterpolation(SR__ratio, `&lambda;__ratio`, SR__stiff, EG__ratio, `f__18.1.250`)

`f__18.2__ _` := ArrayInterpolation(SR__ratio, `&lambda;__ratio`, SR__damp, EG__ratio, `f__18.2.250`)

NULL

NULL


Download Dynamic_Table.mwDynamic_Table.mw

Good Afternoon Everyone,

Would anybody be kind to help me with the interpolation of two variables in a table to obtain a value for f18.1 (Stiffness) and f18.2 (Damping) given SR_ratio and Lamda_ratio.

 

Regards

Moses

Hi:

how i can plot the function f(x) in term of 1/x in maple?for example i have the function f(x)=x^2 and x=0..1,now i plot f(x) in term of 1/x.

expand( (a+b)^n)

 

convert((a+b)^n,Sum) 

 

none  expands in  binomial  form.  Is there any way for Maple to generate  binomial  expansion of (a+b)^n  without

 

entering  manually.

 

martin

It is possible to add groups of questions to an assignment in Maple T.A. But how do you see the grades divided into these groups? As an example, suppose we have two groups of questions say 5 questions in the group "algebra" and 5 questions in the group "geometry". The class grades show the grades for all 10 questions all together, but I would like to see the grades for two groups individually.

 

 

I have few ode's which are solved by dsolve, but I am not able to get a zero from odetest(sol,ode). I tried the implicit option on the one which returns implicit solution, but I still do not get zero. I tried useInt as well.

Is there something else to do to verify the solution? My understanding is that if Maple returns a solution from dsolve, there there should be a way to get odetest() to verify the solution, but I could be wrong. Here are few examples, I have more if needed. This is Maple 18.01 on windows 7

restart;
MathematicalFunctions:-Version();
#       "C:\Program Files\Maple 18\lib\DEsAndMathematicalFunctions18.mla", `2014, July 25, 21:22 hours`
unassign(`print/ODESolStruc`):
ode1:=diff(y(x), x)+2*tan(y(x))*tan(x)-1:
ode2:=2*(diff(y(x), x))-3*y(x)^2-4*a*y(x)-b-c*exp(-2*a*x):
ode3:=(x^2+1)*(diff(y(x), x))+(y(x)^2+1)*(2*x*y(x)-1):
ode4:=x^7*(diff(y(x), x))+(2*(x^2+1))*y(x)^3+5*x^3*y(x)^2:
ode5:=(y(x)-x)*sqrt(x^2+1)*(diff(y(x), x))-a*sqrt((y(x)^2+1)^3):

sol1:=dsolve(ode1,y(x)):
sol2:=dsolve(ode2,y(x)):
sol3:=dsolve(ode3,y(x)):
sol4:=dsolve(ode4,y(x)):
sol5:=dsolve(ode5,y(x)):

odetest(sol1,ode1,implicit);  #not zero
odetest(sol2,ode2);             #not zero
odetest(sol3,ode3,implicit);  #not zero
odetest(sol4,ode4,implicit);  #not zero
odetest(sol5,ode5,implicit);  #not zero

a:=Vector([2,3,4,5]);

select[flatten](x->x>=3,a);

This returns a Vector that satisfies the above condition. What's the most efficient way to get the indices of those entries?

For example, a list l:=[2,3,4] that correspond to the a[l] entries that satisfies the above condition.

l:=[2,3,4];

a[l]; # gives the same answer

 

Thanks,

 

casper

I am going by the assumption that when Maple returns ODESolStruct as solution, then it means it could not solve the ODE. (example below)

My only complaint is that the syntax it uses for saying that the solution is ODESolStruct is not clear. I guess one has to look for & in the solution to know the result is ODEStruct.

http://www.maplesoft.com/support/help/Maple/view.aspx?path=dsolve%2fODESolStruc

Only when I convert the solution to string, then I can see the word "ODESolStruct" displayed.

My question is, how can I make maple display on the screen the word "ODESolStruct" in the solution, instead of using those "&" As that will make it more clear.

I am using worksheet on maple 18. Not document style. Here is an example:

restart;
ode:=diff(y(x),x$2)+a*exp(x)*sqrt(y(x));
sol:=dsolve(ode,y(x));


 The above was using 2D math display as default. If I use Maple notation as output I get:

----------------------------------------

restart:
ode:=diff(y(x),x$2)+a*exp(x)*sqrt(y(x)):
sol:=dsolve(ode,y(x));
sol := y(x) = `&where`(_a/exp(-2*(Int(_b(_a), _a))-2*_C1), [{diff(_b(_a), _a).......

-------------------------------------------

But now

convert(sol,string);
"y(x) = ODESolStruc(_a/exp(-2*Int(_b(_a),_a)-2*_C1),[{diff(_b(_a\ .............."

You can see now that the solution is ODESolStruct, but it is much more clear than the default solution above. But only when looking at the solution as string do I get it to show the word "ODESolStruct". 

Since odetest does not return zero, then maple did not solve it:

odetest(sol,ode);

btw, Compare the above to when Maple returns "DESol" structutre. In this case, it does now display on the screen the word "DESol":

restart;
ode:=diff(y(x), x, x)-y(x)*(a^2*x^(2*n)-1);
dsolve(ode,y(x));

Again, my question is:  Could I configure Maple to display in worksheet the solution using explicit ODESolStruct words instead of using "&" there to indicate more clearly the solution.

 

I have a large system of non-linear equations. Is there any way to get Maple to remove the duplicate equations in the system? For example Maple doesn't recognise that x-y =0 is equal to y-x=0. 

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