Maple Questions and Posts

What is short form of derivative? ...

Asked by: Ramakrishnan 404

December 08 2015

0 2

mydoubt-to-mapleprime.mw
an any one help me understand and correct the following errors in maple document. Thanks.

"(∫)[0]^(L)-E A (((&PartialD;)^2u)/((&PartialD;)^( )x^2)) *v &DifferentialD;x = [- E A *(((&PartialD; )/(&PartialD; x)u) *v dx) ? () ][0]^(L) - (∫)[0]^(L)-E A (&PartialD; u)/(&PartialD; x)(&PartialD; v)/(&PartialD; x) &DifferentialD;x "

Error, dependencies must be declared (Suppress) for short form derivatives

"(∫)[0]^L-E A (((&PartialD;)^2u)/(&PartialD;x^2)) *v &DifferentialD;x = [- E A *(((&PartialD; )/(&PartialD; x)u) *v dx) ? () ][0]^L - (∫)[0]^L-E A (&PartialD; u)/(&PartialD; x)(&PartialD; v)/(&PartialD; x) &DifferentialD;x "

"(∫)[0]^(L)-E A (((&PartialD;)^2)/((&PartialD;)^( )x^2)u) *v &DifferentialD;x = (∫)[0]^(L)-E A (&PartialD; u)/(&PartialD; x)(&PartialD; v)/(&PartialD; x) &DifferentialD;x "

Error, dependencies must be declared (Suppress) for short form derivatives

"(∫)[0]^L-E A (((&PartialD;)^2)/((&PartialD;x)^2)u) *v &DifferentialD;x = (∫)[0]^L-E A (&PartialD; u)/(&PartialD; x)(&PartialD; v)/(&PartialD; x) &DifferentialD;x "

"(∫)[0]^(L)-E A (((&PartialD;)^2)/((&PartialD;)^( )x^2)u) *v &DifferentialD;x = [- E A *(((&PartialD; )/(&PartialD; x)u) *v dx) ? () ][0]^(L) - (∫)[0]^(L)-E A (&PartialD; u)/(&PartialD; x)(&PartialD; v)/(&PartialD; x) &DifferentialD;x "

Error, invalid product/quotient

"(∫)[0]^L-E A (((&PartialD;)^2)/((&PartialD;x)^2)u) *v &DifferentialD;x = [- E A *(((&PartialD;)/(&PartialD;x)u) *v dx) ? () ][0]^L - (∫)[0]^L-E A (&PartialD; u)/(&PartialD; x)(&PartialD; v)/(&PartialD; x) &DifferentialD;x "

Download mydoubt-to-mapleprime.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

Command for product of sets?...

Asked by: MDD 367

December 08 2015

0 5

Is there any Maple command for computing the product of two set A and B?

For example if A={a,b,c} and B={x,y} then we have A*B={ax,ay,bx,by,cx,cy}.

Two-point value boundary problem...

Asked by: Dmitry 30

December 07 2015

1 5

Hello,

I have two regimes. Each regime is characterized by system of state differential equations (diff(S(t), t), diff(K(t), t)) and co-state differential equations (diff(psi[S](t), t), diff(psi[Iota](t), t)) as follows:

(1)

diff(S(t), t) = -eta*K(t)*S(t)/(w*N*(S(t)+K(t))), diff(K(t), t) = eta*K(t)*S(t)/(w*N*(S(t)+K(t)))-upsilon

diff(psi[S](t), t) = eta*K(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2), diff(psi[Iota](t), t) = eta*S(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2)

(2)

diff(S(t), t) = -eta*K(t)*S(t)/(w*N*(S(t)+K(t))), diff(K(t), t) = eta*K(t)*S(t)/(w*N*(S(t)+K(t)))

diff(psi[S](t), t) = eta*K(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2), diff(psi[Iota](t), t) = eta*S(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2)

The first regime is employed from 0 to t1 (where t1 is unknown) and then regime 2, from t1 to T. I know the initial values for the state variables of the first system at t=0, that is, S(0)=S0 and K(0)=K0, as well as boundary conditions for the co-state variables for regime 2 at t=T, that is, psi_S(T)=a and psi_I(T)=b.

I also know that my unknown t1 should satisfy the algebraic equation: -c - psi_S(t1)=0, where psi_S(t1) is the solution of the co-state diff equation of the regime 2 at t=t1.

My question is: If I assume that the systems have not analytical solution, how can I found unknown t1 numerically? Moreover, asssume that all other parameters, such as T, eta, upsilon and others are given.

Plotting irregular data with surfdata...

Asked by: brownr 80

December 07 2015

4 2

I’m using Maple 2015.2 to plot irregular spaced data using the surfplot command. The shape of the plot is as expected, however I’ve been unsuccessful in changing the color of the surface. I would like the surface to be a consistant color instead of the “rainbow” color scheme. I’ve tried both the color and colorscheme options to no avail. I’m sure I’m making a very basic mistake, however I’m having difficulty finding it.

See attached worksheet

feildstrength.mw

Best regards,

Ron

[EDIT]: Worksheet didn't attach the first time

Why error in simplify?...

Asked by: Fred Sachs 15

December 07 2015

0 3

why is simplify is making errors - me or maple?

Ec := (1/2)*Kc*(2*Pi*h0/Pi(a0^2+h0^2)-2*Pi*h/Pi(a^2+h^2))^2;
2
1 / 2 Pi h0 2 Pi h \
- Kc |------------- - -----------|
2 | / 2 2\ / 2 2\|
\Pi\a0 + h0 / Pi\a + h //
simplify(%);
2
2 Kc (-h0 + h)

Simplify is erasing the varibles a0 and a. Is there a secret to using simplify?

Strange bugs of solve command...

Asked by: Kitonum 21925

December 07 2015

4 11

In Maple 2015.1 we have

restart;

solve([sin(2*x)/cos(x+3*Pi/2)=1, x>-4*Pi, x<-5*Pi/2], x, allsolutions, explicit);

solve([sin(2*x)/cos(x+3*Pi/2)=1, x>0, x<2*Pi], x, allsolutions, explicit);

In the first example, the error message is not clear (actually there exists a unique root x=-11*Pi/3), in the second example, one root (x=5*Pi/3) is lost.

Help with optimization...

Asked by: akiel123 10

December 07 2015

0 6

I've got this huge chunk of code which leads to an optimiazation at the very last line (Bestangles:=minimize(maximize()-minimize))). This minization is taking a very long time (havent solved it yet) and I would very much like to reduce that time. As I've understood maple does optimization by differentiating and then finding all extremes and comparing. Would this mean that since I minimize and optimize within a minimization command, it differentiates a ton of times? And if this is the case, can I somehow do the differentiation beforehand, since it is the same function being differentiate all the time? Or is there some other way I can improve the code?
Thanks alot!

Heres the full code:

Get General Solution of PDE...

Asked by: Saima 0

December 06 2015

0 1

I am very beginner about Maple. How to get the general solution from the follwoing equations by Maple. Please help me. Its Urgent. Please help me out.

Finite Element Analysis

by: Ramakrishnan 404 Product: Maple 2015

December 06 2015

2 4

I am learning to use maple for my notes preparation for the subject Finite Element Analysis. It is interesting to know that how often we blame maple or computer for the silly mistakes we made in our commands and expect the exact answers. I have used a small file and find it easy to analyse my mistakes fatser. If we make a small mistake in a big file, it not only gives us problem finding our mistakes, it leads to more mistakes in other parts as well. A command working in one document need not necessarily work the same way in other document.

I have made my first document and people will come with suggestions to make appropriate modifications in the various sections to improve my knowledge on maple as well as the subject.

Download FINITE_ELEMENT_ANALYSIS.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

Certain functions are partly plotted...

Asked by: cktamcu 5

December 06 2015

0 2

why the the software can't plot the function like x^(4/3)*sin(1/x) or x^(1/3)

it could only plot where x>0,but the value is does exist where x<0.

Thanks in advance for your help.

What is my mistake?...

Asked by: Ramakrishnan 404

December 06 2015

1 4

Consider a taper steel plate of uniform thickness mm as shown in the Fig. In addition to its self weight, the plate is subjected to a point load N at its mid point. Find the global force vector [F] , global stiffness matrix [K] , displacement in each element (1 and 2) , stresses in each element (1 and 2) and reaction force at the support.Take N/mm²; kg/m³;

=

Revised areas:

=

m²; is support reaction N; N;

= N/mm²

Number of elements,

=

N/m ; m; elementsl m;

We shall consider a two element system as shown in the Fig.
For element 1 Stiffness matrix K is

$K__1 := A__1e*E/l__e.(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1}))$ = Matrix([[2625000000000000, -2625000000000000], [-2625000000000000, 2625000000000000]])

For element 2 Stiffness matrix K is

$K__2 := A__2e*E/l__e.(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1}))$ = Matrix([[1875000000000000, -1875000000000000], [-1875000000000000, 1875000000000000]])

Global stiffness matrix obtained by adding all the elemental stiffness matrices and given b

$K__g := Matrix(3, 3, {(1, 1) = K__1[1, 1], (1, 2) = K__1[1, 2], (1, 3) = 0, (2, 1) = K__1[2, 1], (2, 2) = K__1[1, 2]+K__2[1, 1], (2, 3) = K__2[1, 2], (3, 1) = 0, (3, 2) = K__2[2, 1], (3, 3) = K__2[2, 2]})$ = Matrix([[K__1[1, 1], K__1[1, 2], 0], [K__1[2, 1], K__1[1, 2]+K__2[1, 1], K__2[1, 2]], [0, K__2[2, 1], K__2[2, 2]]])

For element 1 Load matrix F is

$F__1e := (1/2)*`ρ__1`*A__1e*l__e*(Vector(2, {(1) = 1, (2) = 1}))$ = Vector[column]([[861/25600], [861/25600]])

For element 2 Load matrix F is

$F__2e := (1/2)*A__2e*l__e*`ρ__2`*(Vector(2, {(1) = 1, (2) = 1}))$ = Vector[column]([[123/5120], [123/5120]])

Download wrong_answers.mw wrong_answers.mw wrong_answers.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

Maple on Microsoft Surface Pro 4 ...

Asked by: rad_guy 10

December 06 2015

0 1

Greetings all,

I was wondering if any Maple users out there are using the lastest Microsoft tablet, the Surface Pro 4 with Maple?

I would be interested in any opinions and specifically if the pen is effective when used as an input device with Maple

Thanks

Heat equation by anti-reduction method...

Asked by: wafa 10

December 06 2015

0 4

hello everyone

can any one tell me what is this anti reduction method. In the paper of serdal palmuk,the link is given bellow

http://www.hindawi.com/journals/mpe/2009/202307/

in this paper question #4 is first solved by anti reduction method for exact solution.

but i dont understand this method,

if anybody know this then please also tell me how to solve this,

and in the next (6 & 7 ) examples "in the pourus media equation" they first find its particular exact solution.i also dont understand this,so please tell me

actually i know how to solve ODE to find its exact solution but i dont know how we find exact solutions of partial differtial equations,

so please help me to solve this problem

thanks

Defining functions with n inputs...

Asked by: mkonto 25

December 06 2015

1 2

I wish to define a function with a finite number of inputs, but I do not know that number ahead of time (in other words the user will specify n and my function operates on vectors of size n). How can this be done?

Hard double integral...

Asked by: Markiyan Hirnyk 7819

December 06 2015

1 14

How to find the integral
,

assuming k and n integer?
It is known (McCrea W. H., Whipple F. J. W.Random paths in two and three dimensions, Proc. Roy. Soc. Edinburgh. 1940. V. 60. P. 281–298) that

G(n,n)=2/Pi*sum(1/(2*k-1),k=1..n).

The general case is reduced to the case k=n.
This is not a creature of pure reason: the one appears in electric circuits
(see M. Skopenkov, A. Paharev, A. Ustinov, Through resistor net, Mat. pros. Issue 18 (2014), 33-65, in Russian, http://www.mccme.ru/free-books/matpros/pdf/mp-18.pdf).
I found G(8,8) = 182144/(45045*Pi) in 657.797 s and G(9,9) = 3186538/(765765*Pi) in 4157.687 s on my comp by

restart; s := time():(1/2)*VectorCalculus:-int((1-cos(9*Pi*x)*cos(9*Pi*y))/(sin((1/2)*Pi*x)^2+sin((1/2)*Pi*y)^2), [x, y] = Rectangle(0 .. 1, 0 .. 1)); time()-s;
Mathematica 10.3.0 does G(9,9) in 250.391 s on my comp.

E-Mail Address:
Password:
Remember Me:	Automatically sign in on future visits

E-Mail Address:
Password:
Remember Me:	Automatically sign in on future visits

Ask a Question

Create a Post