Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I have problem: Let  A(2,0,0), B(0,3,0), C(0,0,6) and D(1,1,1) be four points and Delta is the line passing through the point D so that sum of distances from the points A, B, C to Delta maximum. Find a direction vector of Delta.

I tried. Let v(a,b,c) where a^2 + b^2 + c^2 = 1 and my code
 

with(Student:-MultivariateCalculus):
with(Optimization):
A := [2, 0, 0]: 
B := [0, 3, 0]: 
C := [0, 0, 6]: 
DD := [1, 1, 1]: 
v := <a, b, c>: 
d := Line(DD, v): 
d1 := Distance(A, d): 
d2 := Distance(B, d): 
d3 := Distance(C, d): 
S := d1+d2+d3: 
Maximize(S, {a^2+b^2+c^2 = 1});

I didn't get the result. How to get the numbers a, b, c?

Hello,

Is it possible to expand vector calculus identities directly in Maple without taking them to basis form (i.e. their component partial derivatives).

For example: 

restart

with(Physics[Vectors]):

%Curl(u*%Gradient(v)) = u*%Curl(%Gradient(v)+`&x`(%Gradient(u), %Gradient(v)))

 

Given the Left Hand Side, can Maple come up with the RHS on its own?

Many Thanks.

Let (u (n)) be the sequence defined by u (n + 1) = 3.5u(n) (1 - u (n)) and u (0) = 0.4.
1. Create the sequence s whose elements are [k, u (k]) for k varying from 0 to 100.
2. Graph the list of points with the plot function and the style = point option.

1. Write the list of numbers that are the sum of two squares of integers a ^ 2 and b ^ 2 with 0 <= a, b <= 5.
2. Select the odd numbers from the previous list. What seems to be their general form

How 2 argumented matrices can be written in one matrix 

Hello,

I currently have

And was wondering if there's a way to declare x as a real so that this evaluates to 1?

Why, when parsing Pi/6, is it displayed differently in a textplot situation?

parse("Pi/6")
               

with(plots):
textplot([1,1,parse("Pi/6")])

Hellow,I use maple 13 (linux)

 

How can I get a output data file solution of my ODE? For example, the maple resolved the harmonic equation and got a u(t) function, but I want manipulated the data in a external programm, like gnuplot ou xmgrace.

 

Sorry my bad english!

 

wave.mw

 

I just wanted to let everyone know that the Call for Papers and Extended Abstracts deadline for the Maple Conference has been extended to June 14.

The papers and extended abstracts presented at the 2019 Maple Conference will be published in the Communications in Computer and Information Science Series from Springer. We welcome topics that fall into the following broad categories:

  • Maple in Education
  • Algorithms and Software
  • Applications of Maple

You can learn more about the conference or submit your paper or abstract here: 

https://www.maplesoft.com/mapleconference/Papers-and-Presentations.aspx

Hope to hear from you soon!

I describe here a finite difference scheme for solving the boundary value
problem for the heat equation

"(&PartialD; u)/(&PartialD; t)= ((&PartialD;)^)/((&PartialD;)^( )x^)(c(x)(&PartialD; u)/(&PartialD; x)) + f(x,t)   a<x<b,   t>0"

for the unknown temperature u(x, t)subject to the boundary conditions

u(a, t) = alpha(t), u(b, t) = beta(t), t > 0

and the initial condition

"u(x,0)=`u__0`(x),    a < x < b."

 

This finite difference scheme is designed expressly with the goal of avoiding

differentiating the conductivity c(x), therefore c(x) is allowed to be

nonsmooth or even discontinuous. A discontinuous c(x) is particularly
important in applications where the heat conduction takes place through layers
of distinct types of materials.

 

The animation below, extracted from the worksheet, demonstrates a solution 

corresponding to a discontinuous c(x).  The limit of that solution as time goes to

infinity, which may be calculated independently and exactly, is shown as a gray
line.

Download worksheet: heat-finite-difference.mw

 

i wnat to take this export numbers from for loops in the matrix
restart;
with(LinearAlgebra);
f(x) :=  3*x^2+1 :
for i by .5 to 3.5 do print(i, f(i)) end do;

same this pic

I want to get solutions (approximate solutions) of the inequality g(x) > 0. I tried. 
 

restart; 
fprime := x-> (x-1)*(x-2)^2*(x-3)*(x-4); 
f := unapply(simplify(int(fprime(x), x)), x); 
g := unapply(expand(f(3*x+1)-x^3+3*x), x); 
solve(g(x) > 0, x);

I got

Please, I need to use Maple to solve Euler-Bernoulli Beam on Pasternak Foundation using Homotopy Perturbation Method.

The governing equation is 

initial conditions are 

the boundary condition is 

The governing equation represents Euler-Bernoulli beam on a generalized Pasternak viscoelastic foundation under an
arbitrary distributed dynamic load. in which E, I , ρ ,A are the parameters of the beam, representing Young’s modulus of elasticity, moment of inertia, density and area of cross section, respectively. K,C and Gp are spring stiffness, damping coefficient, and shear coefficient of the foundation. Moreover, y(x, t) and F(x, t) are defined as the vertical deflection of the beam and the generic arbitrary dynamic loads, respectively, where the loads distribute along the x-axis and t is time.

 

I will appreciate anyone who can help me with a Maple solution.

 

Thank you.

Would anybody be able to explain to me why I had to rewrite this one baby-procedure that has an if-statement inside my larger procedure, so that I could get a later on if-statement to work? As best I can tell, they mean exactly the same thing.


 

Information that may be pertinent:

 - The entire (overall) procedure worked without throwing any warnings prior to my adding this new if-statement.
 - The if-statement itself worked perfectly fine on another worksheet, though I hadn't tested it inside a procedure.
 - Commenting out the if-statement but retaining the interior commands led to the sheet compiling again, showing that it was in fact the presence of the if-statement causing the issue. 
 - When I commented out the offending baby-procedure that started throwing the warning, the sheet once again compiled.

The added if statement:

if eval_size > 4 then Search(max(seq(eval_cont[i], i = 4 .. eval_size)), eval_cont); evals_pairlist := evals_pairlist[[1 .. 3, %]] fi:

The error I get, and its "positioning": 

Error, invalid expression for inline function

 

Hello,

How I can remove some problems in my code.

I wrote it before in  software, but in some lines, I have some problems with it.

How I can change it in maple to run well?


 

restart

M := 2; B := 1; C := 3; K := 6; f := 2*exp(-t); q0 := 1; qd0 := -1; qd20 := 1; alpha := 1/2; beta := 1/12; gammaa := 1/4; h := .1; Tf := 2

"N:=size(M,1)  T:=0:h:Tf;  lt:=length(T);  F:=subs(f,t,T);  F:=subs(t=T,f);    qd30:=M\(F(1)-B*qd20-C*qd0-K*q0);   q:=zeros(N,lt)  qd:=zeros(N,lt)  qd2:=zeros(N,lt);  qd3:=zeros(N,lt);  q(:,1):=q0  qd(:,1):=qd0  qd2(:,1):=qd20  qd3(:,1):=qd30"

Error, invalid function arguments

"N:=size(M,1)  T:=0:h:Tf;  lt:=length(T);  F:=subs(f,t,T);  F:=subs(t=T,f);    qd30:=M\(F(1)-B*qd20-C*qd0-K*q0);  q:=zeros(N,lt)  qd:=zeros(N,lt)  qd2:=zeros(N,lt);  qd3:=zeros(N,lt);  q(:,1):=q0  qd(:,1):=qd0  qd2(:,1):=qd20  qd3(:,1):=qd30"

 

"A:=M+alpha*h*B+gammaa*(h^2)*C+beta*(h^3)*K;  for n:=1:lt-1 do      D:=F(n+1)-B*(qd2(:,n)+(1-alpha)*h*qd3(:,n))-...          C*(qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n))-...          K*(q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n));      qd3(:,n+1):=A\D;      qd2(:,n+1):=qd2(:,n)+(1-alpha)*h*qd3(:,n)+alpha*h*qd3(:,n+1);      qd(:,n+1):=qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n)+gammaa*(h^2)*qd3(:,n+1);      q(:,n+1):=q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n)+...          beta*(h^3)*qd3(:,n+1);  end do"

Error, invalid function arguments

"A:=M+alpha*h*B+gammaa*(h^2)*C+beta*(h^3)*K;  for n:=1:lt-1 do      D:=F(n+1)-B*(qd2(:,n)+(1-alpha)*h*qd3(:,n))-...          C*(qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n))-...          K*(q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n));      qd3(:,n+1):=A\D;      qd2(:,n+1):=qd2(:,n)+(1-alpha)*h*qd3(:,n)+alpha*h*qd3(:,n+1);      qd(:,n+1):=qd(:,n)+h*qd2(:,n)+(0.5-gammaa)*(h^2)*qd3(:,n)+gammaa*(h^2)*qd3(:,n+1);      q(:,n+1):=q(:,n)+h*qd(:,n)+(h^2)/2*qd2(:,n)+(1/6-beta)*(h^3)*qd3(:,n)+...          beta*(h^3)*qd3(:,n+1);  end do"

 

plot(T, q, 'r-o', 'linewidth', 1.5)

Error, (in plot) unexpected options: [r-o, , 1.5]

 

``


 

Download

 

First 707 708 709 710 711 712 713 Last Page 709 of 2249