Maple Questions and Posts

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Hi. could anyone help on this code? fsovle doesn't solve it;
12.mw

Dear Users,

I have difficulty in finding numerical integration of a function f(r,t) which is a function of position r and time t. Function f(r,t) consists 100 terms (for example : BesselJ(0, 151.5793716314014*r)+BesselJ(0, 151.5793716314014*r)*r^2+......100 terms). For a particular time t=t1, f(r,t1) is calculated and then integrated as follows:

I am using evalf(Int(f(r,t1),r=0..1)

Maple takes a lot of time  to evaluate it as it is integrating it in one shot!  Is there a way to

a) pick the terms individually and integrate it

b) then sum these individual terms up together

c) How reliable is evalf(int(f(r,t1),r=0..1)) is? Is evalf (Int()..)  the best way to evaluate integration?

thanks.

I need Maple code of Bisection method.

I need to know how to compute and manupulate a symbolic equations in vectorial forms in maple. For istance, I need to compute the derivate of the following expression:

r1=T21r2

where ris a vector of three components, representing the position in the reference frame (RF) 1, T21 is the rotation matrix of RF2 w.r.t  RF1 and r2 is the position vector in RF2. In maple I need to derivate (in time) the expression twice to obtain the acceleration.

d(r1)=d(T2)r2 + T21d(r2)

I don't know which command is requested or how should I declare the variables. 

After this I need to substitute the expression:

d(T2) =(T2wo )x

where 'x' is the vectorial product and wo is the angular velocity of thr RF. Of course after the substitution I will need to derivate again the expression.

Is there a way to procede in maple? All this is needed to build a mathematical model of a body in space.

Thank you

EDIT: If the question is not clear, please let me know. This is my first contact with maple and perhaps I am not even understanding what I can do with this software

I have written the following commands in Maple 18.

implicit_func := x^3+y^3 = 9*x*y;
c := 2;
s := evalf(solve(subs(x = c, implicit_func)));
m1 := evalf(eval(implicitdiff(implicit_func, y, x), {x = c, y = s[1]}));
                          0.8000000000
m2 := evalf(eval(implicitdiff(implicit_func, y, x), {x = c, y = s[2]}));
                          -1.257321410
m3 := evalf(eval(implicitdiff(implicit_func, y, x), {x = c, y = s[3]}));
                          0.4573214099

How can I graph all "implicit_func, y - s[1] = m1*(x-c), y - s[2] = m2*(x-c), y - s[3] = m3*(x-c), and the points (c,s[1]), (c,s[2]), and (c,s[3])" in a plane? (Each of them in a different color)     

Hello,

I try to install MapleToolbox2018.0LinuxX64Installer.run I run it as root or with sudo command, but everytime I finish with below message:

Choose Maple 2018 Folder

Please specify the path to your existing Maple 2018 Installation.

 [/opt/maple2018]:  /opt/exp_soft/local/generic/maple/2018

----------------------------------------------------------------------------
Choose MATLAB Folder

Select your MATLAB installation.

 []: /opt/exp_soft/local/generic/matlab/R2016b

Warning: The installer has detected a previous version of the Maple Toolbox in
your MATLAB installation.
Press [Enter] to continue:
Warning: The directory
/opt/exp_soft/local/generic/matlab/R2016b
is not writable by the current user

I'm not sure what to do with it.

---
Regards,

Bartek

 

I am writting the following commands in Maple 18.

imp_fun := -4*x + 10*(x^2)*(y^(-2)) + y^2 =11: c := 2: s := evalf( solve( subs( x = c, imp_fun))): m1 := evalf( subs ( { x = c, y = s[1] }, implicitdiff( imp_fun, y,x)));

Now I expect to see a value for m1 but I see again the last command in blue.

Could you please help me to see the value for m1 by writting these commands?

eval(sin(x), x = .2) is evaluated, eval(sin(x), x = 4) is not evaluated. Why? What should we do to get the answer. x-2n k (pi) can be obtained and evaluated. Why Maplesoft does not simplify and evaluate?

Is there a way out to give proper command for Maple soft to know what to do?

Thanks for answer.

Ramakrishnan V
 

eval(sin(x), x = .2)``

.1986693308

(1)

eval(sin(x), x = 4)

sin(4)

(2)

``


 

Download evalDoubtSinx.mw

How to plot multiple functions with multiple lines (Dot, Dash, Dash-Dot, )  all in one colour?

Like following plot:


Mittag-Leffler function generall simulation for fractional calculus

alpha := 1:

beta := 1:

f1 := sum(x^k/GAMMA(alpha*k+beta), k = 0 .. infinity)

exp(x)

(1)

NULL

NULL

NULL

plot(f1, x = 0 .. 1)

 

``


 

Download Mitag-liffler_Function.mw

I have written a code for minimizing a multivariable function using Gauss newton method. But i am getting error 
 

restart; with(LinearAlgebra); with(Student[MultivariateCalculus]); f := unapply(x1*exp(t*x2-y), x1, x2); tt := Matrix(5, 1, [1, 2, 4, 5, 8]); yy := Matrix(5, 1, [3.2939, 4.2699, 7.1749, 9.3008, 20.259]); ff := f(2.50, .25); for ii to 5 do t := tt[ii][1]; y := yy[ii][1]; Jf := Student[MultivariateCalculus][Gradient](f(x1, x2), [x1, x2] = [2.50, .25]); JF := Transpose(Jf[1]); JR := Transpose(Transpose(ff).JF); HF := Transpose(JF).JF; P := LinearSolve(HF, -JR); printf("%a  \n", P) end do

Vector(2, [0.,-1.], datatype = float[8])  

Error, (in LinearAlgebra:-LA_Main:-BackwardSubstitute) inconsistent system

 

``


 

Download GAUSS_NEWTON_METHOD3.mw

I have a vector A. I want to re-index vector A.

After re-indexing it, I will use the elements of the vector in new calculations.

For example:

 

k:=2:
M:=3:
A:=Vector[column]([seq(seq(p*q,q=0..M-1),p=1..2^(k-1))]);
C:=Vector[column]([seq(seq(c(p,q),q=0..M-1),p=1..2^(k-1))]); 
Equate(C,A);
c(1,0)+c(2,1);

c(1,0)+c(2,1)=2.

But the above code doesn' t work.

How I can solve algebraic differential equation of index 2 in Mae 15?

I have modeled a simple pendulum with large intital amplitude (so we do not approx sin(theta) by theta).

I have a plot of theta agains time but would like to have both theta (position) and theta' (velcocity) on same graph.

Grateful for any suggestions

Pendulum2time.mw
 

Simple pendulum without approximating sin(θ) to θ

restart; with(DEtools)

ode := diff(theta(t), t, t)+g*sin(theta(t))/L = 0; ics := theta(0) = 1, (D(theta))(0) = 0

diff(diff(theta(t), t), t)+g*sin(theta(t))/L = 0

 

theta(0) = 1, (D(theta))(0) = 0

(1)

g := 9.8; L := .75

ans := dsolve({ics, ode}, theta(t), numeric, output = Array([0, .1, .2, .3]))

Matrix(%id = 18446746279246469110)

(2)

NULL

DEplot(ode, theta(t), t = 0 .. 3.5, theta = -1 .. 1, [{ics}], linecolour = blue)

 

with(plots); odeplot(dsolve({ics, ode}, theta(t), numeric), t = 0 .. 3.5, colour = blue)

 

NULL


 

Download Pendulum2time.mw

 

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