Monte Carlo integration uses random sampling unlike classical techniques like the trapezoidal or Simpson's rule in evaluating the integration numerically.

Download MONTE_CARLO_INTEGRATION1.mw

1. Plot the solid that lies between the cone z=(x^2+y^2)^(1/2) and the plane z = 4.

2. Plot the solid that lies above the cone z=(x^2+y^2)^(1/2)  and below the sphere z=x^2+y^2+z^2.

3. Plot the solid that is inside the hemisphere z=sqrt(25-x^2-y^2) , outside the cylinder x^2+y^2 = 4 and above the plane xy − plane.

4. Plot the solid bounded by the hemisphere z=sqrt(16-x^2-y^2)and the paraboloid z=x^2+y^2.

5. Plot the solid that lies within the sphere x^2+y^2_z^2=4 , above the xy − plane and below the cone z=sqrt(x^2+y^2).

This proc is valid, yet Maple mint thinks there is syntax error

foo:= proc(x)
local z := "";
    if not x in ["A","B"] then
        return;
    fi;

    z:=cat("A
            B");    
end proc;

mint t.mpl gives

on line     7:     z:=cat("A
                          ^ Syntax error
A "then" was found without a previous matching "if".
An "end" may be needed to close the "in" construct from line 3.

But these two below procs below it gives no syntax error

foo:= proc(x)
local z := "";
    if not x in ["A","B"] then
        return;
    fi;  
end proc;

And

foo:= proc(x)
local z := "";
    z:=cat("A
            B");    
end proc;

No syntax error on either one. the syntax error only shows up when combining them. 

What does if not x in ["A","B"] then  have to do with the cat  below it? And why when they are combined, the syntax error shows?

I know of workaround, such as changing the cat to  z:=cat("A\nB");     or keep the strings on two lines, but do it like this

    z:=cat("A\n
           B");

Or write it like this

   z:=cat("A "
           "B"); 

But none of these changes were needed before adding the not x in ["A","B"]  before.

Is this a bug in mint? Is there a work around so the first example above still works using 

    z:=cat("A
            B");   

?

Hi,

I didn't use Maple before, I want to use it in this problem 

How to get the displacement equation of the longitudinal vibration of rod (bar) when the boundary and initial conditions are 

Dear Maple Users @acer @Carl Love @Kitonum @Preben Alsholm ,

Greetings.

How to plot a function "Am" for various values of "kt"(eg: kt=-1..1) at a point x=0.

Am vs kt.

The code has provided below.

Waiting for your response.

ktplot.mw

The purpose of this document is:

a) to correct the physics that was used in the document "Minimal Road Radius for Highway Superelevation" recently submitted to the Maple Applications Center;

b) to confirm the values found in the manual for the American Association of State Highway and Transportation Officials (AASHTO) that engineers use to design and build these banked curves are physically sound. 

c) to highlight the pedagogical value inherent in the Maple language to distinguish between assignment ( := )  and equivalence (  =  );

d) but most importantly, to demonstrate the pedagogical value Maple has in thinking about solving a problem involving a physical process. Given Maple's symbolic mathematics capabilities, one can implement a top-down approach to the physics and the mathematics, working from the general principle to the specific example. This allows one to avoid the types of errors that occur when translating the problem into a bottom up approach, from specific values of the example to the general principle, an approach that is required by most other computational systems.

I hope that others are willing to continue to engage in discussions related to the pedagogical value of Maple beyond mathematics.

I was asked to post this document to both here and the Maple Applications Center

[Document edited for typos.]

Minimum_Road_Radius.mw

Hallo;
the following MAPLE code generates 2-vectors. To collect them into a set K unfortunately does not work. K contains vectors two-fold etc. So K is not a set which I hoped to get. What is wrong?

restart:m:=5;#m Module
with(LinearAlgebra[Modular]):
K:={};
M:=Matrix([[3, 4*168], [4,3]]);
L:=Matrix([[3],[4]]);
#with(LinearAlgebra[Modular]):
for s from 0 to 10 do
a:=Mod(m,(M^s).L,integer);
K:=K union {a};
od:
K:=K;

Gerd

Hi experts

with(plots):
#epsilon:=5*Pi/2:
gammaa:=0.4:
gammao:=0.1:
gammab:=0.002:
omegab:=100:
X:=60:
Omega:=6*Pi:
g:=10:
sigmag:=5*gammaa:
a:=1/(sigmag*sqrt(2*Pi)):

#deltao:=1:
D7:=evalf(a*int(g*Omega*(gammao/2-I*Delta)*exp(-0.5*((Delta-deltao)/sigmag)^2)/(gammao^2/4+Delta^2),Delta=-infinity..infinity)):
D8:=evalf(0.5*a*int(g^2*gammao*exp(-0.5*((Delta-deltao)/sigmag)^2)/(gammao^2/4+Delta^2), Delta=-infinity..infinity)):
D9:=evalf(a*int(g^2*Delta*exp(-0.5*((Delta-deltao)/sigmag)^2)/(gammao^2/4+Delta^2), Delta=-infinity..infinity)):
b1 := (deltao-2*X^2*omegab*Y/(gammab^2+omegab^2)-D9)^2:

 f:=Y*((gammaa+D8)^2+(b1))=Im(D7)^2+(epsilon-Re(D7))^2:
#P1:=implicitplot(f,deltao=-70..50,Y=0..1,numpoints=100,axes=boxed,thickness=2,color=black,font=[1,1,20],tickmarks=[4, 3],linestyle=1);

implicitplot3d(f,Y = 0 .. 1,deltao=-40..40,epsilon=0..0.4,numpoints=100,labels=[Y,deltao,E],tickmarks=[3,3,3], style = surface, color = "Niagara Azure");

The above code to plot the implicitplot3d ,

first the figures are not smooth

second thing is how to make contourplot at epsilon= 5*Pi/2.

I appreciated any comments

i wanna solve a system of equations using ''fsolve'', I have found this example:

fsolve({2*x-x*y=0,-y+3*x*y=0},{x,y}, {x=0.1..5,y=0..4});

but i wanna understand how does this work,and what is the signification of term 

thank you for your help.

This exact value of this serie must be calculated with help of a integral and another serie (Maclaurin)

Note: there is Taylor serie and Maclarin is a special case of this Taylor serie. 

The serie is also numerical in Maple calculated , to get a idea of the exact value 

foroum_vraag_3_inleiding.mw 

I enclosed some book taks pdf about alternating series /infinite series and products 
to get a idea what is asked for  

blz_62.pdf

blz_63.pdf

blz64.pdf

blz66.pdf

blz_67.pdf

blz68.pdf

Let say the procedure MyProc returns two variables as

A,B:= MyProc(…);

However, for programming purpose, I do not want to create an unused variable. Assuming one only needs B, not A, is there a way not to create and assign A?

For information, in Matlab, it is a commonly used technique. The syntax is

[~,B]= MyProc(…);

In Maple, the meaning of ~ is different, but I am looking for something similar.

 Today I read the  Problem 5.21 from book Maple and Mathematica, A Problem Solving Approach for Mathematics:

The book uses following codes:

But I think  these codes just verify rather than prove(n is always specific number). This example is not difficult to prove by hand. but I'd like to know Maple how to prove it. It seems not easy.

Write a Maple command to define the function f that is given by

f(x)=x^5+2*x^3+3 .

In the box below, enter the part of your Maple command that is to the right of the ":=".

(Do not include the semi-colon (";") at the end.)

The answer I typed in is x^5 + 2*x^3 + 3 but it is wrong. Can someone help me what am I missing. 

Hi,

How to plot polygon between solutions of Complex equation

Thanks

ComplexQuestion.mw

Is it possible to connect Maple to

altibase