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How would you do a quick sort or bubble sort?

Using the Fourier convolution theorem to solve f(t) =sin (t)

f(t)=R dJ(t)/dt+J(t)/C

R dJ(t)/dt+J(t)/C=f(t)

where f(t) is a driving electromotive force. Use the fourier transform to analyze this equation as follows.



Find the transfer function G(alpha)  then find g(t) .

 Thanks ....


Please I need you to add in the output of my code the order of error defined in the procedure.

Thanks for helping me.

Here, the code.


I am reciving an error code when trying to graph the right circular cylinder in the questions

Attached is what I have done with the question.


Any help will be greatly appreciated. 

How can I use separation of variable to solve heat equation ut=uxx on a rod of length pi/4 with u(0,t)=0, u(pi/4)=0 and u(x,0)=x(pi/4-x) 

then solve heat equation by laplace transform

Hi can you please help me? I want to write a program in Maple code, using the Newton-Raphson method, to solve the equation tan(x) −x-1=0 .  the approximate root is 1.5.
I tried doing this using a while loop to compare the last and current iterates, but something is not working.
so can you please help me do that?


I need to write a procedure that takes an integer N and a boolean function F as in14 as arguments, returns nothing, and plots a square N × N lattice of points, coloring the points (i, j) with F (i, j) true in red and the other ones blue. 

Thank you in advance. Any help with this would be apreciated. 



Please help to use dsolve.

Suppose I have a Matrix A of size two. Y=[u,v].


How can use dsolve this problem.







so i've been having trouble with this one for a while. I think i'm just missing something simple.. maybe yous could help.

all we have to do is to write a maple procedure that takes an integer N and a boolean function F as in14 as arguments, returns nothing, and plots a square N N lattice of points, coloring the points (i; j) with F(i; j) true in red and the other ones blue.


Dear all;

Than you for help.

how  many steps are required to achieve a error of 1.e-3 in the numerical value of y(1).

Here The 3 -step procedure  Range Kutta Method.

## Exact  solution  

### We will modifty N ( number of steps to get error =10^(-3). )


## Procedure Range Kutta

> RK3 := proc (f, a, b, y0, N)

local x, y, n, h, k, vectRK3;

y := Array(0 .. N);

x := Array(0 .. N);

h := evalf(b-a)/N;

x[0] := a; y[0] := 1;

for n from 0 to N-1 do

x[n+1] := a+(n+1)*h;

k[1] := f(x[n], y[n]);

k[2] := f(x[n]+(1/2)*h, y[n]+(1/2)*h*k[1]);

k[3] := f(x[n]+h, y[n]+h*(-k[1]+2*k[2]));

y[n+1] := y[n]+(1/6)*h*(k[1]+4*k[2]+k[3])

end do;

[seq([x[n], y[n]], n = 0 .. N)]; y[1];

end proc;

## Now  we compute the error between y(1) and exact  solution for different value of  N

### I have a problem in this part

 errorRk3 := array(1 .. 29);
 for N from  2 to 30 do

errorrRk3[N] := abs(eval(rhs(res), x = 1)-RK3((x,y)->-y,0,1,N));

if errorrRk3[N] =10^{-3} end ;
end  do ;



write a maple package for quaternion must include the following procedures:

1) for quaternion polynomials f, g:  find degree of f , compute f +g ,f-g, fg.

2)for matrices over quarternion polynomials A,B: compute A+B,A-B, AB.

hint using records to represent quaternions.

Dear All;

Happy, to discuss with you these lines, and thank you to help me.

My goal is:


ode := D(y)(x) = f(x,y(x));
In this expression, is assumed to be a known function of the independant variable
 and the function that we are trying to solve for
.  The simplest numerical stencils to solve this equation will give us an approximation to
 at some point
                                  x = X + h
 given some knowledge of
                                    x = X
.  All of these stencils are based on the Taylor series approximation for
                                    x = X
 to linear order:
eq1 := y(x) = series(y(x),x=X,3);
eq2 := h = x - X;
eq3 := subs(isolate(eq2,x),eq1);
Now, we can remove the first derivative of y
 by making use of the differential equation:
eq4 := subs(x=X,ode);
eq5 := subs(eq4,eq3);

Now we must compute the same for y(x-h)  and then make.  How can I do this please

(a) Design your own 3-stage explicit Runge-Kutta method with one-step error O(h4).

(b) Test your method by solving y= −y. Confirm that the global error in your numerical solution

is O(h3).

Write a Maple procedure that solves for y(1) in the initial value problem

                     y= f(y),     y(0) = 1,



using a numerical stencil based on the nth order Taylor series expansion of y. The procedure’s arguments should include an arbitrary function f, an integer n representing the accuracy of the Taylor series expansion, another integer N representing the number of steps between x = 0 and x = 1. Pick a test problem and compare your results with the output of dsolve/numeric.

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