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Derive the orbit of the Moon around the Earth by doing a Verlet algorith of Molecular Dynamics simulation. Use one hour for your step τ. Place the stationary Earth at the origin of the Cartesian system. For initial conditions, use the position and the speed of the Moon when it is at its apogee (furthest from Earth). Plot the orbit.

(a) Show that if {an} ∞ n=1 is Cauchy then {a 2 n} ∞ n=1 is also Cauchy. (b) Give an example of a Cauchy sequence {a 2 n} ∞ n=1 such that {an} ∞ n=1 is not Cauchy

Hi EveryOne!

In the the answer of the question "How to find k^th root of the given matrix over finite field (at URL: Carl Love helped to find k^th root of the given matrix M over GF(2m)/f(x).

Now, I need to compute direct exponentiation of the given matrix M in finite field. (If M = [mi,j], we say Direct Exponent (element-wise exponent matrix), Mdk of M is a matrix whose each element is the result of exponentiation of corresponding elements of M. If k=2, then we say Md2 is a direct square matrix of M )

Please help me!!! Thank you very much.

Determine wether the sequence below converges or diverges, and if it converges, find the limit.






Restrict calculation to real numbers.

Using y' = u, express the oscillator equation: y" + 3y' + 2y = cos(t) as a first order system. 

Plot an approximate solution curve for the specified initial conditions.

[x0=5, y0=1],[x0=-2, y0=-4],[x0=0, y0=.1],

This is what i have so far but i am not sure if its correct.

Eulers modified method: 


x[0] := 0;

y[0] := 5;


h := .1;

for n to 100 do

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

k1 := x[n-1]+y[n-1];

k2 := h*k1+x[n]+y[n-1];

k := 1/2*(k1+k2);

y[n] := h*k+y[n-1]

end do;

data := [seq([x[n], y[n]], n = 0 .. 100)];
G1 := plot(data, style = point, color = "blue");

  1. Work with the function 

f(x) = 5x^2-125/x^2-16

  1. Find the horizontal asymptotes
  2. Draw the graph of the function.  Show all horizontal and vertical asymptotes on your graph.  Edit the domain and the range to get a “good window” that clearly shows the shape of the function and all the important features, such as zeros, intercepts, maxima and minima, horizontal and vertical asymptotes. 

I am new to maple and I need help.

Let x=x(t) and y=y(t) be functions in t. Suppose that x'=2x−5y+t and y'=4x+9y+sint such that x(0)=y(0)=0. Find y(1).

How do I go about doing this question?


Hi EveryOne!

In the the answer of the question "How to find roót of polynomial in finite field and extension finite field (at URL: Carl Love helped compute eigenvalues (x1,x2,...,xn)and eigenvectors of the given matrix M over GF(28)/(y^8+y^4+y^3+y+1).

I need to do:

1. Get matrix D from these eigenvalues (x1,x2,...,xn), with D[i,i] = xi and D[i,j≠i] = 0 (D will be diagonalizable matrix. Some xi may be in extension finite field  GF((28)2))

2. Get matrix P from eigenvectors corresponding to the above eigenvalues, compute P-1

3. Compute matrix B = P x D1/4 x P-1 in  extension finite field  GF((28)2).

Please help me!!! 

My task is to develop a mathematical model of time-variant temperature
distribution in a bar with Maple. 
The bar is made of aluminum. The length is 202 mm and the diameter
is 8mm.
Heat is supplied from the kitchen lighter where the flame burns on butane.
The height of the flame is about 4 mm.
Your model should be able to answer how long the time it takes to reach
a certain value of temperature at the distance of 10 cm from the heat source.


anyone can help to answer this? im totally new to maple.. hopefully some1 can help me to answer this..

Please see attached document.


The 2 bits of data I am working with are a Constraint Function and Objective Function:



I need some pointers on how to do this. I keep getting solutions of

and I am ont receving an x value for some reason and leaving me unable to continue with the problem.

If anyone can send me some code I would be grateful. If anyone would like to send the correct full working code so I can see how to do this and review it I would be grateful.


 Code I had so far was:




Write a Maple code that performs the Gaussian elimination for an nxn matrix, converting it to an upper triangular matrix. 

(Hint: you will need to use three for .. do loops.)

Write a recursive Maple procedure, called “decToBin”, that converts an integer from decimal (base 10) to binary (base 2). Ensure that only integers are allowed as arguments to the procedure. Passing a negative integer should result in no output. Test your procedure by outputting the result of the following:
decToBin(“A”) # should result in an “invalid input” error

Hi Clever guys,
I am sorry if I asked for too much, but I am really in a big problem, I had a family problem and I didn't attend most of the lectures, and now I have to hand in an assignment before easter hollydays, and to be honest with you, I don't know from where to start, I know I will have to understand this stuff, but now I don't have enough time to do the assignment, so if anyone can help me, please please, for you guys it will maybe take 20min to do it, i ll need days and days and in the end it will be all wrong. I am going to try to do the other questions, there are 5 questions :(  
Please help me , I am really not a very bad student that just want to copie, but if nobody does this for me this time I will fell, please do this question for me please.. maybe you will say start it and then ask to check if it is correct, I am really trying my best, please.

that is one question:

By integrating a third order Newton Gregory Polynomial, derive Simpson’s

three eights rule given by

∫ f(x)dx (from x0 to x3 ) =3/8*ℎ(y0 + 3y1 + 3y2 + y3)

(b) Find the order of accuracy of Simpson’s rule and Simpson’s three eights rule.


thank you very much 

Hello Everyone,


I would like  to write a code to calculate the riemann sum approximation of the curve sin(sqrt(x^2+y^2)+1 

calculate the actual volume using integration

use the ranges x=[-2pi to 2pi]=y, and 20 subdivisions.

also display the curve and the parallelepiped approximations on the same plot.

 my code give me  an error..please someone can advise me which part of my code is not correct..

Thanks very much in advance!

> g := proc (x, y) options operator, arrow; sin(sqrt(x^2+y^2))+1 end proc;

 Z := g(x, y);


 X := Array(0 .. n); Y := Array(0 .. n); Z := Array(0 .. n);


c := -2*Pi; d := 2*Pi;

a := -2*Pi; b := 2*Pi;

n := 15;

s := 0;

X[0] := a; Y[0] := c; Z := g[X[0], Y[0]]; s := 0;

dX := (b-a)/N;dY := (d-c)/N;

    for i from 0 to N do      for j from o to N do     s:=s+Z[i]*dX*dY     X[i]:=X[i-1]+dX: Y[i]:=Y[i-1]+dY: Z[i]:=g([Xi],[Yi])  end do;

This the error message i am getting (Error, unterminated loop)









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