MaplePrimes Questions

I have 2nd order nonlinear ode I try to solve with Runge Kutta 4th order method in maple but all I get from the outcome was 1 and 0.This is the equation:theta_ode1.mw . How do I do it Or how do I write the code to solve it with maple using  Runge Kutta 4th order method?

Evaluate the limit \lim_{x\rightarrow 0}\frac{x-\sin(x)}{x^3} without using hopital rule or taylor series.

Good morning sir.

 

I request your kind support to the above cited question.

 

 

With thanks & Regards

 

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Dear Mapleprimes members,

I am trying to understand some known classical theorems of geometry (thales intersection thm, ceva, menelaus ) from the perspective of affine geometry and projective geometry.(my paper/pencil work is ok.. But I would like to use  Maple to visualize -if possible - geometrically some theorems and properties in a graph)

How could I do it in maple? Where may I get some examples?

thank you,

 

JeanJ

I have 2nd order nonlinear ode I try to solve with Runge Kutta 4th order method in maple but all I get from the out is 1 and 0.This is the equation: theta_ode.mw . How do I do it Or how do I write the code to solve it with maple using  Runge Kutta 4th order method?

Maple can plot a function that is a convolution of Dirac delta-function and some regular function.

restart

with(plots); a := 1.0

f := proc (x) options operator, arrow; exp(-abs(x)) end proc
G := proc (x, xi, t) options operator, arrow; `if`(t = 0, Dirac(x-xi), (1/2)*exp(-(1/4)*(x-xi)^2/(a^2*t))/sqrt(Pi*a^2*t)) end proc


u := proc (t, x) options operator, arrow; int(G(x, xi, t)*f(xi), xi = -infinity .. infinity) end proc; plot(u(0., x), x = -3*Pi .. 3*Pi)

1.0

 

proc (x) options operator, arrow; exp(-abs(x)) end proc

 

proc (t, x) options operator, arrow; int(G(x, xi, t)*f(xi), xi = -infinity .. infinity) end proc

 

 

Hovewer, it is unable animate this function (the first frame is empty).

n := 10:

 

``

Is it a bug? Is there a nice workarround of this bug?

Download Heat_Equation2.mw

How do you find the perimeter of an ellipse using maple?

For eg, x^2/20+y^2/13=1

Need help with starting this question. Thanks!

If a sequence is defined by X0=0, X1=1, X2=2 and Xn=n(Xn-3+Xn-2+Xn-1), n>=3

How many digits will X2013 have?

I have no idea how to start to answer this question. Please help Thanks!

Let G(x) denote the no. of ways of representing n as the sum of two prime numbers.

For eg, G(10)=2: where 10=3+7=5+5

           G(20)=2: where 20=3+17=7+13

           G(30)=3: where 30=7+23=11+19=13+17

How do you find G(10 000 000)?

I assign a function like so: f:=x->0.2*x^2*(x-3)^3

Then using d/dx in the expression palette I differentiate: d/dx f(x)

Get the following: 0.6x^2 (x-3)^2 D(x^2)(x-3)

What is the "D" in the last expression? What hasn't the whole differentiation been completed?

I'm having problem dealing with this question on Maple and would appreciate any help possible.

If f(x) = x/2, if x is even
   f(x) = 3x-1, if x is odd

which sequence will 2013^1102 fall in
1->1->1...
5->7->5...
17->25->37->55->41->61->91->17...

Thanks!


x11 := Vector([0.208408965651696e-3, -0.157194487523421e-2, -0.294739401402979e-2, 0.788206708183853e-2, 0.499394753201753e-2, 0.191468321959759e-3, 0.504980449104750e-2, 0.222150494088535e-2, 0.132091821964287e-2, 0.161118434883258e-2, -0.281236534046873e-2, -0.398055875132037e-2, -0.111753680372819e-1, 0.588868146012489e-2, -0.354191562612469e-2, 0.984082837373291e-3, -0.116041186868374e-1, 0.603027845850267e-3, -0.448778128168742e-2, -0.127561485214862e-1, -0.412027655195339e-2, 0.379387381798949e-2, -0.602550446997765e-2, -0.605986284736216e-2, -0.751396992404410e-2, 0.633613424008655e-2, -0.677581832613623e-2]):
y11 := Vector([ -21321.9719565717, 231.709204951251, 1527.92905167191, -32.8508507060675, 54.9408176234139, -99.4222178124229, -675.771433486265, 42.0838668074923, -12559.3183308951, 5.21412214166344*10^5, 1110.50031772203, 3.67149699000155, -108.543878970269, -8.48861069398811, -521.810552387313, 26.4792411876883, -8.32240296737599, -1085.40982521906, -44.1390030597906, -203.891397612798, -56.3746416571417, -218.205643256096, -178.991498697065, -42.2468018350386, .328546922634921, -1883.18308996621, 111.747881085748]):
z11 := Vector([ 1549.88755331800, -329.861725802688, 8.54200301129155, -283.381775745327, -54.5469129127573, 1875.94875597129, -16.2230517860850, 6084.82381954832, 1146.15489803104, -456.460512914647, 104.533252701641, 16.3998365630734, 11.5710907832054, -175.370276462696, 33.8045539958636, 2029.50029336951, 1387.92643570857, 9.54717543291120, -1999.09590358328, 29.7628085078953, 2.58210333216737*10^6, 57.7969622731082, -6.42551196941394, -8549.23677077892, -49.0081775323244, -72.5156360537114, 183.539911458475]):

 

> seq({round(x11[k]), round(y11[k]), round(z11[k])}, k = 1 .. 27);
{-21322, 0, 1550}, {-330, 0, 232}, {0, 9, 1528}, {-283, -33, 0}, {-55, 0, 55},

{-99, 0, 1876}, {-676, -16, 0}, {0, 42, 6085}, {-12559, 0, 1146},

{-456, 0, 521412}, {0, 105, 1111}, {0, 4, 16}, {-109, 0, 12}, {-175, -8, 0},

{-522, 0, 34}, {0, 26, 2030}, {-8, 0, 1388}, {-1085, 0, 10},

{-1999, -44, 0}, {-204, 0, 30}, {-56, 0, 2582103}, {-218, 0, 58},

{-179, -6, 0}, {-8549, -42, 0}, {-49, 0}, {-1883, -73, 0}, {0, 112, 184}

 

https://drive.google.com/file/d/0B2D69u2pweEvS0RVTFZWTnVKWms/edit?usp=sharing

{-49, 0}

there is a missing comma in this, is it the built in robot in maple playing human or my window make a joke?

 

this bug make me get an misunderstanding from mathematica stackexchange

 

https://drive.google.com/file/d/0B2D69u2pweEvZXp5WndMN0x5VGs/edit?usp=sharing

 

i can not display web correctly, What's wrong with me?

How to copy decimal number into notepad without scientific notation

after apply formating and copy the result to notepad, it still have scientific notation e

for rounding

 

x11 := Vector([0.208408965651696e-3, -0.157194487523421e-2, -0.294739401402979e-2, 0.788206708183853e-2, 0.499394753201753e-2, 0.191468321959759e-3, 0.504980449104750e-2, 0.222150494088535e-2, 0.132091821964287e-2, 0.161118434883258e-2, -0.281236534046873e-2, -0.398055875132037e-2, -0.111753680372819e-1, 0.588868146012489e-2, -0.354191562612469e-2, 0.984082837373291e-3, -0.116041186868374e-1, 0.603027845850267e-3, -0.448778128168742e-2, -0.127561485214862e-1, -0.412027655195339e-2, 0.379387381798949e-2, -0.602550446997765e-2, -0.605986284736216e-2, -0.751396992404410e-2, 0.633613424008655e-2, -0.677581832613623e-2]):
y11 := Vector([ -21321.9719565717, 231.709204951251, 1527.92905167191, -32.8508507060675, 54.9408176234139, -99.4222178124229, -675.771433486265, 42.0838668074923, -12559.3183308951, 5.21412214166344*10^5, 1110.50031772203, 3.67149699000155, -108.543878970269, -8.48861069398811, -521.810552387313, 26.4792411876883, -8.32240296737599, -1085.40982521906, -44.1390030597906, -203.891397612798, -56.3746416571417, -218.205643256096, -178.991498697065, -42.2468018350386, .328546922634921, -1883.18308996621, 111.747881085748]):
z11 := Vector([ 1549.88755331800, -329.861725802688, 8.54200301129155, -283.381775745327, -54.5469129127573, 1875.94875597129, -16.2230517860850, 6084.82381954832, 1146.15489803104, -456.460512914647, 104.533252701641, 16.3998365630734, 11.5710907832054, -175.370276462696, 33.8045539958636, 2029.50029336951, 1387.92643570857, 9.54717543291120, -1999.09590358328, 29.7628085078953, 2.58210333216737*10^6, 57.7969622731082, -6.42551196941394, -8549.23677077892, -49.0081775323244, -72.5156360537114, 183.539911458475]):

 

 

Hello

 

I am not that good at english, but i will try to tell you what my problem is. 

 

I have a worksheet in maple where i can't find out to make the results appear. 

 

Maybe it is easiere for you guys to help me if i can send you the document. 

 

Looking forward to hear form you


Regards

Niclas 

Hi there!

I want to have a procedure, which takes as one of it's arguments an algebraic, say sin(x) for instance. So far thats easy, I just type:

proc(arg)

Within this proc I would like to define a function now, which has this expression on it's image side. So it should look like f:=x->sin(x). What I tried is:

 

minexample := proc(arg)

  local f:

  f := x -> arg:

  f(pi)

  end proc:

minexample(sin(x));

 

But this code would produce sin(x), as a result and not 0, as I would expect. Could anyone tell me what I do wrong, and how I can get it right please? : )

What I would also like to know is, what kind of data type expressions such as sin(x), or algebraic expressions are, so I can specify that in the definition already to make the proc more transparent to use.

 

Thanks!

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