So I am working on doing some trajectory simulations in Maple using standard Newton's Laws, some force expressions, and initial conditions.

Anyway, the numerical solution works fine if I let the initial conditions I specified (for z=-1) be actually for z=-0.9. To illustrate, when I give an initial condition like this:

x(-1) = x_0, D(x)(-1) = xd_0, Vz(-1) = v_0

the results don't make any sense. However, when using the same x_0, xd_0, and v_0 and I give initial conditions like this:

x(-.9) = x_0, D(x)(-.9) = xd_0, Vz(-0.9) = v_0,

the solutions at least make a bit of sense.

What's weird is that, when I let z -> 0.93 or so, the solution changes discontinuously. And this shouldn't happen. The initial conditions were calculated for and should work for z = -1. I don't understand why they aren't.

Here is my Maple document. ics1 are the problem.

dsolve_field_traject.mw

Do you guys have any idea what could be going on?

the question is as follow:

The partition does not always have to be equal intervals. Consider evaluating f(x)=x³ between 3 and 5, but splitting up the interval into a partition in which the end points of the subintervals are in a geometric progression. The common ratio r has to be chosen so that 3 is the first term and 5 is the last. Also the subintervals must be capable of getting smaller as n the number of subintervals increases. Check that the geometric series

a, ar, ar², ar³,.....arⁱ, .....arⁿ =b

with r=  and suitable choices for a and b satisfies these criteria. Treating the difference between arⁱ and ar^(i-1) as the width of the subinterval and using the right hand endpoint of the subinterval, evaluate the Riemann sum to n terms for f(x)=x³. Find the limit as n tends to infinity to show that the partition does not affect the result.

here is what i have got so far, can anyone check if im doing it right? thanks

>a:=3:

>b:=a*r^10:

>r:=(5/3)^1/10:

>for i from 0 to 5 do a*r^i end do; -> a list of number appear in sequence ie:3, 3.157...,3.323...3.497...etc

>restart;

>a:=3:

>b:=a*r^100:

>r:=(5/3)^1/100:

>dxj:=a*r^i-a*r^i-1

>xj:=i*dxj+a

>f:=x->x^3

>evalf(sum(f(xj^*)dxj,i=1..100)) -> my value is sth like 162.4788870...

I tried to find the limit, but maple 16 freezed so i think i must have done sth seriously wrong?

<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi>b</mi><mo>&coloneq;</mo><mi>a</mi><mo>&sdot;</mo><msup><mi>r</mi><mrow><mn>10</mn></mrow></msup><mo>&#x3b;</mo><mo>&nbsp;</mo></mrow></math>

Is there any way to write a function that determines the area of any n-sided polygon determined by a sequence of points? ie [[x_1, y_1]. [x_2, y_2], ... [x_n, y_n]] while returning 0 if any of the 2 segments intersect, otherwise print the area. Thanks for any help

Hello,

would you please help me how can i introduce a probability distribution function to maple in document mode?

I want to calculate integral of x f(x)dx, while I want maple to know f(x) is a probability distribution function.

I do not have any assumption about f(x)(for example normal or exponential distriburion)

Thanks

I really very much like this package since it works just perfectly converting units and also supports CGS for people doing calculations in theoretical physics. I have just a suggestion concerning the formattig: As is explained in many physics books and also at the units standard website http://physics.nist.gov/, units shouldn't be placed in square brackets since these brackets are defined such that [m] = kg means: unit of m is kg. To write is m = 3 [kg] is a very common and unharmful mistake, also used very often when labelling axes in figures, e.g. m [kg] instead of the correct m/kg or m (kg). Another issue is that units shouldn't be printed italic but upright and any physics journal requests its authors to consider this rule. Again, this is not a "mistake" but on the other hand the Maple pretty-print output is already so nice that considering such rules would even make it perfect.

I am fully aware that omitting the brackets could be considered harmful if someone has an algebraic expression in front of the unit where symbols and units could be mixed. On the other hand having the usual interspace between unit and expression, the unit being upright and maybe even coloured (analogously to e.g. operators in the physics package) units and symbols could be easily held apart.

Hello, everyone!

Last week I’ve encountered problems with integration of Maple 17 in Microsoft Office Excel 2013. The Maplesoft note on the point (http://www.maplesoft.com/support/faqs/detail.aspx?sid=32651) offers some ways of fixing it up, though I’ve run all of them the problem is the same:

While the connection is established, after entering the formula “=Maple(“x+x”)”, the Excel returns “Critical Error in Formula”

Before contacting the Maplesoft Technical Support, I want to ask here whether someone had the same case and managed to solve it.

Many thanks in advance.

I have f₁=x, and f_n=x+sin(f_n-1).

I would like to write a procedure that would allow me to find the first derivative of f_n. Thanks.

the question is as follow:

1)receive two integers p and q

2)declare two local p1 and q1 and give them intial values and q

3)check if p o q are equal or less to zero print works only with positive integers

4)while p1 not equal to q1 then p1-a1 otherwise q1-p1

5)whenever p1=q1 we have the GCD

note:must use procedure and call it for different values of p and q after the procedure is written

-by following the instruction above this is what i got

GCD:=proc(p,q)

local p1,q1;

p1:=p;

q1:=q;

if p<=0 OR Q<=0 then 'works only with positive integers'
else while p1<>q1 do if q1<p1 then p1-q1 else q1-p1

end if;

end do;

end if;

end proc;

but when I call two integers eg:p=2, q=6 -> GCD(2,6) maple just freeze...evaluating....forever. is it because i got the procedure wrong etc? it would be helpful if anyone can help me with this. thanks

I am using the ColumnSpace command (from the LinearAlgebra package) to generate a basis for the column space of a matrix. Is there any way to "force" the command to express the basis in terms of columns of A and not in the canonical form with leading 1's?

For example, for

A:=Matrix([[-3,6,-1,1-7],[1,-2,2,3,-1],[2,-4,5,8,-4]]):

I would like to obtain the following basis for the column space:

{[-3,1,2],[-1,2,5]}

Solve the following initial value problem for y(t), z(t).

dy/dt + dz/dt =t

dy/dt-2 dz/dt=t^2

with initial condition y(0)=1, z(0)=2.

Thanks.

Here is the question:

Consider f(x)=x³ over [a,b] and a partition P of [a,b] into n equal subintervals. Find the length of this subinterval and assign it to dxj.

a) Assign the rightmost point of the jth subinterval to xj. Set up an expression corresponding to the Riemann sum for this partition with  as the rightmost point xj in each subinterval.

b) Find the limit of this expression as n->∞. Integrate f(x) between a and b and comment on your evaluation of the integral and the value of the limit.

 d) Show that the limit of the Riemann sum remain unchanged if

xj = the left most point in the jth interval

or if

xj = the midpoint in the jth interval

anyone know how to go about this question? thanks

I am trying to find what values of x f(x) is increasing without estimating from the graph

Hi,
     I'm comparing a numerical (asymptotic series solution) to a analytical one in Maple 14, 16 and17 (I have many different machines). I make a substitution S(r) = r^(l+1) R(r) to remove singularities and ask maple to solve for S(r) numerically. Then simply

R(r) = S(r)/ r^(l+1) where S(r) is a numeric procedure
and
diff(R(r), r) = diff(S(r),r)/ r^(l+1) - (l+1) S(r)/ r^(l+2) by the  chain rule, and diff(S(r),r) is another numeric procedure returned by maples dsolve.


Now |
S(r)_numeric agrees with S(r)_analytic,
R(r)_numeric agrees with R(r)_analytic,
diff(S(r),r)_numeric agrees with diff(S(r),r)_analytic
BUT diff(R(r),r)_numeric DOES NTO AGREE WITH  diff(R(r),r)_analytic
 
To me this seems that the formula from the chain rule most be wrong. Does anyone have any ideas? I've attached a .msw file too

Thanks,
Matt
testingDRoutside.mw

Dear Experts,

Analytical integration is not a choice for the integrals listed here. Hence, Maple is not able to find the numerical integration for the following oscillatory functions. However mathematica can. However, before I take the mathematica results, just need to check with you.

Following link shows that for a diverging series, the (Numerical) integral is finite.

http://books.google.com.sg/books?id=vntDnyh0gacC&pg=PA664&lpg=PA664&dq=nintegrate++seqlim&source=bl&ots=iNYR1o6kVd&sig=VuiQuiUMDEEGOBnguSwfcPPSHQA&hl=en&sa=X&ei=k_J4UofXJYjNkwW79IDYBw&ved=0CE4Q6AEwBA#v=onepage&q=nintegrate%20%20seqlim&f=false

1)

 Maple: 

eval(int(r^2 BesselJ(1,r)* BesselJ(0,r), r = 0..infinity)) 

Float(undefined)

Mathematica: 

NumberForm[ NIntegrate[BesselJ[0, x]*BesselJ[1, x]*x^2, {x, 0, Infinity},   AccuracyGoal -> 20], 15]

SequenceLimit::seqlim: The general form of the sequence could not be determined, and the result may be incorrect. >>

-95982.37707206068

2)  Maple:
       eval(int(r* BesselJ(0,r), r = 10..infinity)) 

                         Float(undefined)

Mathematica: 

NumberForm[ NIntegrate[BesselJ[0, x]*x, {x, 10, Infinity},   AccuracyGoal -> 20], 15]

SequenceLimit::seqlim: The general form of the sequence could not be determined, and the result may be incorrect. >>

-0.434727

Any conclusions on the result.

a) Why maple not able to evaluate the integrals.  b) Are the result of the Mathematica can be considered as appropriate.

Attached is the maple file for your consideration.

Integrations.mw 

Lookinf forward to your reply.

Thanks.

Hello!

Im a regular student and Math is a really difficult topic for me, and every once in a while i run into a problen that i am unable to solve. This time i would like to ask this commmunity for some help. Many thanks in advance.

The function itself is: y = sqrt((x^2-5*x+6)/log[10]((x+10)^2))

I was able to determine the domain (X), but i am having very big trouble with finding the range (Y). Also i should be able to do it with pen on paper, but so far i have wasted 2 days and many papers on pointless scribblig.

Could anyone please explain how could i find the range of that function and provide a step by step solution?