The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the world (regardless of the students' nationalities). One can see some problems and answers here. I find it remarkable that a lot of these problems can be done with Maple. Here is a sample (The DirectSearch package should be downloaded from http://www.maplesoft.com/applications/view.aspx?SID=101333 and installed in your Maple.).

Hope the reader will try to continue the above.

Download Putnam_done_with_Maple.mw

files.mw

From art of problem solving ws: "Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of the files take up 0.8 MB, 12 of the files take up 0.7 MB, and the rest take up 0.4 MB. It is not possible to split a file onto 2 different disks. What is the smallest number of disks needed to store all 30 files?"

The answer is 13: 3*[0.4,0.8]+6*[0.7,0.7]+4*[0.4,0.4,0.4]

How to accomplish this in maple? my attempt doesnt work, unsurprisingly...

How do you move plot labels individually? Just click-hold-and-drag does not work.

"A Virtual 3D Solar System": http://www.maplesoft.com/applications/view.aspx?SID=4484&view=html#mapleautobookmark5

How do you color the orbits individually?

How do you plot different kinds of data simultaneously in one graph? E.g. surfdata and spacecurve?

I am trying to do a substitution as shown in the attached document. I know variants of this question have been asked before but dont quiet get what to do. It is problem with algsubs and how it handles denominators I think. Can get substiturion to work for simple fractions but more complicated ones fail. Would appreciate any guidance here.

Download UHG5_substitution.mw

Dear Maple experts,

I want to solve the following problem with Maple. I appreciate if you can help.

n:=1+(2/Pi)*evalf(Int((x*0.187549975)/(x²-10.69²), x=0..infinity));

Hi,

How do you plot a list of values/an array into a surface?

E.g.

t = [seq(0+i*(2*evalf(Pi)*(1/10)), i = 0 .. 10)]

x:=[3,4,2*evalf(Pi), 7.83]:

y:=[2.5,4.3,6,2*evalf(Pi)+2]:

z:=[-2,0.3,1.5,evalf(Pi)]:

plot3d([x[i]*cos(t), x[i]*sin(t), y[i]*cos(t-z[i])],-10..10,-10..10);

Hello,

I use maple for the determination of the symbolic relations between the geometric relations on multibody system.

I would like to create a dll function for the functions that I have determined symbolically.

I have already a paper presenting : 
- the transformation Maple --> code C with the package with(CodeGeneration)
- and the transformation code C --> another software.

I would like to directly create a dll function from my maple function with using code C. Is it possible and how ?

Thanks a lot for your help.

Hi there,
I have the following set of equation which I want to solve using Maple's dsolve command:

d[V(t)*C(t)]/dt = G - K *C(t)
dV(t)/dt = alpha - beta

where V is the volume, C is the concentration, and t is the time variable. G, K, alpha and beta are constant parameters of the problem.

The solution for V(t) is easy to find operating the second equation:
V(t) = V_0 + (alpha - beta)*t

But solving for C(t) is a bit harder.

I would like Maple to solve the system, but the result I get does not really make sense to me. My attempt is this: Maple_artificial_kidney.mw

Any thoughts about how to introduce the equations successfully?

Thank you,
jon

Hello everybody,

I am working on a somewhat complicated analytical problem, which includes the evaluation of the following (finite and singularity free) double integral (the stated numerical parameters may vary):

There are no unevaluated variables inside (all the e's are real exp()s). However, when putting it through evalf(), Maple returns it (after calculating for some time) unevaluated. I have no idea why, as a simple box sum should succeed.

Any input would be appreciated. Best regards,

  K. Reuther

P.S.: Raw expression for further deliberations

Int(exp(18.1818*(Int((0.579160e-1*sqrt(x)*Ei(1., 0.500000e-4*x)+(1072.23*(.999950-1.*exp(-0.500000e-4*x)))/sqrt(x))/sqrt(x), x = 1. .. eta))-9.10000*eta)/eta, eta = 1. .. 100.)

Hello,

we have a "little" Multibody Dynamics Project in our University. We try to compute a system with 4 DOF with Lagrange. The problem is that in the end our dsolve give us an error. We checked the whole system like 5 times and searched only for the dsolve problem over 6 hours.

Error from dsolve:

"Error, (in DEtools/convertsys) numeric exception: division by zero"

This error shouldnt be possible because we have no divisions at all in our system or somekind of inifity though arctan or what ever.

Any help would be perfekt.

Thanks a lot

Wackeraf

MultibodyDynamics_Gruppe_aktuell_V3.mw

Hallo. I'm solving a initial value problem for system of 7 ODE:

dsn := dsolve({expand(maineq[1, 1]), expand(maineq[1, 2]), expand(maineq[1, 3]), expand(maineq[1, 4]), expand(maineq[1, 5]), expand(maineq[1, 6]), expand(maineq[1, 7]), T(0) = .5, u(0) = u0, Y[1](0) = .8, Y[2](0) = .2, Y[3](0) = 0, Y[4](0) = 0, Y[5](0) = 0}, numeric, method = lsode[backfull])

Is there easy way how to plot result?

Is there a way with Maple 18 to place a bracket as shown below to contain two DE's? I am not trying to solve them. Only for note-taking purposes. If there is can you please share how to do it?

How to solve the equation
2^(sin(x)^4-cos(x)^2)-2^(cos(x)^4-sin(x)^2) = cos(2*x)
symbolically? The solve command produces a weird answer. Evalfing all its values, one sees
0.7853981634, -0.7853981634, 2.356194490, -2.356194490,

1.570796327 - 1.031718534 I, -1.570796327 + 1.031718534 I,

1.570796327 + 1.031718534 I, -1.570796327 - 1.031718534 I,

0.7853981634, -0.7853981634, 2.356194490, -2.356194490,

1.570796327 - 1.031718534 I, -1.570796327 + 1.031718534 I,

1.570796327 + 1.031718534 I, -1.570796327 - 1.031718534 I

The identify command
interprets the real solutions on -Pi..Pi as -3*Pi/4, -Pi/4, Pi/4, 3*Pi/4
(for example,
identify(2.356194490);

3*Pi/4 ).
Is it possible to obtain these with Maple in a simpler way?

PS. Mathematica 10 does the job.

PPS. So does even Mathematica 7.

Hello people in mapleprimes,

I have a question of labels of equations.

For example, suppose that there is a following description in a worksheet.

>2*x+y=5;

  2*x+y=5   (1)

>3*x+y=6;

  3*x+y=6   (2)

>solve({(1),(2)},{x,y});

 {x=1,y=3}          (3)

subs((3),100+x+100*y)

    400   

And, when I moved (2) to the next to (1) with dragging, and then, clicked !!! to execute it, then the worksheet 

changes as follows, which is wrong as accompanying ??

>2*x+y=5;3*x+y=6;

  2*x+y=5

 3*x+y=6   (1)

>solve({(1),??},{x,y})

{x = x, y = -3*x+6}          (2)

>subs({(1),??},100*x+100*y)

-200*x+600

Do you know some good way for ?? not to appear in the above sitiation.

I will appreciate when you tell me some measures about this.

Best wishes.

taro