Hello Maple


I am preparing for an examination in Calculus, but my worksheet in Maple 18 doesn't cooperate. 

A lot of my studypartners use Maple 16 and they have no problems. 


I meet the following error: 

- Error, (in solve) invalid input: hastype expects 2 arguments, but received 1


I'm totally sure, that I'm typing correctly, because I write just the same as my studypartners. 
So is it an error, which only is seen in Maple 18 and can I do anything to solve the problem?

Kind regards
Anders Kristensen

PS: I can't figure out how to add a picture

I solve the problem on computational geometry: "A cube of side one contains two cubes of sides a and b having non-overlapping interiors. How to prove the inequality a+b≤1?" To this end I use the DirectSearch package , namely,

Here are some comments to it. The cube of side a is centered at (x_1,y_1,z_1) and rotated by the angles phi_1, psi_1, theta_1 (see http://uk.wikipedia.org/wiki/%D0%95%D0%B9%D0%BB%D0%B5%D1%80%D0%BE%D0%B2%D1%96_%D0%BA%D1%83%D1%82%D0%B8 ) and the cube of side b is centered at (x_2,y_2,z_2) and rotated by the angles phi_2, psi_2, theta_2. The procedure

calculates the distance between these cubes, for example,

st := time(); dist(.2, .9, .2, .2, .2, .7, .7, .7, 0, 0, 0, 0, 0, 0); time()-st;

[HFloat(5.453016092898238e-11), [s1 = HFloat(0.2646161775314957),

  s2 = HFloat(0.2828503247068887),

  s3 = HFloat(0.29444713116943216),

  t1 = HFloat(0.2646161774916062),

  t2 = HFloat(0.28285032471998384),

  t3 = HFloat(0.2944471311346344)], 2527]
                            191.133
Unfortunately, my code (which is syntactically correct) is spinning on my wondercomp during 10 hours without any output. I don't understand it at all. Your advices are welcome.

twocubes.mw

Hi there,

I have an ODE system which apparently needs some initial conditions to have its vector field plotted.

I am giving Maple's dfieldplot function the following arguments:

dfieldplot([de1, de2], [A(t), G(t)], t = 0..1, [A(0) = 25, G(0) = 0], A = 0..900, G = 0..200)

But Maple yields an error that reads:

Error, (in DEtools%2Fdfieldplot) invalid use of initial points or option - see phaseportrait

I would say that the initial conditions are correctly stated, according to the documentation of the function.

This is the attempt: MaplePrimes_Malaria_infection_cont.mw

Any ideas on what's missing?

Thanks,

jon

Hi there,

I would like to have the Jacobian matrix of an ODE system evaluated, and their eigenvalues computed, at the steady states of the system.

I know how to get the Jacobian matrix evaluated and the eigenvalues computed on an individual basis, setting manually each steady state as the argument of the matrix.

However, I would like to have it in a loop, so that the loop manages all steady states, that is:

steadyStates:= solve(mySystem); # would yield a set of pairs/lists

for each steadyState

m:=Jacobian(steadyStateN); # evaluate the Jacobian matrix

ev:= eigenvals(m); # compute the eigenvalues and save them to another variable/array and print them

end for:

First, I am not to find a way to loop over my steadyStates.

Attached is an example where the Jacobian matrix and eigenvalues are computed individually, where the steady states have been hard-coded once they have been computed: MaplePrimes_Predator_prey_model_Jacobian.mw

Any ideas on how to do this?

Thanks,

jon

Hi there,

I would like to compute and display the nullclines of a set of ordinary differential equations.

AFAIK, I can compute the nullclines in Maple by defining the equations and solving the system

e.g.:

# Define the equations
eq1 := u(t)*(1-u(t)/kappa)-u(t)*v(t) = 0;
eq2 := g*(u(t)-1)*v(t) = 0;

# Solve the system (i.e. compute the nullclines)
sol := solve({eq1, eq2}, {u(t), v(t)});

However, I am not quite able to imagine how to display them over a dfieldplot or a phaseportrait.

Attached is an example with some differential equations, and their vector field and trajectories: MaplePrimes_Predator_prey_model_nullclines.mw.

It can be use to illustrate how to (compute and) display the nullclines.

Thank you,

jon

Hi there,

I would like to have an operator (in this case, the natural logarithm) applied to a list/array of points defined as:

ydata := [0.572594976618e-1, 0.327865007249e-1, 0.280821589546e-1, 0.114365745192e-1, 0.578537931608e-2, 0.139154661062e-2, 0.641467839994e-3, 0.18013801847e-3];

How can I apply Maple's ln() operator to the whole array (i.e. avoid to apply it to ydata [1], ydata [2], etc.)?

Thank you,

jon

Aslam-u-Alikum. Hope you will be fine. I facing the problem of the last line to the attached program. I need the values of lambda in decimal.

Help.mw

PhD (Scholar)
Department of Mathematics

Hi,

I am trying to solve following expression

int(int((1-exp(-5.5/cos(x)))*sin(x), x = 0 .. arctan(300*cos(y)+sqrt(12.25-90000*sin(y)^2))), y = 0 .. Pi)

But I am not getting results.

Please help me!!!

Thanks

Cannot calculate derivative (gradient) of a procedure returned by dsolve.

Say, I solve the equation:

S1 := dsolve([diff(y(x), x$2)-1.0325*diff(y(x), x)+1.36*y(x)=sin(2*x), y(0)=0, y(1)=1], numeric, y(x), 'output' = listprocedure);

Its solution easily can be retrieved and looks fine:

H:=rhs(S1[2]); 

plot(H(t), t = 0..1, thickness = 4);

But when I try to calculate the gradient of H, I receive the error:

H1 := codegen[GRADIENT](H);

Error, (in intrep/statement) unable to translate Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(8, {(1) = .0, (2) = .14817993189456188, (3) = .31785812820433257, (4) = .47163479035679234, (5) = .6130306894371967, (6) = .7460958115245858, (7) = .8741894219027533, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 2, {(1, 1) = .0, (1, 2) = .47692145669848085, (2, 1) = 0.7710429970702501e-1, (2, 2) = .5707930170882397, (3, 1) = .1866916935738028, (3, 2) = .7299040171277492, (4, 1) = .3128649714509215, (4, 2) = .9171936...

Gradient of procedures defined by  ":= proc()" is calculated properly.

When you label a function of curve, this label is put just next to it. Is there a way to move this label to another position of the same curve?

Hello friends!

I 'm a student and I don't know a lot about Maple, so I would be really grateful if anyone could help me.

I want to solve a system of two equations and I have two unknowns, which are k and εα. However I don't know what I am doing wrong and I can't solve it.

I have attached my file.

Thank you very much in advance!agogos_2.mw

I am trying to fit an experimental data C[A](t)  vs t, with modelled ODE equation by solving it with numerical method. But the process gives problems here ha code and also find attached maple file.

Input is time =[0, 30, 60, 90, 120, 150, 180, 210, 240]

and output exptal data = [7647.5, 7397.5, 6755, 6252.5, 5860, 5530, 5440, 5107.5, 4857.5]

I want to find k,K[A] parameters;

EXPT_datafittinh_LHHW.mw

For my research at my school, I need to plot the Schrodinger equation using my given wave function. I am having issues though as I am receiving an error telling me that I need to submit my argument in standard or parametric form.

restart;

schro := {[4*(x^2-1)*(diff(psi(x, y), x, x))/(x^2-y^2)+2*x*(diff(psi(x, y), x))-(y^2-1)*(diff(psi(x, y), y, y))-2*y*(diff(psi(x, y), y))+(-2/(x+y)-2/(x-y)+1)*psi(x, y)] = energy};

psi := proc (x, y) options operator, arrow; e^((-1)*.5*[2*x+2*y])+e^((-1)*.5*[2*x-2*y]);

plot3d(schro, x= 1..100, y = -1 ..1);

Unfortunately, I am unable to plot my function. I was able to substitute my psi(x,y) function into my schro equation, but I am unable to do much else. I want to plot my function such that my energy is represented in the z-axis as a relationship between x and y which are a specific coordinate system (conical coordintes). 

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...