Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hi 

I need yours help to solve the given integral 
 

restart

A = 3*(q-1)^(-1/(1+r))*GAMMA(q-3/(2+2*r))*GAMMA(3/(2+2*r))/(GAMMA(5/(2+2*r))*GAMMA(q-5/(2+2*r)));

g := int(`ε`*(1+(`ε`/(A*t))^(1+r)/(q-1))^(-q)*c*exp(-`ε`/a), `ε` = 0 .. infinity);

``

NULL

NULL

q,c,a and r are parameters.
Γ is a gamma function.

Download Karim.mw
 

 

 

I am trying to draw a tetrahedron and square based pyramid, having its triangular faces the same asthat of the tetrahedron.  While the geom3d package in Maple 7 has several polyhedra, a pyramid, or pentahedron(?) seem to be missing.  The closest is the octohedron - but this is two square pyramids "glued" together!   I'm totally bamboozled by the Polyhedron command with all its options.  Is it possible to somehow cut the octohedron in two, to get a pyramid?  Below is my Maple program, including at the end aplottools command to draw a separate ocotohedron.  

  Any help gratefully received.

     David

restart:
> #Puzzle Problem with tetrahedron and pyramid.  How many faces will
> #resultant polyhedron have when a triangular face of the pyramid is "glued" to  the tetrahedron.
> with(geom3d):

> print(`A pyramid and tetrahedron are shown: the triangular faces of each being the same dimensions. The`);
> print(`triangular face of the pyramid is attached to a triangular face of the tetrahedron.`);

> print(`How many faces does the resulting polyhedron have?`);
> print(`  a.) 5    b.) 6     c.) 7     d.) 8     e.) 9`);

> # octahedron, hexahedron, cube, icosahedron, dodecahedron - but pentahedron not supported in Maple 7 :-(
> RegularPolyhedron(d,[3,4],point(o,4,4,0),3):
> #dodecahedron(t,point(p,5,0,0),3):

> tetrahedron(t,point(p,5,0,0),3):
> #draw([d(color=red),t(color=green)],cutout=7/8,lightmodel=light4,
> draw([d(color=red),t(color=green)],title=`Tetrahedron & pyramid`,orientation=[45,45]);
> with(plottools):
> f := octahedron([0,0,0],1):  #, octahedron([1,1,1],0.5):
> plots[display](f,style=patch);

Dear Team, I have used RKF45 to solve my ODE with Maple. now I am required to solve same ODE using RK4 for comparison of solution. Ps help me with an example. Pls find my Parameters, intial values and ODE below:


 

``

ODE*equations

ODE*equations

(1)

diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t)

diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)

diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t)

NULL

diff(r(t), t) = eta*i(t)+v(t)*f*theta[2]-(a+epsilon)*r(t)

``

``

My*parameters

My*parameters

(2)

v(0) := .4

.4

(3)

NULL

s(0) := 0.6e-1

0.6e-1

(4)

e[0] := .24

.24

(5)

i[0] := .17

.17

(6)

r[0] := .13

.13

(7)

c := 0.4e-1

0.4e-1

(8)

f := .4

.4

(9)

beta := .2

.2

(10)

epsilon := .8

.8

(11)

theta[1] := .1

.1

(12)

theta[2] := .3

.3

(13)

alpha := .9

.9

(14)

rho := .7

.7

(15)

eta := .99

.99

(16)

delta := .3

.3

(17)

a := 0.4e-1

0.4e-1

(18)

phi := 1

``

``

``


 

Download ODE_EQNS.mw

How can I solve this non-linear ODE exactly or approximately in some series solution?

Non_linear_ode.mw

I'm a new Maple user so there may be a better way to do this, but Maple is not handling units the way I would expect.

Here is an example document (inline graphical below, also here: Plots_With_Units.mw) showing the impedance of a parallel resistor, inductor, and capacitor.  The plot is correct and it shows kHz along the abscissa like I want.  In order to get this I used kHz in the range fr, which is fine, but I had to also use kHz in the basic definition functions for Zl and Zc.

Now in order to get correct results from any of the Z functions I must use them with a kHz argument for f.  If I want to use them where other unit multipliers are more appropriate they won't work right, and many times I don't know what the appropriate multiplier should be until I'm into the design.  Then I need to go back and change the multipliers in the functions.  Or maybe in a single design I'll want to show Hz and kHz for the same function.

This seems like confusing units and dimensions.  The dimensions of inductive impedance (Zl), for example, can be expressed as frequency times inductance.  Whether the frequency is in units of Hz, kHz, or uHz doesn't matter and should simply scale the results.  I should be able to specify functions in dimensions and use units elsewhere as I want for convenient plotting and result formatting.

Is there a better way to do this, or is it a limitation in Maple?  The overall goal is to define functions with units but be able to use them and to format plots in whatever other units I like.

Hi,

I am trying to solve a 2nd order ODE. But I get the Error:

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

I have uploaded the worksheet. Can anybody please help me?

I am teaching a course in biofluid mechanics and am looking to help the students get more use out of Maple. Often it is advantageous to scale a differential equation (and initial conditions) using dimensionless variables to reduce the number of free parameters in a problem. For example, the simple linear oscillator differential equation:

Eq(1)         m*d2x(t)/dt2 + k*x(t)=0

where k and m are parameters.  If we define a dimensionless time, s=t/T, and a dimensionless position, X=x/L, where T and L are constants, , Eq(1) becomes

Eq(2)         (mL/T2 ) *d2X(s)/ds2 +  kL*X(s)=0

Then choosing T=sqrt(m/k) we arrive at

Eq(3)         d2X(s)/ds2 +  X(s)=0

which has no parameters.  Can this sequence be done in Maple for a differential equation...i.e. change of variables?

Thanks

 

I recently moved to a new research institute and have to make a decision on either buy a licence for Maple or Mathematica. My needs are PDE hyperbolic system (e.g. shallow water, tsunami...) resolution and when possible export to standalone C/Fortran code based on package like MathPDE.

I know a little of Mathematica, but have a bunch of notebooks. I tried with the help of MapleSoft support to import them into Maple with no success so far.

So as I'm not tied to any of both, I have the impression that I would be more comfy with Mma but Maple is cheaper and seems more open. Is there any rationals for picking one over the other?


I have a difficult problem by NLPSolve & mnimize (optimization)

How do I solve the erroe"unexpected parameters" in Maple?

The code is uploade under the line.
Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/example1.mw .

Download example1.mw

Irrational numbers: numbers that cannot be represented as a ratio of integers. The decimal form of a rational number is non-repeating and non-terminating.

Change to:

Irrational numbers: numbers that cannot be represented as a ratio of integers. The decimal form of an irrational number is non-repeating and non-terminating. 

or change to

Irrational numbers can be represented by decimal fractions in which the digits go on forever without ever repeating a pattern.  See Downing, Douglas. Dictionary of Mathematics Terms. 2nd ed. Hauppauge, NY: Barron's Ed. Series, Inc., 1995, p. 176).

For most expressions e, op(0,e) gives the type, e.g. this works if e is of type string, list, set, Array, Vector, Matrix, '+', etc. This is not the case for procedure calls and indexed expressions, but these differences make sense. However, there are other puzzling differences, at least in Maple 2017.2, for which I can see no rationale.

Specifically, if e is a numeric type such as integer, float, or fraction, complex, then op(0,e) returns the capitalized version of the type, e.g. Integer. Note also that type(e,Integer) will generate an error message saying that type 'Integer' does not exist.

A Google search shows that in an old programming guide for Maple (Release V, p.135; copyright 1998), op(0,x) is "integer" if x is an integer, whereas in a more recent programming guide (the 2009 introductory one, p.53), it is capitalized, consistent with the behaviour in Maple 2017.

I do not understand why this change was made. Can anybody shed light on the situation?

The Joint Mathematics Meetings are taking place this week (January 10 – 13) in San Diego, California, U.S.A. This will be the 101th annual winter meeting of the Mathematical Association of America (MAA) and the 124nd annual meeting of the American Mathematical Society (AMS).

Maplesoft will be exhibiting at booth #505 as well as in the networking area. Please stop by our booth or the networking area to chat with me and other members of the Maplesoft team, as well as to pick up some free Maplesoft swag or win some prizes.

There are also several interesting Maple-related talks and events happening this week - I would definitely not miss the talk by our own Paulina Chin on grading sketch graphs.

 

Using Symbol-Crunching to find ALL Sucker's Bets (with given deck sizes). 

AMS Special Session on Applied and Computational Combinatorics, II 
Wednesday January 10, 2018, 2:15 p.m.-2:45 p.m.

Shalosh B. Ekhad, Rutgers University, New Brunswick 
Doron Zeilberger*, Rutgers University, New Brunswick 
 

Collaborative Research: Maplets for Calculus. 

MAA Poster Session: Projects Supported by the NSF Division of Undergraduate Education 
Thursday January 11, 2018, 2:00 p.m.-4:00 p.m.

Philip B. Yasskin*, Texas A&M University 
Douglas B. Meade, University of South Carolina 
Matthew Barry, Texas A&M Engineering Extension Service 
Andrew Crenwelge, Texas A&M University 
Joseph Martinson, Texas A&M University 
Matthew Weihing, Texas A&M University

 

Automated Grading of Sketched Graphs in Introductory Calculus Courses. 

AMS Special Session on Visualization in Mathematics: Perspectives of Mathematicians and Mathematics Educators, I 

Friday January 12, 2018, 9:00 a.m.

Dr. Paulina Chin*, Maplesoft 

 

Semantic Preserving Bijective Mappings of Mathematical Expressions between LaTeX and Computer Algebra Systems.

AMS Special Session on Mathematical Information in the Digital Age of Science, III 
Friday January 12, 2018, 9:00 a.m.-9:20 a.m.

Howard S. Cohl*, NIST 

 

Interactive Animations in MYMathApps Calculus. 

MAA General Contributed Paper Session on Mathematics and Technology 
Saturday January 13, 2018, 11:30 a.m.-11:40 a.m.

Philip B. Yasskin*, Texas A&M University 
Andrew Crenwelge, Texas A&M University 
Joseph Martinsen, Texas A&M University 
Matthew Weihing, Texas A&M University 
Matthew Barry, Texas A&M Engineering Experiment Station 

 

Applying Maple Technology in Calculus Teaching To Create Artwork. 

MAA General Contributed Paper Session on Teaching and Learning Calculus, II 
Saturday January 13, 2018, 2:15 p.m.

Lina Wu*, Borough of Manhattan Community College-The City University of New York

 

If you are attending the Joint Math meetings this week and plan on presenting anything on Maple, please feel free to let me know and I'll update this list accordingly.


See you in San Diego!

Daniel

Maple Product Manager

hello

How I can remove these errors?

Thanks

erorr.mw
 

NULL

 

 

restart; eq31g := diff(u(t), `$`(t, 2))+u(t)+mu[s]*(diff(u(t), t))^3 = (1-mu[s])*(diff(u(t), t))*(diff(u(t), `$`(t, 2)))

diff(diff(u(t), t), t)+u(t)+mu[s]*(diff(u(t), t))^3 = (1-mu[s])*(diff(u(t), t))*(diff(diff(u(t), t), t))

(1.1)

 

 

 

eq33a:=subs(t=tau/omega,value(subs(u(t)=u(omega*t),eq31g)));

diff(diff(u(tau), tau/omega), tau/omega)+u(tau)+mu[s]*(diff(u(tau), tau/omega))^3 = (1-mu[s])*(diff(u(tau), tau/omega))*(diff(diff(u(tau), tau/omega), tau/omega))

(2.1)

omgRule:=omega=1+add(epsilon^i*omega[i],i=1..2);

omega = epsilon^2*omega[2]+epsilon*omega[1]+1

(2.2)

uExpRule:=u(tau)=add(epsilon^i*u[i](tau),i=1..3);

u(tau) = epsilon*u[1](tau)+epsilon^2*u[2](tau)+epsilon^3*u[3](tau)

(2.3)

temp:=subs(uExpRule,omgRule,convert(eq33a,diff));

Error, invalid input: diff received tau/omega, which is not valid for its 2nd argument

 

eq33b:=convert(series(lhs(temp),epsilon,4),polynom)=0;

Error, invalid input: lhs received temp, which is not valid for its 1st argument, expr

 

eqEps:=seq(coeff(lhs(eq33b),epsilon,i)=0,i=1..3);

Error, invalid input: lhs received eq33b, which is not valid for its 1st argument, expr

 

The general solution of the first-order equation, eqEps[1], can be expressed as

sol1:=dsolve({eqEps[1],u[1](0)=a,D(u[1])(0)=0},u[1](tau));

Error, (in dsolve) not a system with respect to the unknowns [u[1](tau)]

 

eq33c:=subs(u[1]=u[2],lhs(eqEps[1])=lhs(eqEps[1]))-subs(sol1,0=lhs(eqEps[2]));

Error, invalid input: lhs received eqEps[1], which is not valid for its 1st argument, expr

 

Expanding the right-hand side of eq33c in a Fourier series using trigonometric identities yields

eq33c_RHS:=combine(rhs(eq33c));

Error, invalid input: rhs received eq33c, which is not valid for its 1st argument, expr

 

Eliminating the terms,  and , demands that . Then, the particular solution of eq33c can be expressed as

sol2:=combine(subs(_C1=0,_C2=0,dsolve(subs(omega[1]=0,eq33c),u[2](tau))));

Error, (in dsolve) expecting an ODE or a set or list of ODEs. Received eq33c

 

Substituting sol1 and sol2 into the third-order equation, eqEps[3], and using the fact that , we obtain

eq33d:=subs(u[1]=u[3],lhs(eqEps[1])=lhs(eqEps[1]))-subs(sol1,sol2,omega[1]=0,0=lhs(eqEps[3]));

Error, invalid input: lhs received eqEps[1], which is not valid for its 1st argument, expr

 

Expanding the right-hand side of eq33d in a Fourier series using trigonometric identities, we have

eq33d_RHS:=combine(rhs(eq33d));

Error, invalid input: rhs received eq33d, which is not valid for its 1st argument, expr

 

Eliminating the terms that lead to secular terms from eq33d_RHS demands that

omg2Rule:=omega[2]=solve(coeff(eq33d_RHS,cos(beta+tau)),omega[2]);

omega[2] = omega[2]

(2.4)

As discussed above, for a second-order uniform expansion, we do not need to solve for . Combining the first- and second-order solutions, we obtain, to the second approximation, that

combine(subs(sol1,sol2,uExpRule));

Error, invalid input: subs received sol1, which is not valid for its 1st argument

 

where

tau=subs(omega[1]=0,omg2Rule,subs(omgRule,omega*t));

tau = (epsilon^2*omega[2]+1)*t

(2.5)

``


 

Download erorr.mw

 

How do I take the square root of :

    X:= r2 (R + r cos(v))2

with the condition that R and r are positive and R>r and get:

r (R+ r cos(v))

I assume I need to use simplify with some assumptions, but I cannot figure it out.  

browsing on math.stackexchange I came across this maple code:

asympt(int(sqrt(-k^2+1)*exp(I*k*x), k = -1 .. 1), x, 2)

that gave the correct answer:

https://math.stackexchange.com/questions/532394/how-to-analyze-the-asymptotic-behaviour-of-this-integral-function

so I wondered would it not be great if maple done asymptotic expansion of integrals in general.

say as an example Li(x).  Can maple expand Li(x) and how?

 

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