Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

 

A simple (?)  int and too many levels of recursion

 

J := Int(cos(2*x)/(1+2*sin(3*x)^2), x = 0 .. Pi);

Int(cos(2*x)/(1+2*sin(3*x)^2), x = 0 .. Pi)

(1)

evalf[30](J);

-0.321451052376028387436461558651e-32

(2)

value(J);

Error, (in csgn) too many levels of recursion

 

 

 

The workaround I know (for J = 0) it is not very simple.
Can you find an easy one?

 

 

Download int-too-many-levels-of-recursion.mw

Hello again, I posted a thread here earlier and received some great responses. I've made some progress in Maple since then but once again I've ended up on a question where I am completely stuck. I am only meant to solve this one in maple as the answer is written below the question. The question is:

https://imgur.com/rhFNh2l

I realise this is alot to ask for but I'm studying from afar and I don't have as many options for help as other students at the moment. I have managed to solve a), and I know how to solve b) the traditional way (pen and paper), but I have no idea how to do it in maple. My solution for a) is attached below. c) and d) strictly rely on the answer from b) so I'd greatly appreciate if I could have some help with it so I atleast could attempt the others on my own. This is the final question I have so once I'm done with this I'll pretty much be a master Maple... or not.. :P

I have commented the maple document so it is easier to understand what I've done and what I want help with. Also, I very much apologise if something that I write don't make sense, English is not my native language.

 


 

 

Hello, I just started working in Maple and I am struggling with a question that I found in my book. The question goes as follows:

Consider the set of vectors T = {v1, v2, v3​​​​, v4} in ℝwith

v= (2,5,-2,0), v2 = (-2,-4,b,4), v3 = (-1,2,-2,-5), v= (b,2,5,3)

Find all values of b, such that T is a linearly independent set

I am supposed to first solve it by hand and then in maple. I can solve it by hand but I have no clue how to do it in maple.The only thing I've done so far is create a matrix that contains the vectors in the set S as column entries.

I know that the columns of A are linearly independent if  det A ≠ 0. This is where my near non-existent knowledge in Maple stops me...

The answer is for all {2}

I appreciate any tips...

 

 

Hi maple users

I'm about to do an assignment on the Joukowski transformation, where I have modelled and airfoil resembling the NACA-64015 airfoil. The parameters of the circle in z-plane are as follows: r=1.1241, x=-0.1241, y=0.0, where r is the radius of the circle, and x and y is the parameters used to offset the center of the circle. The problem is that I can't seem to plot the airfoil with contuours showing the fluid flow. I would therefore like to know if any of you guys has solved this before? Any help is much appreciated.

Yesterday, I accidentally discovered a nasty bug in a fairly simple example:

restart;
Expr:=a*sin(x)+b*cos(x);
maximize(Expr, x=0..2*Pi);
minimize(Expr, x=0..2*Pi);
                                    

I am sure the correct answers are  sqrt(a^2+b^2)  and  -sqrt(a^2+b^2)  for any real values  a  and  b .  It is easy to prove in many ways. The simplest method does not require any calculations and can be done in the mind. We will consider  Expr  as the scalar product (or the dot product) of two vectors  <a, b>  and  <sin(x), cos(x)>, one of which is a unit vector. Then it is obvious that the maximum of this scalar product is reached if the vectors are codirectional and equals to the length of the first vector, that is, sqrt(a^2+b^2).

Bugs in these commands were noted by users and earlier (see search by keywords bug, maximize, minimize) but unfortunately are still not fixed. 

How I can extract data about figure as matrix format.

I want to save data from figure as matrix for each curve in figure as i.e.,  x and y .

for example as this format.

fig10.mw

sol := Vector[column](4, [` 1001 x 4 `*Matrix, `Data Type: `*anything, `Storage: `*rectangular, `Order: `*Fortran_order])

 

Is it possible to export data from Maple to Excel where data are generated by Maple using Optimization:-LSSolve or DirectSearch:-SolveEquations function?

I have attached a file, where n is the primary variable. For n=1, 2, 3, .......... 20, I have got solution individually. But it is more time consuming event. Is it possible to use array or a vector for the variable n and solve equations at a time for all value of n and stored a excel file?
Any advice for me? @Preben Alsholm , @tomleslie or anybody
system_equations_(10.12.2008).mw
 

Hello,

I cannot find a solution for multiplying matrices containing vectors. I seems that matrix operations are not overloaded for accepting vectors. Here is a minimum example :

restart;
with(LinearAlgebra);
with(VectorCalculus);
A := Matrix([u, v]);
B := Transpose(A) . A;

# Entries of A are in fact vectors
u := `<,>`(u1, u2);
v := `<,>`(v1, v2);

# Here are the expected entries of matrix B

u . u;
v . v;
u . v;

# but entries cannot be calculated
simplify(B);

B := Transpose(A) . A;

Of course I can obtain the result if I construct the matrix A with the components of u and v but  my goal is to manipulate more concise expressions with vectors rather than components. May I find a solution in some other package ?

Would it be a complicated task to develop the missing operators or tell Maple to use the dot operator (for matrices and vector) when performing matrix multiplication ?

Thanks for your insights.

Hi, everytimes I enter anythings, it turn out with Typesetting:-mparsed( bla1bla2, bla1bla2;"_noterminate")

example:

Dear authors,
How to solve this ode problem.

Download link ode.mw

In this problem the boundary condition is

Note: F=g in our problem.

eta approaches N.

Thank you.

 

Hi, I'm investigating an equation of motion, and I'm attempting to plot t against different values of thetabn. I have acquired a list of my data points (in the real domain) of the form [thetabn1, t1], [thetabn2, t2] ... etc. But I am struggling to figure out how to plot it. Using dataplot gives me a graph but it is incorrect. I would like a scatterplot, ideally once I have refined my range of thetabn I would like to be able to join it up with a line to create a nice looking plot. Also any improvements to my method would be appreciated. v[i], thetavn and omegac are set variables and s[n] is my function which I am setting equal to zero, and solving for t.

 

with(RealDomain);
v[i] := 145000;
thetavn := (1/6)*Pi;
omegac := .1;
s[n] := v[i]*cos(thetavn)*(cos(2*thetabn)*tan(thetabn)+sin(2*thetabn)*sin(omegac*t)/omegac);
for thetabn from evalf((1/100)*Pi) by evalf((1/100)*Pi) to evalf(Pi) do assign('result', [op(result), [thetabn, solve(v[i]*cos(thetavn)*(cos(2*thetabn)*tan(thetabn)+sin(2*thetabn)*sin(omegac*t)/omegac) = 0, t)]]) end do;
dataplot(result);

 

hello everyone,

I am trying to optimize expressions symbolically. I need to find out the maximum value possible for an variable, so that the expressoin still have a valid solution.

For Example:

expr:=a-b/b-a^3;  # a=(0,10), b=(0,10)

In this eypression b=a^3 is the only case where undefined solution is possible, for a given interval of variables

This looks fine for simple expression. But in reality there are complex equations to solve with more than 2 varibles.

1) first thing is to find out all values of a variable resulting in undeifined output(or infinite)
2) assign a symbolic value(variable < or > some value) to the variable so that the undefined result can be eliminated.

 I need to optimize the given expression so that it does not have any undefined cases when solving. I understood that when optimizing, there always be a condition on variables(in this case variable max is the condition, maximum value the variable can take). output of an expression is always a real value

OptimizedExpr:=a-b[max]/b[max]-a^3 --> b[max]>a^3 or b[max]<a^3

(it is easy to to say b[max] is not equal to a^3 , also a^3 is the limiting value. In some case it is more resonable to just ignore other part of limiting value. Hence, I would like to optimize using greaterthan or lessthan of limiting value).

I would be very glad to know how I can find Optimized expressions. I tried using the solve function but observed that expressions are equalled to zero and solving. which is completely opposite to what I was looking. I really do not know is there any way to find out undefined cases in expressions and on what varibale at what values.

I tried to explain the situation at my best and I welcome for any suggested edits or furthur information required.

 

Thank you

how I can determied  this integral in figure below or compute area in figure which adressed in the following website?

https://en.m.wikipedia.org/wiki/Spherical_cap

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