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These are answers submitted by Markiyan Hirnyk

How about this?

with(OrthogonalExpansions):FourierSeries(ln(cos(x)), x = -(1/2)*Pi .. (1/2)*Pi, 14, 'Coefficients');

Because Maple does not find the integral

int(ln(cos(x))*cos(2*i*x), x = -(1/2)*Pi .. (1/2)*Pi) assuming i::posint ,

the number 14 cannot be replaced by infinity (but it can be replaced by 1400 e. g.). One can easily deduce the general formula.

This can be done by the textplot3d command.

with(plots): with(plottools):textplot3d([1, 2, 3, u[i, j]^k], axes = frame);

It is known that the geometry and geom3d packages have problems with creating indexed objects. However, this can be done as follows.

If you want two subscripts and one superscript, then (-1,-1,1) tensor should be created instead of Array.

But I find it to be art for the art's sake because the points in R^3 are not coordinates of any tensor of type (-1,-1,1) by their nature.

Download indexed_points.mw

Look at http://www.mapleprimes.com/questions/120636-Give-Me-The-Index-In-A-List-or-Vector .

This link can be found by the "index" search in MaplePrimes at the top of this page.

A simple general solution is obtained in the case b=0:

restart; sys := {diff(A(x, t), t) = exp(-2*x*b)*(Y(x, t)-A(x, t)), diff(Y(x, t), `$`(x, 2)) = exp(-2*x*b)*(A(x, t)-Y(x, t))};ibc := {A(x, 0) = 0, Y(0, t) = .1, (D[1](Y))(0, t) = 0};sol := pdsolve(eval(sys, b = 0));

PS.

pdetest(sol,eval( sys),b=0);

{0}

Download case_b=0.mw

Here is the corrected code which works. The plot looks like a straight line.

Download corrected_code.mw

Here are the results of googling "Schwarzschild metric with Maple ".

plot(eval(int(1/sqrt(a*x^3+1), x), [x = X, a = 1/10])-(eval(int(1/sqrt(a*x^3+1), x), [x = 0, a = 1/10])), X = 0 .. 1);

Here is an example for your code. This is done as follows.

1, A matrix of the coordinates of the plot points is formed by getdata command .

2. The equation of the form A*cos(omega1*x+phi1)*sin(omega2*x) is fitted to correspond these coordinates by the FitData command of the DirectSearch package.

Download DataFit.mw

Your w is piecewise concerning y=(x-a)/t in fact. Making use of that, we obtain

Download piecewise.mw

Without loss of generality we may assume h=1. Putting n=4, we obtain

Putting n=5, we obtain

In view of the above, we define

test1.mw

Download nonzero.mw

Edit. The last three commands.

F := -(int(del_u0(x)*(diff(N_xx(x), x)), x = 0 .. L))+del_u0(L)*N_xx(L)-del_u0(0)*N_xx(0)+ibp2+ibp3:

select(has, F, int);

As far as I remember it, a similar question was asked and answered. I can't find a reference in short time.

See http://www.mapleprimes.com/questions/142211-Correct-Upto-7-Decimal-Figurs-not-Significant-Digits

Don't hesitate to ask for further explanation in need.

PS. This link can be found by the "digits" search in MaplePrimes at the top of this page.

I recommend http://www.maplesoft.com/support/help/Maple/view.aspx?path=UserManual/Contents and

http://www.maplesoft.com/support/help/Maple/view.aspx?path=ProgrammingGuide/Contents

Papers on Maple are outdated because a new version of Maple is presented every year.

This can be done as follows.

restart;w123 := convert(c1*r*Heaviside(r-a), piecewise, r)+c2*r;simplify(combine(int(r*(int((diff(w123, r))^2/r, r)), r)), size) assuming 0< r <lambda and a<lambda and 0<a and 0<lambda

simplification.mw

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