Download open_series_and_take_derivative.mw

restart;
_local(D, O);
with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [a, 0, 0];
C := [a, b, 0];
D := [0, b, 0];
S := [0, 0, h];
O := [x, y, z];
lineSC := Line(S, C);
lineSD := Line(S, D);
H := Projection(A, lineSC);
K := Projection(A, lineSD);
OH := H - O;
OK := K - O;
OC := C - O;
M := Matrix([OH, OK, OC]);
O := eval(O, %);
simplify(Distance(O, H));
                               O

Error, invalid input: eval received Matrix(3, 3, {(1, 1) = -x+h^2*a/(a^2+b^2+h^2), (1, 2) = -y+h^2*b/(a^2+b^2+h^2), (1, 3) = -z+h*(a^2+b^2)/(a^2+b^2+h^2), (2, 1) = -x, (2, 2) = -y+h^2*b/(b^2+h^2), (2, 3) = -z+h*b^2/(b^2+h^2), (3, 1) = -x+a, (3, 2) = -y+b, (3, 3) = -z}), which is not valid for its 2nd argument, eqns
How to correct this error ? Thank you.

if there is any other way for graph please share with me

Download complexplot3d.mw

restart;
with(Plot);
params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7};
xi := beta[3]*(2*alpha*k*t + x)*sqrt(1/(36*alpha*beta[4] + 36*gamma*beta[4]));
params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7}

          xi := beta[3] (2 alpha k t + x) 

                                                 (1/2)
            /                 1                 \     
            |-----------------------------------|     
            \36 alpha beta[4] + 36 gamma beta[4]/     


sol1n := u(x, t) = U(xi)*exp((-sqrt(1/(36*alpha*beta[4] + 36*gamma*beta[4]))*x + w*t + theta)*I);
                     /                          
                     |                          
 sol1n := u(x, t) = U|beta[3] (2 alpha k t + x) 
                     \                          

                                        (1/2)\    /  /
   /                 1                 \     |    |  |
   |-----------------------------------|     | exp|I |
   \36 alpha beta[4] + 36 gamma beta[4]/     /    \  \
                                       (1/2)                \\
  /                 1                 \                     ||
 -|-----------------------------------|      x + w t + theta||
  \36 alpha beta[4] + 36 gamma beta[4]/                     //



plot3d(rhs(sol1n), x = 0 .. 250, t = 0 .. 4);

how plot the the solution of PDE of this kind of function?

Download plot.mw

before run file remove all (:) i want calculate equation but with a condition for example: when a=4 then find other parameter in my equation with respect to a=4 find other

usesol.mw

when i finding parameter i want just choose a case for example a_1=a_1  and any other case a_2=0,and remove other case how i can do in maple

Download choose_case.mw

i am looking for simplify this type of simplifying assume beta is Real and there is any stuf package for working with complex and conjugate automaticaly

Download simplify.mw

Hi
i write my code for calculate this type of function but the result is so different from mine i  will post here i hope someone tell me where is problem

i have this

i want this

Download EX1.mw

Hi
i did calculation part by part of adomian laplace method but if we can make a loop for it is gonna be so great and take back a lot of time

for get definition use this pdf for fractional derivation

[Copyrighted material removed by moderator - see https://doi.org/10.4236/am.2018.94032]

Download solving_example_1.mw

Hi

i use other code for equation too when i use allvalues(Root(...)) it is more near but question is this why not satisfy the ode equation this is my equation this parameter are find for this ODe why not satisfy otherwise my equestions must be wrong!

same_equation_different_parameter.mw

display([plottools[arc]([op(coordinates(Omega))], r, t .. t + Pi/2, color = red, t4), plottools[arc]([op(coordinates(Omega))], r, t + Pi .. t + (3*Pi)/2, color = coral, t4), plottools[arc]([op(coordinates(Omega))], r, t - Pi/2 .. t, color = cyan, t4), plottools[arc]([op(coordinates(Omega))], r, t + Pi/2 .. t + Pi, color = green, t4)],
draw([Cir(color = blue, t4), cir(color = grey, t4), sT(color = black, t4), XXp(color = black, l3), YYp(color = black, l3), L1(color = black, l3), L2(color = black, l3), N1(color = blue, symbol = solidcircle, symbolsize = 15), N2(color = blue, symbol = solidcircle, symbolsize = 15), N3(color = blue, symbol = solidcircle, symbolsize = 15), M1(color = blue, symbol = solidcircle, symbolsize = 15)]), axes = none, view = [-30 .. 10, -10 .. 10], size = [800, 800])::
plots:-animate(Proc, [t], t = 0 .. 2*Pi, frames = 30).;

why the instruction concerning the arcs is not resected ? Thank you.

Download pde-solve.mw

restart;
Proc := proc(t) local t4, l3, R, r, eq, sol; _EnvHorizontalName := 'x'; _EnvVerticalName := 'y'; t4 := thickness = 4; l3 := linestyle = dot; R := 9; r := 1/2*R; geometry:-point(OO, 0, 0); geometry:-circle(Cir, [OO, R]); geometry:-point(K, R*cos(t), R*sin(t)); geometry:-point(Omega, r*cos(t), r*sin(t)); geometry:-circle(cir, [Omega, r]); eq := geometry:-Equation(cir); geometry:-line(XXp, y = 0); geometry:-line(YYp, x = 0); geometry:-line(L1, y = x); geometry:-line(L2, y = -x); geometry:-projection(M1, K, XXp); geometry:-coordinates(M1); geometry:-point(K2, geometry:-coordinates(M1)[1] - 2*R, 0); geometry:-coordinates(K2); geometry:-segment(sT, K2, M1); geometry:-point(N1, 0, R*sin(t)); subs(y = x, eq); sol := solve(%, x); geometry:-point(N2, sol[2], sol[2]); subs(y = -x, eq); sol := solve(%, x); geometry:-point(N3, sol[2], -sol[2]); plots:-display(geometry:-draw([Cir(color = blue, t4), cir(color = grey, t4), sT(color = black, t4), XXp(color = black, l3), YYp(color = black, l3), L1(color = black, l3), L2(color = black, l3), N1(color = blue, symbol = solidcircle, symbolsize = 15), N2(color = blue, symbol = solidcircle, symbolsize = 15), N3(color = blue, symbol = solidcircle, symbolsize = 15), M1(color = blue, symbol = solidcircle, symbolsize = 15)]), axes = none, view = [-30 .. 10, -10 .. 10], size = [800, 800]); end proc;
plots:-animate(Proc, [t], t = 0 .. 2*Pi, frames = 200);
NULL;
I am trying to program  this drawing, how to improve this code ? Thank you.

restart;
with(plots);
with(geometry);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
xA := 5;
yA := 0;
point(A, xA, yA);
xB := 5;
yB := -7;
point(B, xB, yB);
midpoint(C, A, B);
segment(sg1, A, B);
xP := -12;
yP := 0;
point(P, xP, yP);
PerpenBisector(L, C, P);
line(YYp, y = yB);
line(XXp, y = 0);
intersection(M, L, YYp);
line(PM, [P, M]);
projection(H, C, PM);
triangle(CMP, [C, M, P]);
triangle(ABH, [A, B, H]);
distance(B, H);
circle(cir, [B, 7]);
display(textplot([[coordinates(A)[], "A"], [coordinates(B)[], "B "], [coordinates(C)[], "C"], [coordinates(M)[], "M"], [coordinates(H)[], "H"], [coordinates(P)[], "P"]], align = {"above", 'right'}),
draw([YYp(color = red), XXp(color = black), PM(color = green), L(color = green), sg1(color = black), cir(color = magenta), P(color = black, symbol = solidcircle, symbolsize = 10), M(color = black, symbol = solidcircle, symbolsize = 10), H(color = black, symbol = solidcircle, symbolsize = 10), A(color = blue, symbol = solidcircle, symbolsize = 10), B(color = blue, symbol = solidcircle, symbolsize = 10), CMP(color = blue, filled = true, transparency = 0.8), ABH(color = red, filled = true, transparency = 0.8), C(color = blue, symbol = solidcircle, symbolsize = 10)]),
axes = none, view = [-15 .. 14, -15 .. 3]);
I want to change this figure when xP varies from -12 to 12; Is it possible to use Explore or animate ? Thank you.

Sq := proc(n::integer)
local aS, oS, aC, oC, s, dr, pc, u;
aS := -i/n;
oS := sum(1/s, s = 1 .. n);
aC := 1/2*aS;
oC := oS - 1/2*1/((n + 1)*n);
point(S, aS, oS); point(C, aC, oC);
MakeSquare(K, [S, 'center' = C]);
u := (x, i) -> sum(exp(-x*k)/k, k = 1 .. i);
pc := plot(u(x, n), x = 0 .. 4, color = green);
dr := draw([K]);
display({dr, pc});
end ;Sq(1);
Error, (in geometry:-draw) non-numeric coordinate encountered, cannot determine plot view
How to correct this procedure ?