## Routine Simplification Error...

Doing a routine simplification but got an error...Dont know where the mistake comes from.

simplification_error.mw

## How do I discretise the 4th order PDE?...

Dear All.

Please kindly help to correct the attached code on discretization of fourth order PDE using method of line.
Thank you and kind regards.

 Discretization of parabolic equation with method of line Convert the BC to finite difference Convert the governing equation to finite difference form

## How to prevent debug values displaying in the work...

When executing DEBUG within inline code (not within a procedure) the values displayed in successive debug windows (on clicking continue) are added to the end of my worksheet. How can the latter display be prevented?

## How do I differentiate this in Maple?...

Dear Experts,

Please how do I carry out the differentiation of

`y[1](t)*y[2](t)*(y[1](t)+y[2](t))^3`

with respect to y[1] using maple? I know how to use maple if the derivative is with respect to t.
Thank you in anticipation

## Boolean variable not working...

I don't understand why maple is ignoring my predicate in this worksheet

Maple Worksheet - Error

## Win10 high contrast mode...

I'm using Win10, maple 2016.

I'm using high contrast mode (dark mode, white on black). Maple looks broken, the text is black on black, and in the side panel, some of the buttons are shiney white.

How do I set maple to support high contrast?

## How to solve system of equation without Rootof...

solve({sigma*E-(mu+alpha+gamma)*I = 0, gamma*E+Lambda*N*P-(mu+alpha)*R = 0, Beta__1*S*E+Beta__2*S*I/(I*M+1)-(mu+sigma)*E = 0, Lambda(1-p)*N-mu*S-Beta__1*S*E-Beta__2*S*I/(I*M+1) = 0}, {E, I, R, S}, explicit)

## How can type limit as mathtype?...

How can type limit proc() and use print to export expression as mathtype?

 (1)

## Shade Area/Region Between Polar Curve...

with(plots);
P1 := plot([-sin(t), t, t = 0 .. 2*Pi], coords = polar, color = red);
P2 := plot([cos(t), t, t = 0 .. 2*Pi], coords = polar, color = blue);
display(P1, P2, scaling = constrained);

I have two polar equation in the same graph but how do i shade the region between those two polar curve?

## What could have happened to solve command?...

Good day house.

Please I don't know why the solve command does not display any results in the following code. Kindly assist. Thank you in anticipation.

```restart;
omega := v/h;
t := sum(a[j]*x^j, j = 0 .. 6)+a[7]*cos(omega*x)+a[8]*sin(omega*x);
r1 := diff(t, x\$2);
r2 := diff(t, x\$4);
c1 := eval(t, x = q+2*h) = y[n+2];
c2 := eval(r1, x = q) = f[n];
c3 := eval(r1, x = q+h) = f[n+1];
c4 := eval(r1, x = q+2*h) = f[n+2];
c5 := eval(r1, x = q+3*h) = f[n+3];
c6 := eval(r2, x = q) = g[n];
c7 := eval(r2, x = q+h) = g[n+1];
c8 := eval(r2, x = q+2*h) = g[n+2];
c9 := eval(r2, x = q+3*h) = g[n+3];
b1 := seq(a[i], i = 0 .. 8);
`k&Assign;solve`({c1, c2, c3, c4, c5, c6, c7, c8, c9}, {a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8]});
```

## Can someone help with the simplification of this c...

Please I found out that the MatrixInverse on the assignment statement P3 does not run for about three days now. Please kindly help to simplify the code. Thank you and kind regards.

```restart; omega := v/h;
r := a[0]+a[1]*x+a[2]*sinh(omega*x)+a[3]*cosh(omega*x)+a[4]*cos(omega*x)+a[5]*sin(omega*x);
b := diff(r, x);

c := eval(b, x = q) = f[n];
d := eval(r, x = q+3*h) = y[n+3]; e := eval(b, x = q+3*h) = f[n+3];
g := eval(b, x = q+2*h) = f[n+2];
i := eval(b, x = q+h) = f[n+1];
j := eval(b, x = q+4*h) = f[n+4];
k := solve({c, d, e, g, i, j}, {a[0], a[1], a[2], a[3], a[4], a[5]});
Warning,  computation interrupted
assign(k);
cf := r;
s4 := y[n+4] = simplify(eval(cf, x = q+4*h));
s3 := y[n+2] = simplify(eval(cf, x = q+2*h));
s2 := y[n+1] = simplify(eval(cf, x = q+h));
s1 := y[n] = simplify(eval(cf, x = q));

with(LinearAlgebra);
with(plots);
h := 1;
YN_1 := seq(y[n+k], k = 1 .. 4);
A1, a0 := GenerateMatrix([s1, s2, s3, s4], [YN_1]);
eval(A1);
YN := seq(y[n-k], k = 3 .. 0, -1);
A0, b1 := GenerateMatrix([s1, s2, s3, s4], [YN]);
eval(A0);
FN_1 := seq(f[n+k], k = 1 .. 4);
B1, b2 := GenerateMatrix([s1, s2, s3, s4], [FN_1]);
eval(B1);
FN := seq(f[n-k], k = 3 .. 0, -1);
B0, b3 := GenerateMatrix([s1, s2, s3, s4], [FN]);
eval(B0);
ScalarMultiply(R, A1)-A0;
det := Determinant(ScalarMultiply(R, A1)-A0);
P1 := A1-ScalarMultiply(B1, z);
P2 := combine(simplify(P1, size), trig);
P3 := MatrixInverse(P2);
P4 := A0-ScalarMultiply(B0, z);
P5 := MatrixMatrixMultiply(P3, P4);
P6 := Eigenvalues(P5);
f := P6[4];
T := unapply(f, z);
implicitplot(f, z = -5 .. 5, v = -5 .. 5, filled = true, grid = [5, 5], gridrefine = 8, labels = [z, v], coloring = [blue, white]);

```

## How to get the real and imaginary parts of complex...

Hi all,

How to get the real and imaginary parts of this complex expression.

real_imag_parts.mw

## How do I sort a formula in the following form...

Hello,

I want to sort the formulae to Psi and Beta, but I don't know how it works. I have tried it with sort, simplify, isolate, but that isn't what I'm searching.

It should looks like the simplier formula in the picture.

ab := (diff(Psii(t), t, t))*J-l[f]*(F[s, f, l]+F[s, f, r])+l[r]*(F[s, r, l]+F[s, r, r])-(1/2)*b[r]*(-F[s, r, l]*delta[l]+F[s, r, r]*delta[r]) = 0;
/ d  / d         \\
|--- |--- Psii(t)|| J - l[f] (F[s, f, l] + F[s, f, r])
\ dt \ dt        //

+ l[r] (F[s, r, l] + F[s, r, r])

1
- - b[r] (-F[s, r, l] delta[l] + F[s, r, r] delta[r]) = 0
2
bc := (diff(betaa(t), t, t))*m*v*betaa(t)+F[s, r, l]*delta[l]+F[s, r, r]*delta[r]-(diff(Psii(t), t)) = 0;
/ d  / d          \\
|--- |--- betaa(t)|| m v betaa(t) + F[s, r, l] delta[l]
\ dt \ dt         //

/ d         \
+ F[s, r, r] delta[r] - |--- Psii(t)| = 0
\ dt        /
cd := (diff(betaa(t), t))*m*v+F[s, r, l]+F[s, r, r]+F[s, f, l]+F[s, f, r]-(diff(Psii(t), t)) = 0;
/ d          \
|--- betaa(t)| m v + F[s, r, l] + F[s, r, r] + F[s, f, l]
\ dt         /

/ d         \
+ F[s, f, r] - |--- Psii(t)| = 0
\ dt        /
F[s, f, l] := c[fl]*alpha[fl];
c[fl] alpha[fl]
F[s, f, r] := c[fr]*alpha[fr];
c[fr] alpha[fr]
F[s, r, l] := c[rl]*alpha[rl];
c[rl] alpha[rl]
F[s, r, r] := c[rr]*alpha[rr];
c[rr] alpha[rr]
alpha[fl] := (-v*betaa-l[f]*(diff(Psii(t), t)))/(-v+(1/2)*b[f]*(diff(Psii(t), t)));
/ d         \
-v betaa - l[f] |--- Psii(t)|
\ dt        /
-----------------------------
1      / d         \
-v + - b[f] |--- Psii(t)|
2      \ dt        /
alpha[fr] := (-v*betaa-l[f]*(diff(Psii(t), t)))/(v-(1/2)*b[f]*(diff(Psii(t), t)));
/ d         \
-v betaa - l[f] |--- Psii(t)|
\ dt        /
-----------------------------
1      / d         \
v - - b[f] |--- Psii(t)|
2      \ dt        /
alpha[rl] := delta[l]+(-v*betaa+l[r]*(diff(Psii(t), t)))/(-v+(1/2)*b[r]*(diff(Psii(t), t)));
/ d         \
-v betaa + l[r] |--- Psii(t)|
\ dt        /
delta[l] + -----------------------------
1      / d         \
-v + - b[r] |--- Psii(t)|
2      \ dt        /
alpha[rr] := delta[r]+(-v*betaa+l[r]*(diff(Psii(t), t)))/(-v-(1/2)*b[r]*(diff(Psii(t), t)));
/ d         \
-v betaa + l[r] |--- Psii(t)|
\ dt        /
delta[r] + -----------------------------
1      / d         \
-v - - b[r] |--- Psii(t)|
2      \ dt        /

ab;
/
|
/ d  / d         \\          |
|--- |--- Psii(t)|| J - l[f] |
\ dt \ dt        //          |
|
\

/                / d         \\
c[fl] |-v betaa - l[f] |--- Psii(t)||
\                \ dt        //
-------------------------------------
1      / d         \
-v + - b[f] |--- Psii(t)|
2      \ dt        /

/                / d         \\\        /      /
c[fr] |-v betaa - l[f] |--- Psii(t)|||        |      |
\                \ dt        //|        |      |
+ -------------------------------------| + l[r] |c[rl] |delta[
1      / d         \       |        |      |
v - - b[f] |--- Psii(t)|       |        |      |
2      \ dt        /       /        \      \

/ d         \\
-v betaa + l[r] |--- Psii(t)||
\ dt        /|
l] + -----------------------------|
1      / d         \  |
-v + - b[r] |--- Psii(t)|  |
2      \ dt        /  /

/                           / d         \\\          /
|           -v betaa + l[r] |--- Psii(t)|||          |
|                           \ dt        /||   1      |
+ c[rr] |delta[r] + -----------------------------|| - - b[r] |
|                  1      / d         \  ||   2      |
|             -v - - b[r] |--- Psii(t)|  ||          |
\                  2      \ dt        /  //          \
/                           / d         \\
|           -v betaa + l[r] |--- Psii(t)||
|                           \ dt        /|
-c[rl] |delta[l] + -----------------------------| delta[l]
|                  1      / d         \  |
|             -v + - b[r] |--- Psii(t)|  |
\                  2      \ dt        /  /

/                           / d         \\         \
|           -v betaa + l[r] |--- Psii(t)||         |
|                           \ dt        /|         |
+ c[rr] |delta[r] + -----------------------------| delta[r]| =
|                  1      / d         \  |         |
|             -v - - b[r] |--- Psii(t)|  |         |
\                  2      \ dt        /  /         /

0
bc;
/ d  / d          \\
|--- |--- betaa(t)|| m v betaa(t)
\ dt \ dt         //

/                           / d         \\
|           -v betaa + l[r] |--- Psii(t)||
|                           \ dt        /|
+ c[rl] |delta[l] + -----------------------------| delta[l]
|                  1      / d         \  |
|             -v + - b[r] |--- Psii(t)|  |
\                  2      \ dt        /  /

/                           / d         \\
|           -v betaa + l[r] |--- Psii(t)||
|                           \ dt        /|
+ c[rr] |delta[r] + -----------------------------| delta[r]
|                  1      / d         \  |
|             -v - - b[r] |--- Psii(t)|  |
\                  2      \ dt        /  /

/ d         \
- |--- Psii(t)| = 0
\ dt        /
cd;
/ d          \
|--- betaa(t)| m v
\ dt         /

/                           / d         \\
|           -v betaa + l[r] |--- Psii(t)||
|                           \ dt        /|
+ c[rl] |delta[l] + -----------------------------|
|                  1      / d         \  |
|             -v + - b[r] |--- Psii(t)|  |
\                  2      \ dt        /  /

/                           / d         \\
|           -v betaa + l[r] |--- Psii(t)||
|                           \ dt        /|
+ c[rr] |delta[r] + -----------------------------|
|                  1      / d         \  |
|             -v - - b[r] |--- Psii(t)|  |
\                  2      \ dt        /  /

/                / d         \\
c[fl] |-v betaa - l[f] |--- Psii(t)||
\                \ dt        //
+ -------------------------------------
1      / d         \
-v + - b[f] |--- Psii(t)|
2      \ dt        /

/                / d         \\
c[fr] |-v betaa - l[f] |--- Psii(t)||
\                \ dt        //   / d         \
+ ------------------------------------- - |--- Psii(t)| = 0
1      / d         \          \ dt        /
v - - b[f] |--- Psii(t)|
2      \ dt        /

## How can the center of this sphere be determined?...

The sphere with radius 0.5 whose center has y coordinate = 0.5 and z coordinate = 0.5 is tangent internally to the ellipsoid centered on the origin with principal semi axes of 5, 3 and 2.

How can the x coordinate of the sphere's center be determined?