## 266 Reputation

19 years, 114 days

## Drawing on Joe Riel's...

Drawing on Joe Riel's solution (much clever than mine!), you could try the following (though I haven't tested it against Maple 9.5):
```> restart;
> A := Vector([4, 5, 3, 0, 8, 12]);
[ 4]
[  ]
[ 5]
[  ]
[ 3]
A := [  ]
[ 0]
[  ]
[ 8]
[  ]
[12]

> elim := [2, 3, 5];
elim := [2, 3, 5]

> A[subsop(op(map(proc (x) options opera\
> tor, arrow; x = NULL end proc, elim)), [seq(n, n = 1 .. op(1, A))])]
> ;
[ 4]
[  ]
[ 0]
[  ]
[12]

```
Note that if Maple 9.5 returns any error messages, it would be helpful that you post them on this forum. Hope this helps, -- Jean-Marc

## Drawing on Joe Riel's...

Drawing on Joe Riel's solution (much clever than mine!), you could try the following (though I haven't tested it against Maple 9.5):
```> restart;
> A := Vector([4, 5, 3, 0, 8, 12]);
[ 4]
[  ]
[ 5]
[  ]
[ 3]
A := [  ]
[ 0]
[  ]
[ 8]
[  ]
[12]

> elim := [2, 3, 5];
elim := [2, 3, 5]

> A[subsop(op(map(proc (x) options opera\
> tor, arrow; x = NULL end proc, elim)), [seq(n, n = 1 .. op(1, A))])]
> ;
[ 4]
[  ]
[ 0]
[  ]
[12]

```
Note that if Maple 9.5 returns any error messages, it would be helpful that you post them on this forum. Hope this helps, -- Jean-Marc

## It takes less than 3s (CPU time) to eval...

but the output is empty. ``` restart; Digits := 10; t := .335; r1 := .47066796; r2 := .791898; r3 := 1.12193314; r4 := 1.45162704; b1 := r1/r2; b2 := r2/r3; b3 := r3/r4; sys := diff(f1(x), x, x)-f1(x)+f2(x) = 0, diff(f2(x), x, x)-f2(x)+f3(x)+b1*(f1(x)-f2(x)) = 0, diff(f4(x), x, x)+b3*(f3(x)-f4(x)) = 0, diff(f3(x), x, x)-f3(x)+f4(x)+b2*(f2(x)-f3(x)) = 0; ics := f1(0) = 0, f2(0) = 0, f3(0) = 0, f4(0) = (r1+r2+r3+r4)/r4; kernelopts(version); st := time(); sol := dsolve([sys, ics]); time()-st; Maple 13.00, APPLE UNIVERSAL OSX, Apr 13 2009, Build ID 397624 2.658 ``` Regards, -- Jean-Marc

## It takes less than 3s (CPU time) to eval...

but the output is empty. ``` restart; Digits := 10; t := .335; r1 := .47066796; r2 := .791898; r3 := 1.12193314; r4 := 1.45162704; b1 := r1/r2; b2 := r2/r3; b3 := r3/r4; sys := diff(f1(x), x, x)-f1(x)+f2(x) = 0, diff(f2(x), x, x)-f2(x)+f3(x)+b1*(f1(x)-f2(x)) = 0, diff(f4(x), x, x)+b3*(f3(x)-f4(x)) = 0, diff(f3(x), x, x)-f3(x)+f4(x)+b2*(f2(x)-f3(x)) = 0; ics := f1(0) = 0, f2(0) = 0, f3(0) = 0, f4(0) = (r1+r2+r3+r4)/r4; kernelopts(version); st := time(); sol := dsolve([sys, ics]); time()-st; Maple 13.00, APPLE UNIVERSAL OSX, Apr 13 2009, Build ID 397624 2.658 ``` Regards, -- Jean-Marc

## You could use *seq* or write a two-line ...

as illustrated below:
```> restart;
> f := x^2-10-10*sin(x);

2
x  - 10 - 10 sin(x)

> g := cos(x);
cos(x)
> h := f-g;

2
x  - 10 - 10 sin(x) - cos(x)

> plot([f, g, h], x = -5 .. 5);

```
```> Student[Calculus1]:-Roots(h, x = -10 .. 10, numeric);

[-4.367042332, -3.390886872, -1.144307303, 3.088083981]

> [seq([x, f(x)], `in`(x, %))];

[[-4.367042332, -0.338522877], [-3.390886872, -0.969086791],
[-1.144307303, 0.413676882], [3.088083981, -0.9985687470]]

> mySolve := proc (fun) local xs;
xs := Student[Calculus1]:-Roots(fun, x = -10 .. 10, numeric);
[seq([x, f(x)], `in`(x, xs))]
end proc;

> mySolve(f-g);
[[-4.367042332, -0.338522877], [-3.390886872, -0.969086791],
[-1.144307303, 0.413676882], [3.088083981, -0.9985687470]]

> help("proc");
```
HTH, -- Jean-Marc

## You could use *seq* or write a two-line ...

as illustrated below:
```> restart;
> f := x^2-10-10*sin(x);

2
x  - 10 - 10 sin(x)

> g := cos(x);
cos(x)
> h := f-g;

2
x  - 10 - 10 sin(x) - cos(x)

> plot([f, g, h], x = -5 .. 5);

```
```> Student[Calculus1]:-Roots(h, x = -10 .. 10, numeric);

[-4.367042332, -3.390886872, -1.144307303, 3.088083981]

> [seq([x, f(x)], `in`(x, %))];

[[-4.367042332, -0.338522877], [-3.390886872, -0.969086791],
[-1.144307303, 0.413676882], [3.088083981, -0.9985687470]]

> mySolve := proc (fun) local xs;
xs := Student[Calculus1]:-Roots(fun, x = -10 .. 10, numeric);
[seq([x, f(x)], `in`(x, xs))]
end proc;

> mySolve(f-g);
[[-4.367042332, -0.338522877], [-3.390886872, -0.969086791],
[-1.144307303, 0.413676882], [3.088083981, -0.9985687470]]

> help("proc");
```
HTH, -- Jean-Marc

## Note that your system of...

Note that your system of equation can be written as a single expression, which has four zeroes that can be found by Roots.
```> expr := -12+x^2-10*sin(x);
2
-12 + x  - 10 sin(x)
> plot(expr);
```
```> Student[Calculus1]:-Roots(expr, x = -10 .. 10, numeric);
[-4.690152208, -2.574460734, -1.442831640, 3.271613316]

```
Regards, -- Jean-Marc

## Note that your system of...

Note that your system of equation can be written as a single expression, which has four zeroes that can be found by Roots.
```> expr := -12+x^2-10*sin(x);
2
-12 + x  - 10 sin(x)
> plot(expr);
```
```> Student[Calculus1]:-Roots(expr, x = -10 .. 10, numeric);
[-4.690152208, -2.574460734, -1.442831640, 3.271613316]

```
Regards, -- Jean-Marc

## Info for the third edition are now avail...

Doug, As of today, the info is displayed at the bottom of the page, finally :-) Take care, -- Jean-Marc P.S. Seems to be a well written book, easy to read, and very informative.

## Error, (in pdsolve/numeric) unable to ha...

Here is what I got on my system (Maple 12.02, Mac OS X Leopard 10.5.6):
```> restart;
> sys5 := [10^6*v(x, y)*(diff(T(x, y), x))-.1*(diff(T(x, y), y, y))-
10^3*(diff(v(x, y), y))^2 = 0, diff(v(x, y), x) = 0];
IBC := {T(-.3, y) = 400, T(.3, y) = 350, T(x, 0) = 400, v(0, y) = 150,
v(x, 1) = 300};
pds := pdsolve(sys5, IBC, [T, v], numeric);
[
[
sys5 := [
[
[

/  2         \                     2
/ d         \       | d          |        / d         \
1000000 v(x, y) |--- T(x, y)| - 0.1 |---- T(x, y)| - 1000 |--- v(x, y)|  = 0,
\ dx        /       |   2        |        \ dy        /
\ dy         /

]
d             ]
--- v(x, y) = 0]
dx            ]
]
IBC := {T(-0.3, y) = 400, T(0.3, y) = 350, T(x, 0) = 400, v(0, y) = 150,

v(x, 1) = 300}

Error, (in pdsolve/numeric) unable to handle elliptic PDEs
```
Regards, -- Jean-Marc

## Error, (in pdsolve/numeric) unable to ha...

Here is what I got on my system (Maple 12.02, Mac OS X Leopard 10.5.6):
```> restart;
> sys5 := [10^6*v(x, y)*(diff(T(x, y), x))-.1*(diff(T(x, y), y, y))-
10^3*(diff(v(x, y), y))^2 = 0, diff(v(x, y), x) = 0];
IBC := {T(-.3, y) = 400, T(.3, y) = 350, T(x, 0) = 400, v(0, y) = 150,
v(x, 1) = 300};
pds := pdsolve(sys5, IBC, [T, v], numeric);
[
[
sys5 := [
[
[

/  2         \                     2
/ d         \       | d          |        / d         \
1000000 v(x, y) |--- T(x, y)| - 0.1 |---- T(x, y)| - 1000 |--- v(x, y)|  = 0,
\ dx        /       |   2        |        \ dy        /
\ dy         /

]
d             ]
--- v(x, y) = 0]
dx            ]
]
IBC := {T(-0.3, y) = 400, T(0.3, y) = 350, T(x, 0) = 400, v(0, y) = 150,

v(x, 1) = 300}

Error, (in pdsolve/numeric) unable to handle elliptic PDEs
```
Regards, -- Jean-Marc

## What does that mean by that?...

What does that mean by that? For instance, if you are talking about the limit of the ratio xi/n, this makes sense only if you specifies which of xi or n is approaching some finite or infinite value. Regards, -- Jean-Marc

## What does that mean by that?...

What does that mean by that? For instance, if you are talking about the limit of the ratio xi/n, this makes sense only if you specifies which of xi or n is approaching some finite or infinite value. Regards, -- Jean-Marc

## Why?...

i think the integral exists.
Why? Why do you believe that? What is your line of reasoning? Have you investigated what Robert Israel hinted you previously? What result did you get? What can be inferred in term of convergence? Regards, -- Jean-Marc

## Why?...

i think the integral exists.
Why? Why do you believe that? What is your line of reasoning? Have you investigated what Robert Israel hinted you previously? What result did you get? What can be inferred in term of convergence? Regards, -- Jean-Marc
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