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gulliet

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Drawing on Joe Riel's...

gulliet 266
August 12 2009
0 0
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...

gulliet 266
August 12 2009
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...

gulliet 266
August 11 2009
0 0
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...

gulliet 266
August 11 2009
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 ...

gulliet 266
July 06 2009
0 0
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);
97_xyintercept.jpg 
> 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 ...

gulliet 266
July 06 2009
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);
97_xyintercept.jpg 
> 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...

gulliet 266
July 04 2009
0 0
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);
97_fourzeroes.jpg 
> Student[Calculus1]:-Roots(expr, x = -10 .. 10, numeric);
           [-4.690152208, -2.574460734, -1.442831640, 3.271613316]
Regards, -- Jean-Marc

Note that your system of...

gulliet 266
July 04 2009
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);
97_fourzeroes.jpg 
> 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...

gulliet 266
June 17 2009
Doug, As of today, the info is displayed at the bottom of the page, finally :-) 97_Getting_Started_with_Maple_3rd_ed_Willey.png 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...

gulliet 266
March 08 2009
0 0
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...

gulliet 266
March 08 2009
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?...

gulliet 266
March 08 2009
0 0
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?...

gulliet 266
March 08 2009
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?...

gulliet 266
March 08 2009
0 0
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?...

gulliet 266
March 08 2009
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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