gulliet

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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 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
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
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
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
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 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 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
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.
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
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? 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? 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
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
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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