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Operators

Problem :define the operator where D is the differentiation operator.

>> L := (D-id) @ (D+2*id);

                          (- id + D )@(2 id + D)

In MuPAD, id stand for the identity, and @ is the composition operator.

Problem :compute where L is the above defined operator.

>> L(f);

                          - 2 f + D(f) + D(D(f))

Problem :compute where L is the above defined operator.

>> L(g)(y);

                      - 2 g(y) + D(g)(y) + D(D(g))(y)

Problem :define the operator T such that .

>> T:=proc(f) begin
&>    eval(subsop(hold(func(f,x,a)),
&>      1=_plus(f(a),_fconcat(D$k)(f)(a)/fact(k)*(x-a)^k$k=1..2)))
&> end_proc:

Problem :evaluate T for an unknown function f.

>> T(f);

      func(f(a) + (-a + x)*D(f)(a) + (-a + x)^2*D(D(f))(a)*1/2, x, a)

Problem :evaluate T for an unknown function g and a generic point .

>> T(g)(y,b);

                                                             2
                                        D(D(g))(b) (- b + y ) 
            g(b) + D(g)(b) (- b + y ) + ----------------------
                                                  2

Problem :evaluate T for the function and a point .

>> T(sin)(z,c);

                                                            2
                                           sin(c) (- c + z ) 
              sin(c) + cos(c) (- c + z ) - ------------------
                                                   2



Andre Heck
Sun Apr 23 10:32:10 MDT 1995