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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