### The Maxima on-line user's manual

Algebra Calculator

#### Atvalue

Function: atvalue (<expr>, [<x_1> = <a_1>, ..., <x_m> = <a_m>], <c>)

Function: atvalue (<expr>, <x_1> = <a_1>, <c>) Assigns the value <c> to <expr> at the point `<x> = <a>`. Typically boundary values are established by this mechanism.

<expr> is a function evaluation, `<f>(<x_1>, ..., <x_m>)`, or a derivative, `diff (<f>(<x_1>, ..., <x_m>), <x_1>, <n_1>, ..., <x_n>, <n_m>)` in which the function arguments explicitly appear. <n_i> is the order of differentiation with respect to <x_i>.

The point at which the atvalue is established is given by the list of equations `[<x_1> = <a_1>, ..., <x_m> = <a_m>]`. If there is a single variable <x_1>, the sole equation may be given without enclosing it in a list.

`printprops ([<f_1>, <f_2>, ...], atvalue)` displays the atvalues of the functions `<f_1>, <f_2>, ...` as specified by calls to `atvalue`. `printprops (<f>, atvalue)` displays the atvalues of one function <f>. `printprops (all, atvalue)` displays the atvalues of all functions for which atvalues are defined.

The symbols `@1`, `@2`, ... represent the variables <x_1>, <x_2>, ... when atvalues are displayed.

`atvalue` evaluates its arguments. `atvalue` returns <c>, the atvalue.

Examples:

```          (%i1) atvalue (f(x,y), [x = 0, y = 1], a^2);
2
(%o1)                          a
(%i2) atvalue (diff (f(x,y), x), x = 0, 1 + y);
(%o2)                        @2 + 1
(%i3) printprops (all, atvalue);
!
d             !
--- (f(@1, @2))!       = @2 + 1
d@1            !
!@1 = 0```

2 f(0, 1) = a

```          (%o3)                         done
(%i4) diff (4*f(x,y)^2 - u(x,y)^2, x);
d                          d
(%o4)  8 f(x, y) (-- (f(x, y))) - 2 u(x, y) (-- (u(x, y)))
dx                         dx
(%i5) at (%, [x = 0, y = 1]);
!
2              d           !
(%o5)     16 a  - 2 u(0, 1) (-- (u(x, y))!            )
dx          !
!x = 0, y = 1```

```(%o1)                                true
(%i2) ```

### Related Examples

##### atvalue-cos-desolve-diff-integrate-pi-ratsimp

eq: diff(y(x),x)-x*y(...

atvalue(y(x),x=0,1);

atvalue(diff(y(x),x),...

Calculate

##### atvalue-diff-log-ode2-plot3d

log(k1)=7.176-(3.85/T...

log(k2)=9.942-(4.05/T...

OH=10^(pH-14);

Calculate

##### atvalue-delta-diff-ilt-lambda-laplace-map-solve

atvalue(x(t), t = 0, 0);

atvalue('diff(x(t), t...

dgl: 'diff(x(t), t, 2...

Calculate

##### atvalue-diff-ilt-lambda-laplace-map-ratsimp-solve

/* y'' - 10 y' + 9 y ...

lap: laplace(rovniceL...

atvalue('diff(y(x),x)...

Calculate

##### atvalue-desolve-diff-ratsimp

eqn : ’diff(y(t),t) =...

atvalue (’y(t), t=0, 1);

gsoln : ratsimp(desol...

Calculate

##### atvalue-diff

e:25=24*i1(t)-10*i2(t);

e:0=6*'diff(i2(t),t)-...

atvalue(i1(t),t=0,0);

Calculate

##### atvalue-desolve-diff-ilt

e:100=0.1*'diff(i1(t)...

atvalue(i1(t),t=0,10);

desolve(e,[i1(t)]);

Calculate

##### atvalue-bc2-diff-ode2

enq: 'diff(y(x),x,2)-...

atvalue(y(x),x=1,-2);

atvalue(y(x),x=3,0);

Calculate

##### atvalue-desolve-diff-exp-plot2d

e:100=0.1*'diff(i1(t)...

atvalue(i1(t),t=0,10);

desolve(e,[i1(t)]);

Calculate

##### atvalue-depends-diff-log-ode2-plot3d

log(k1)=7.176-(3.85/T...

log(k2)=9.942-(4.05/T...

OH=10^(pH-14);

Calculate