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The Maxima on-line user's manual

Algebra Calculator

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Atvalue Calculator

Atvalue

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

globalsolve:true;
Vs:120;
R:4;
L:4;
C:1;
de1: -Vs+R*C*diff(vc(t),t,1)+L*C*diff(vc(t),t,2)+vc(t)=0;
atvalue(vc(t),t=0,0);
atvalue(diff(vc(t),t),t=0,0);
sol:desolve(de1,vc(t));
plot2d(rhs(sol),[t,0,20]);
plot2d(C*diff(-60.0*t*%e^(-0.5*t)-120.0*%e^(-0.5*t)+120,t),[t,0,20]);
plot2d(C*diff(-60.0*t*%e^(-0.5*t)-120.0*%e^(-0.5*t)+120,t),[t,1,3]);
ilt(log((s^2+4*s+13)/(s^2)),s,t);

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) 

Atvalue Example

Related Examples

atvalue-diff-exp-ode2-plot3d
plot3d(

k1:exp(7.176-(3.85/Te...

k2:exp(9.942-(4.05/Te...

OH:10^(pH-14);

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atvalue-desolve-diff

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

desolve(V0 = y(t) + C...

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atvalue-diff-ode2-plot2d-rhs
 plot2d(rhs(sol1),[x,1,3]);

eqn: 'diff(y,x,2)-3*'...

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

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

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atvalue-desolve-diff

eqn1:diff(y(x),x)=z(x);

eqn2:diff(z(x),x)=y(x);

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

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atvalue

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

Calculate

atvalue-desolve-diff

eqn1:diff(y(x),x) = z...

eqn2:diff(z(x),x) = 3...

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

Calculate

atvalue-desolve-diff-exp

eqn1:diff(y(x),x) = z...

eqn2:diff(z(x),x) = 3...

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

Calculate

atvalue-desolve-diff-exp-integrate-plot2d
plot2d(sol,[t,0,5]);

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

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

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

Calculate

atvalue-diff-ilt-lambda-laplace-map-partfrac-solve

unitstep(x):= if x<...

ode: 'diff(y(t), t, 2...

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

Calculate