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assume-cos-exp-inf-integrate

assume(a > 0);

assume(b > 0);

integrate(exp(-k)*(co...

Calculate

assume-inf-integrate

assume(s>=0);

assume(c>=0);

integrate(integrate((...

Calculate

assume-diff-ev-integrate-plot2d-sin
plot2d ([yexa(x),yvar(x),yment(x)], [x, 0, 2],[legend,"exacta","variacional", "mentira"],[style,lines]);

y(x):=A*sin(%pi*x/(2*...

dy(x):=diff(y(x),x);

ddy(x):=diff(dy(x),x);

Calculate

assume-diff-ev-integrate-plot2d
plot2d ([yexa(x),yvar3(x)], [x, 0, L],[legend,"exacta","variacional 3 orden"],[style,lines]);

/*exacta*/yexa(x):=-(...

/*Aproximación de 3 o...

dy3(x):=diff(y3(x),x);

Calculate

assume-debugmode-diff-integrate-ratsimp-true

debugmode(true);

k1(Temp):=10^(7.176-(...

k2(Temp):=10^(9.942-(...

Calculate

assume-expand-ratsimp-tex

prnt: "Your CGS expre...

expr: curl*B - (1/c)*...

/* Put your ...

Calculate

assume-diff-log-sqrt

assume(sigma > 0);

f:2*(sigma^2)*log(eps...

diff(f,sigma);

Calculate

assume-integrate

assume(dt>0);

f(t):= t+1;

g(t):= t-dt+1;

Calculate

assume-diff-exp-pade-taylor

assume(a>1);

assume(T>0);

assume(b<0);

Calculate

assume

Run Example
(%i1)assume(V>
0, R>
0, L>
0, C>
0);
(%o1)                    [V > 0, R > 0, L > 0, C > 0]
(%i2) assume(C*R^2 - 4*L >
 0);
                                     2
(%o2)                            [C R  > 4 L]
(%i3) ec  : R*x(t) + L*diff(x(t),t) + integrate(x(t), t)/C = V;
                                             /
                                             [
                                             I x(t) dt
                                             ]
                              d              /
(%o3)               x(t) R + (-- (x(t))) L + --------- = V
                              dt                 C
(%i4) ecd : diff(ec, t);
                                     2
                    d               d               x(t)
(%o4)              (-- (x(t))) R + (--- (x(t))) L + ---- = 0
                    dt                2              C
                                    dt
(%i5) e2:laplace(ecd,t,s);
                                                     !
                                            d        !
(%o5) (s laplace(x(t), t, s) - x(0)) R + (- -- (x(t))!
                                            dt       !
                                                     !t = 0
                    2                                   laplace(x(t), t, s)
                 + s  laplace(x(t), t, s) - x(0) s) L + ------------------- = 0
                                                                 C
(%i6) atvalue( x(t), t=0, 0);
(%o6)                                  0
(%i7) atvalue( diff(x(t), t), t=0, V/L);
                                       V
(%o7)                                  -
                                       L
(%i8) e4:solve(e2,laplace(x(t),t,s));
                                                   !
                                          d        !
                              x(0) C R + (-- (x(t))!      + x(0) s) C L
                                          dt       !
                                                   !t = 0
(%o8)  [laplace(x(t), t, s) = -----------------------------------------]
                                                  2
                                         s C R + s  C L + 1
(%i9) ilt(e2,s,t);
(%o9) ilt((s laplace(x(t), t, s) - x(0)) R, s, t)
                   !
          d        !         2
 + ilt((- -- (x(t))!      + s  laplace(x(t), t, s) - x(0) s) L, s, t)
          dt       !
                   !t = 0
       laplace(x(t), t, s)
 + ilt(-------------------, s, t) = 0
                C
(%i10) 
Run Example
assume(A>
0,d>
0,y>
0,%lambda>
0,D>
0);
(%o1)              [A > 0, d > 0, y > 0, %lambda > 0, D > 0]
(%i2) test:4*A^2*cos(%pi*d*y/(%lambda*D))^2;
                                2    2  %pi d y
(%o2)                        4 A  cos (---------)
                                       %lambda D
(%i3) l:diff(test,y,1);
                             2      %pi d y        %pi d y
                    8 %pi d A  cos(---------) sin(---------)
                                   %lambda D      %lambda D
(%o3)             - ----------------------------------------
                                   %lambda D
(%i4) solve(l=0,y);

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
                                        %lambda D
(%o4)                       [y = 0, y = ---------]
                                           2 d
(%i5) 
Run Example
assume(r>
0);
(%o1)                               [r > 0]
(%i2) assume(d>
0);
(%o2)                               [d > 0]
(%i3) assume(b>
0);
(%o3)                               [b > 0]
(%i4) rr(t):=sqrt(r*r+rp*rp-2*r*rp*cos(t));
(%o4)           rr(t) := sqrt(r r + rp rp + (- 2) r rp cos(t))
(%i5) x(t):=rr(t)/(2*d);
                                         rr(t)
(%o5)                            x(t) := -----
                                          2 d
(%i6) f(t):=1/d*(6/5-2*x(t)^2+3/2*x(t)^3-5*x(t)^5);
                        1  6      2      3  3             5
(%o6)           f(t) := - (- - 2 x (t) + - x (t) + (- 5) x (t))
                        d  5             2
(%i7) expand(f(t)*sin(t));
                               2    2 5/2
        5 (- 2 r rp cos(t) + rp  + r )    sin(t)
(%o7) - ----------------------------------------
                             6
                         32 d
                          2    2 3/2                                 2
   3 (- 2 r rp cos(t) + rp  + r )    sin(t)   r rp cos(t) sin(t)   rp  sin(t)
 + ---------------------------------------- + ------------------ - ----------
                        4                              3                 3
                    16 d                              d               2 d
    2
   r  sin(t)   6 sin(t)
 - --------- + --------
        3        5 d
     2 d
(%i8) integrate(expand(f(t)*sin(t)),t);
                               2    2 7/2                          2    2 5/2
        5 (- 2 r rp cos(t) + rp  + r )      3 (- 2 r rp cos(t) + rp  + r )
(%o8) - --------------------------------- + ---------------------------------
                        6                                  4
                   224 d  r rp                         80 d  r rp
                                       2        2           2
                               r rp cos (t)   rp  cos(t)   r  cos(t)   6 cos(t)
                             - ------------ + ---------- + --------- - --------
                                      3             3           3        5 d
                                   2 d           2 d         2 d
(%i9) integrate(f(t)*sin(t),t);
                                2    2 7/2                          2    2 5/2
         5 (- 2 r rp cos(t) + rp  + r )      3 (- 2 r rp cos(t) + rp  + r )
(%o9) (- --------------------------------- + ---------------------------------
                         5                                  3
                    224 d  r rp                         80 d  r rp
                                    2        2           2
                          - r rp cos (t) + rp  cos(t) + r  cos(t)   6 cos(t)
                        + --------------------------------------- - --------)/d
                                              2                        5
                                           2 d
(%i10) 
[abs,assume,ceiling,declare,floor,max,tex] [abs,assume,if,is,ratsimp] [apply1,assume,defrule,diff,ev,ident,inf,integrate,load,matrix,sqrt,transpose] [assume,atvalue,diff,laplace,limit,solve] [assume,bessel_j,besselexpand,factor,inf,integrate,pi,print,quit,radexpand,true] [assume,binomial,simpsum] [assume,carg,declare,float,solve] [assume,changevar,integrate,nouns] [assume,constant,cos,declare,diff,let,letsimp,sin,solve,trigsimp] [assume,constant,cos,declare,diff,let,letsimp,sin,subst,trigsimp] [assume,cos,expand,integrate,sin,sqrt,tex] [assume,cos,expand,integrate,sin,sqrt] [assume,cos,integrate,phi,sin,sqrt] [assume,cos,integrate,plot2d,sin,sqrt] [assume,cos,integrate,plot2d,sin,subst] [assume,cos,integrate,plot2d,sin] [assume,cos,integrate,sin] [assume,cos,integrate] [assume,declare,ev] [assume,define,plot2d,sin,sqrt,subst] [assume,diff,ev,ic1,ic2,ode2,plot2d] [assume,diff,ev,integrate,plot2d,sin] [assume,diff,ev,integrate,plot2d] [assume,diff,exp,pade,taylor] [assume,diff,factor,integrate,log,ratsimp] [assume,diff,facts,forget,ode2] [assume,diff,integrate,plot2d] [assume,diff,integrate] [assume,diff,is,solve] [assume,diff,ode2] [assume,diff] [assume,dim,integrate,log,ratsimp] [assume,exp,inf,integrate] [assume,exp,inf,limit] [assume,exp,integrate] [assume,expand,matrix,subst] [assume,inf,integrate] [assume,inf,limit] [assume,integrate,log,ratsimp] [assume,integrate,log] [assume,integrate,sin] [assume,integrate,sqrt] [assume,integrate] [assume,is] [assume,linsolve] [assume,solve,sqrt] [assume,solve] [assume,sqrt,tan,taylor] [assume,taylor] [assume]

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