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cos-integrate

f(x):=x^2*cos(x),x;

integrate(f(x),x);

Calculate

cos-phi

phi:0.785;

xi:0.15;

cos(phi-xi);

Calculate

cos-plot2d-unit_step
plot2d(e^(-22*t) * unit_step(t) * cos(2*pi*22*t) + e^(22*t)*unit_step(-t)*cos(2*pi*22*t), [t, -20,20], [y,-20,20]);

plot2d(e^(-22*t) * un...

Calculate

cos-diff-display2d-false-pi-sin

display2d:false;

s = h*Q/B - (h/2*pi)*...

diff(h*Q/B - (h/2*pi)...

Calculate

cos-gramschmidt-integrate-load-map-matrix-sin

load (eigen);

x: matrix ([1,1,1,1]...

y: gramschmidt (x);

Calculate

cos-plot2d-sin
 plot2d([L(x),f(x)],[x,-2*%pi,2*%pi]);

f(x):=cos(2*x)+sin(1....

L(x):=-0.4*((x-0.7)*(...

plot2d([L(x),f(x)],[...

Calculate

cos-plot2d
plot2d(f(x), [x, -%pi, %pi]);

f(x):=if x< 0 then...

plot2d(f(x), [x, -%pi...

lim(f(x), x,0);

Calculate

cos-diff-ev-ratsimp-sin

vr(r,th):=(1 - 3/(2*r...

vth(r,th):=(-1 + 3/(4...

p_script(r,th):=-3/(2...

Calculate

cos

cos(4*%pi/3);

Calculate

cos-exp-integrate-sin

integrate(cos(x)+sin(...

Calculate

cos

Run Example
(%i1)eq:'diff(y,x,2)+9*y = 9/((cos (3*x))^2);
                              2
                             d y             9
(%o1)                        --- + 9 y = ---------
                               2            2
                             dx          cos (3 x)
(%i2) ode2(eq, y, x);
          sin(3 x) log(sin(3 x) + 1) - sin(3 x) log(sin(3 x) - 1) - 2
(%o2) y = -----------------------------------------------------------
                                       2
                                                  + %k1 sin(3 x) + %k2 cos(3 x)
(%i3) 
Run Example
derivabbrev:true ;
(%o1)                                true
(%i2) mainvar: t;
(%o2)                                  t
(%i3) x(t):= r(t)*sin(theta(t));
(%o3)                     x(t) := r(t) sin(theta(t))
(%i4) y(t):=r(t)*cos(theta(t));
(%o4)                     y(t) := r(t) cos(theta(t))
(%i5) xdot(t):= diff(x(t), t, 1);
(%o5)                     xdot(t) := diff(x(t), t, 1)
(%i6) ydot(t):= diff(y(t), t, 1);
(%o6)                     ydot(t) := diff(y(t), t, 1)
(%i7) xdotdot(t):= diff(xdot(t), t, 1);
(%o7)                  xdotdot(t) := diff(xdot(t), t, 1)
(%i8) ydotdot(t):= diff(ydot(t), t, 1);
(%o8)                  ydotdot(t) := diff(ydot(t), t, 1)
(%i9) thetadot(t):= diff(theta(t), t, 1);
(%o9)                 thetadot(t) := diff(theta(t), t, 1)
(%i10) thetadotdot(t) := diff(thetadot(t), t, 1);
(%o10)             thetadotdot(t) := diff(thetadot(t), t, 1)
(%i11) Assumption1: xdotdot(t)=0;
                                                                      2
(%o11) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
                                  t t                               t
                  + 2 r(t)  cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
                          t                       t       t t
(%i12) solve(Assumption1, r(t));
                 sin(theta(t)) r(t)    + 2 cos(theta(t)) theta(t)  r(t)
                                   t t                           t     t
(%o12) [r(t) = - -------------------------------------------------------]
                                                                      2
                 cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
                                       t t                          t
(%i13) Assumption2: ydotdot(t)=0;
                                                                        2
(%o13) - r(t) sin(theta(t)) theta(t)    - r(t) cos(theta(t)) (theta(t) )
                                    t t                               t
                  - 2 r(t)  sin(theta(t)) theta(t)  + r(t)    cos(theta(t)) = 0
                          t                       t       t t
(%i14) E1_1: subst(rdot(t), diff(r(t), t, 1), Assumption1);
                                                                      2
(%o14) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
                                  t t                               t
                + 2 rdot(t) cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
                                                  t       t t
(%i15) E1_2: subst(rdotdot(t), diff(diff(r(t), t, 1),t,1), E1_1);
                                                                      2
(%o15) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
                                  t t                               t
             + 2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t)) = 0
                                               t
(%i16) E1_3: subst(rr(t), r(t), E1_2);
                                                                        2
(%o16) rr(t) cos(theta(t)) theta(t)    - rr(t) sin(theta(t)) (theta(t) )
                                   t t                                t
             + 2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t)) = 0
                                               t
(%i17) E1_4: solve(E1_3, rr(t));
                  2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t))
                                                  t
(%o17) [rr(t) = - ------------------------------------------------------------]
                                                                          2
                     cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
                                           t t                          t
(%i18) E1_5: subst(r(t), rr(t), E1_4[1]);
                2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t))
                                                t
(%o18) r(t) = - ------------------------------------------------------------
                                                                        2
                   cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
                                         t t                          t
(%i19) 
Run Example
plot2d ([cos(x),cos(x)^2,/*sin(x)^2,*/cos(x)-cos(x)^2], [x,0,2*%pi]);
plotplot2d ([cos(x),cos(x)^2,/*sin(x)^2,*/cos(x)-cos(x)^2], [x,0,2*%pi]);i:A*sin(2500*t);
(%o2)                            sin(2500 t) A
(%i3) v:diff(i,t)*L;
(%o3)                        2500 cos(2500 t) A L
(%i4) integrate(v,t);
(%o4)                           sin(2500 t) A L
(%i5) 

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