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Online Algebra Calculator
Many of users do not use powerful Maxima computer algebra system for systematic work, but for ad hoc algebraic calculations – equations, functions, matrixes, etc. only. To do this job, it is not useful to download the whole application from a web site.
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assume-diff-ev-facts-integrate-rhs
(assume (x*y>0),fa...
integrate(%e^(-t^2),t...
f(x,y)=integrate(%e^(...
assume-atvalue-diff-laplace-limit-solve
assume(R0>0, R1>...
atvalue(vc(t),t=0,Vc0);
atvalue(il(t),t=0,Il0);
assume-constant-cos-declare-diff-expandwrt_factored-globalsolve-let-letsimp-posfun-ratcoef-realonly-sin-subst-tlimswitch-trigsimp-true
globalsolve: true;
realonly: true;
/* Standard (x,y)->...
![plot2d ([yexa(x),yvar(x)], [x, 0, 2],[legend,"exacta","variacional"],[style,lines]);](http://maxima-online.org/plot.html?g=p-1030457959.png&t=img&db=r161735029)
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,desolve,diff,draw,draw2d,ev,explicit,integrate,load,rhs] [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] [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]
