Integrální a diferenciální počet

Limity

Limit[((Sin[x])/x),x->0]

Limit[((3Sin[x])/x),x->0]

Limit[(1/x),x->0]

FullForm@Limit[(1/x),x->0]

- >

Limit[(1/x),x->0,Direction->1]

Derivace

D[2x+1,x]

D[(E^(-(x^2))),x]

D[(E^(-(x^2))),{x,20}]

D[(E^(-(x^2)+2(y^2))),y,x]

Rychlost

D[{Sin[t],Cos[t],(E^t)},t]

D[{Sin[t],Cos[t],(E^t)},t,t]

Taylorův rozvoj

Series[Sin[x],{x,0,5}]

Manipulate[Series[Sin[x],{x,0,i}],{i,1,10,1}]

Integrál

Integrate[f,x]

∫Sin[x]\[DifferentialD]x

∫((Sin[x])/x)\[DifferentialD]x

Integrate[Sin[x],{x,0,π}]

Integrate[Sin[x],{x,0,∞}]

(∫_0^∞)Sin[x]\[DifferentialD]x

Součet řady

Sum[(i^2),{i,1,10}]

(∑_(i=1)^10)(1/(i^2))

(∑_(i=1)^∞)(1/(i^2))

Diferenciální rovnice

DSolve[y''[t]==-y[t],y[t],t]

DSolve[y''[t]==-y[t],y,t]

Počáteční podmínky

DSolve[{y''[t]==-y[t],y'[0]==0},y[t],t]

DSolve[{y''[t]==-y[t],y'[0]==v0,y[0]==y0},y[t],t]

DSolve[{y''[t]==-y[t],y[2]==y02,y[0]==y0},y[t],t]

DSolve[{y''[t]==-y[t],y'[2]==y02,y'[0]==y0},y[t],t]