Calculus

Differentiation

D[x^n,x]

D[2x^3-x^2+6x-1,x]

% /. x-> 0

%7 /. x -> 1

D[Sin[n Pi x/L],x]

D[Sin[n Pi x/L],{x,2}]

D[x^2 Sin[a x],x]

sol=D[r^2 Exp[-2r/a],r]

Solve[sol ==0, r]

D[ν^3/(Exp[h ν/k T]-1),ν]

sol=D[ν^3/(Exp[h ν/k T]-1),ν]

Solve[sol==0,ν]

NSolve[sol==0,ν,3]

eqn=x+3 Exp[-x]==3

FindRoot[eqn,{x,3}]

NSolve[eqn,x]

D[x^2+y^2,{{x,y}}]

Integration

Integrate[x^n,x]

Integrate[5/x+3/x^2,x]

Integrate[x^2+2x+1,x]

Integrate[Exp[-r/a],r]

Integrate[(Sin[n Pi x/L])^2,x]

Integrate[Exp[-α x^2],x]

Integrate[r^2 Exp[-2r/a],r]

Integrate[r^2 Exp[-2r/a],{r,0,Infinity}]

Integrate[Exp[-α x^2],{x,0, Infinity}]

Integrate[(Sin[n Pi x/L])^2,{x,0,L}]

Integrate[Sin[x],{x,0,Pi}]

psi0[y_]=(α/Pi)^(1/4)Exp[-y^2/2]

Integrate[psi0[y]^2/α^(1/2),{y,-Infinity,Infinity}]

Integrate[psi0[y]^2/α^(1/2),{y,1,Infinity}]

N[%]

p_forb=2*%