2+2

a

a=1
b=3
a+b

c=3;

Sin[π/2]

(*  u(x,0)=f(x);
    (∂_t)u(x,0)=g(x);
u(x,t)=((f(x+vt)+f(x-vt))/2)+(1/(2v))(∫_(x-vt)^(x+vt))g(w)\[DifferentialD]w
y=vt
(Subscript[(∂^2), x])u=(1/(v^2))(Subscript[(∂^2), t])u -> (Subscript[(∂^2), x])u=(Subscript[(∂^2), y])u
*)

f[x_]:=Sin[π x]
Plot[f[x],{x,0,1}]

u=-(1/2)Cos[π(x+y)]+(1/2)Cos[π(x-y)]

D[u,{x,2}]-D[u,{y,2}]

d=1

2d

(((x+1))^2)/.{x->y}

x

f=u/.{y->0}

u

g=D[u,{y,1}]/.{y->0}

Plot[g,{x,0,1}]

g/.{x->0}

g/.{x->1}

g/.{x->1/2}

g/.{x->0.5}

(*  
Vamos a resolver el caso particular en el que
(Subscript[(∂^2), x])u=(Subscript[(∂^2), y])u
u(x,0)=f(x)=0;
    (∂_t)u(x,0)=g(x)=π Sin[π x];
*)

Plot3D[u,{x,0,1},{y,0,3},AxesLabel->{"x","y"}]

ContourPlot[u,{x,0,1},{y,0,3},AxesLabel->{"x","y"}]

u/.{x->1/2,y->5/2}

DensityPlot[u,{x,0,1},{y,0,3},AxesLabel->{"x","y"},ColorFunction->"TemperatureMap"]

i=1
x=1.23
z=4+I 3

Integrate[Cos[x z],x]

Simplify[(x^2)+2 x+1]

Integrate[Exp[-((x^2)/v)],{x,-∞,∞},Assumptions->{v>0}]

Simplify[(Sqrt[-(x^2)]),Assumptions->{x∈Reals}]

ClearAll

Clear[a,b,c,d]

lista={a,b,c,d}

i=3
lista[[i]]

lista={a,b,{c,d,e}}

lista[[1,1]]

mat1={{2,1},{3,2}};
mat2={{3,5},{6,9}};

mat1[[1,1]]

MatrixForm[mat1]
MatrixForm[mat2]

mat1.mat2

sol=Solve[x+4==6,x]

1+4==6

sol=Solve[(x^2)+4==6,x]

sol[[2]]

x+6+Log[x]/.sol[[2]]

sol=Solve[{(x^2)+y==6,x-y==4},{x,y}]