1 + 
      1

(10 + 5)*3

(3/2)^10

N[%, 8]

1.5^10

\(\(\(N[%, 8]\)\(
\)
    \)\)

(3/2)^100

N[%, 40]

1.5^100

N[%, 40]

f[x_] := x + Cos[x]

f[1]

f[1. ]

Plot[f[x], {x, 0, 10}, AxesLabel -> {x, y}]

\(plo = 
      Plot[f[x], {x, 0, 10}, Frame -> True, 
	
        FrameLabel -> {x, f, " f= x+Cos[x]", " "}]\)

SetDirectory["c:/courses/compu/notebooks"]

Print[FileNames[]]

Display["f1.EPS", plo, "EPS", 
        ImageSize -> 
          500, 
ImageOffset -> {30, 30}];

Display["f2.JPEG", plo, "JPEG", 
        ImageSize -> 
          500, 
ImageOffset -> {30, 30}];

ima = Import["f2.JPEG"]

Show[ima]

Export["f3.EPS", ima]

aa = 1; bb = 2;
g[x_] := aa + bb*x;
g[y]

aa = 3; bb = 4;
g[y]

aa = 1; bb = 2;
h[x_] = aa + bb*x;
h[y]

aa = 3; bb = 4;
h[y]

(*Loops*) 
x[0] = 0

Do[x[n + 1] = x[n] + 1, {n, 0, 10}]

x[1]

x[2]

taa = Table[x[n], {n, 0, 10}]

ListPlot[taa]

ParametricPlot[{Cos[5*x], Sin[3*x]}, {x, 0, 2*Pi}]

ParametricPlot[{Cos[5*x], Sin[3.354678*x]}, {x, 0, 20*Pi}]

I^2

\(\(\(Re[1 + I]\)\(
\)
    \)\)

Plot[Re[Zeta[1/2  + I*x]], {x, 0, 500}]

\(Plot[Abs[Zeta[1/2\  + I*x]], 
	{x, 0, 20}, PlotPoints -> 2000, 
      PlotRange -> All]\)

\(Plot[Abs[Zeta[1/4\  + I*x]], 
	{x, 0, 10}, PlotPoints -> 2000, 
      PlotRange -> All]\)

?Zeta

f[y]

D[f[y], y]

D[f[y], {y, 2}]

Integrate[f[x], {x, 0, y}]

tt = (a + b)*(c + d)

uu = Expand[tt]

Factor[uu]

vv = (a - b)*(a + b)/(a^2 - b^2)

Simplify[vv]

?Random

Random[]

Random[Real, {0, 3}]

Do[Print[Random[Real, {0, 3}]], {nn, 1, 10}]

?PutAppend

Do[
      PutAppend[Random[Real, {0, 3}], "datafile"], {nn, 1, 
        10}]

aa = << datafile

!! datafile

Do[
      Put[Random[Real, {0, 3}], "datafile"], {nn, 1, 10}]

!! datafile

Do[
      PutAppend[Random[Real, {0, 3}], "datafile"], {nn, 1, 
        10}]

!! datafile

?Import

tabb = Import["datafile", "Table"]

tabb = Import["datafile", "List"]

?If

aa

bb

va := If[aa < bb, xx, yy]; va

bb = 4; va

?&&

seri = 
      Series[Cos[x], {x, 0, 8}]

seri^2

ff[x_] := 
      If[x < -1, 0, If[x < 1, 1, 0]]; 
    Plot[ff[x], {x, -2, 2}]

sol1 = 
Solve[x^2 + 3*x + 1 == 0, x]

sol1[[1]]

x /. {x -> qqq}

x /. sol1

x /. sol1[[1]]

Solve[x^6 + 4*x^5 + x^2 + 3*x + 1 == 0, x]

NSolve[x^6 + 4*x^5 + x^2 + 3*x + 1 == 0, x]

Solve[39*x^4 + 258  x^3 + x^2 + 3*x + 1 == 0, x]

Integrate[Exp[-a*t]*t^b, {t, 0, Infinity}]

Integrate[Exp[-a*t]*t^b, {t, 0, Infinity}, 
      Assumptions -> {a > 0, b > 0}]

NIntegrate[
      Exp[-(1/2)*x^2]*x^(40), {x, 15. , Infinity}]

Integrate[
      Exp[-(1/2)*x^2]*x^(40), {x, 15. , Infinity}]

NIntegrate[Exp[-(1/2)*x^2]*x^(40), {x, 15, Infinity}, 
      AccuracyGoal -> 30, WorkingPrecision -> 80]

Plot[Exp[-(1/2)*x^2]*x^(40), {x, 1, 20}]

Plot[Exp[-(1/2)*x^2]*x^(40), {x, 1, 20}, 
      PlotRange -> All]

Plot[Exp[-(1/2)*x^2]*x^(40), {x, 15, 20}, 
      PlotRange -> All]

Do[x[n] = Random[], {n, 1, 1000000}]