Einführung in Mathematica

1

Solve[x^2 - 3 x + 2 == 0, x]

1

{{x -> 1}, {x -> 2}}

1

Solve[x^2 - 3 x + 2 == 0 && 0 <= x <= 2, x, Integers]

1

{{x -> 1}, {x -> 2}}

1

Solve[{x + y == 3, x - y == 1}, {x, y}]

1

{{x -> 2, y -> 1}}

1

Reduce[x^2 - 3 x + 2 > 0, x]

1

x < 1 || x > 2

1

D[x^2, x]

1

2 x

1

Integrate[x^2, x]

1

x^3/3

1

Limit[1/x, x -> 0]

1

Infinity

1

Sum[1/n^2, {n, 1, Infinity}]

1

π^2/6

1

m = {{1, 2}, {3, 4}}

1

m . m

1

{{7, 10}, {15, 22}}

1

Inverse[m]

1

{{-2, 1}, {1.5, -0.5}}

1

Eigensystem[m]

1

{{5, 0}, {{1, 1}, {1, -1}}}

1

{1, 2} . {3, 4}

1

11

1

Cross[{1, 2, 3}, {4, 5, 6}]

1

{-3, 6, -3}

1

Norm[{1, 2, 3}]

1

√14

1

ArcCos[{1, 2} . {3, 4}/(Norm[{1, 2}] Norm[{3, 4}])]

1

ArcCos[11/(√5 √25)]

1

{1, 2} . {3, 4}/Norm[{3, 4}] {3, 4}/Norm[{3, 4}]

1

{11/5, 22/5}

1

RotationMatrix[π/2].{1, 0}

1

{0, 1}

1

TranslationTransform[{1, 2}][{3, 4}]

1

{4, 6}

1

ScalingTransform[{2, 3}][{1, 1}]

1

{2, 3}

1

ReflectionTransform[{1, 1}][{1, 1}]

1

{0, 0}

1

RandomReal[]

1

0.123456

1

RandomInteger[]

1

123456

1

RandomReal[{1, 10}]

1

5.6789

1

RandomInteger[{1, 10}]

1

5

1

RandomVariate[NormalDistribution[0, 1]]

1

0.123456

1

RandomVariate[NormalDistribution[0, 1], 10]

1

{0.123456, 0.234567, ..., 0.987654}

1
2

SeedRandom[12345]
RandomVariate[NormalDistribution[0, 1], 10]

1

{0.123456, 0.234567, ..., 0.987654}

1
2
3

Map[Sqrt, {1, 4, 9}]
Sqrt /@ {1, 4, 9}
Map[#^(1/2)&, {1, 4, 9}]

1

{1, 2, 3}

1
2

f = Function[x, x^2]
f[3]

1

9

1
2
3
4

f = Function[x, x^2]
g = Function[x, x + 1]
h = Function[x, f[g[x]]]
h[3]

1

16

1

% + 1

1

17

1

(#+3)&[5]

1

8

1
2

Select[{1, 2, 3, 4, 5}, EvenQ]
Select[{1, 2, 3, 4, 5}, Mod[#,2]==0&]

1

{2, 4}