Analysis

A1

Series[(1/(((1 - x))^2)), {x, 0, 5}]

D[(1/(1 - x)), x]

(∑_(k = 0)^∞) (x^k)

(∑_(k = 0)^∞) k (x^(k - 1))

A2

Series[((1 + x)/(1 - x)), {x, 0, 10}]

A3

Plot[Log[x - Sin[x]]/Log[1 - Cos[x]], {x, 0, 1}]

Limit[Log[x - Sin[x]]/Log[1 - Cos[x]], x -> 0]

Plot[Log[Cos[x]]/Log[Cosh[x]], {x, -1, 1}]

Limit[Log[Cos[x]]/Log[Cosh[x]], x -> 0]

ser = Series[Log[Cos[x]]/Log[Cosh[x]], {x, 0, 5}]

Lineare Algebra

L1

A = {{3, -15, 1}, {10, 12, -1}, {7, 9, 2}, {4, 
          0, -1}}

B = {{5, 9, 2}, {-15, 12, 9}, {1, -1, 2}, {2, 7, 8}}

Transpose[A] . B

Transpose[B] . A

Bekanntlich ist ja (A^T) B = (((A (B^T)))^T). Gibt man ein falsches Produkt ein, so erhält man

A . B

L2

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

b = {{-1}, {0}, {1}, {2}, {3}}

Transpose[a] . b

a . Transpose[b]

Wieder ist dies gleich

Transpose[b . Transpose[a]]

L3

Clear[a]

A = {{a, I, 1}, {1, 1, I}, {0, 
          1, -1}}

RowReduce[A]

Solve[A . {{x}, {y}, {z}} == 0, {x, y, z}]

Reduce[A . {{x}, {y}, {z}} == 0, {x, y, z}]

RowReduce[A /. {a -> 1}]