(2) (2) (1) (1)
(4) (4)
(5) (5) (3) (3)
Bitte zur Übung kommen -> Evaluierung der
Übungsgruppen !!
zu schwer zu langsam
zu leicht/zu schnell
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7
(6) (6)
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zu schwer zu langsam
zu leicht/zu schnell
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Vectors and Matrices
(7) (7) (8) (8) (6) (6)
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0 1 2 3
50 100 150 200
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(10) (10) (9) (9) Let us inspect (column) vectors.
0 2
Now, we want to compute the shortest distance from point q := <2,1> to the line.
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0 1 2
1 2 3 4 5
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Q hq
hit
q Hit
p r
0 1 2
1 2
Remarks:
q = hit+hq, thus hq=q-hit
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(24) (24) (23) (23)
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now, we demand that hq t r, thus hq·r = 0, and therefore (q - (p+r)) · r = 0
Remarks:
resorting (
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0 1 2
1 2
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in general:
cf. G. Fischer, Lineare Algebra, S. 71ff, Verknüpfungen von Matrizen
Graphs
What is a graph?
An undirected graph consists of a pair G=(V,E), where E 4{{u,v} | u,v2 V}.
The elements of E are not ordered..
Elements from V are called nodes (or vertices; Knoten in dt.), elements from E are called edges (Kanten in dt.)
A directed graph (gerichteter Graph) is as well a pair G=(V,E). However, the elements of E are ordered pairs of elements from V. Thus, E 4 {(u,v) | u,v 2 V}.
Elemente of V are called nodes, elements from E are called edges (im dt.: gerichtete Kanten oder Bögen)
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(32) (32) (31) (31) (30) (30) .
Repetition: Flow Control (if, for, while, ...)
if <conditional expression> then <statement sequence>
| elif <conditional expression> then <statement sequence> | | else <statement sequence> |
end if
(Note: Phrases located between | | are optional.)
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(32) (32) The for ...while ... do loop
1) Print even numbers from 6 to 10.
6 8 10
2) Find the sum of all two-digit odd numbers from 11 to 99.
2475 3) Multiply the entries of an expression sequence.
3) Add together the contents of a list.
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"1C3*q^2*3"
145
Similar-to-Fibonacci-Numbers are
103361417709716646143
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(32) (32)
