Mathematik für Ingenieure Teil 2
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| 001 | BV046157502 | ||
| 003 | DE-604 | ||
| 005 | 20230511 | ||
| 007 | t | ||
| 008 | 190912s2020 gw |||| |||| 00||| ger d | ||
| 016 | 7 | |a 1187767646 |2 DE-101 | |
| 020 | |a 9783947506323 |c Broschur : EUR 24.99 (DE), EUR 24.99 (AT) |9 978-3-947-50632-3 | ||
| 020 | |a 3947506325 |9 3-947506-32-5 | ||
| 035 | |a (OCoLC)1120138248 | ||
| 035 | |a (DE-599)BVBBV046157502 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c XA-DE-NW | ||
| 049 | |a DE-83 |a DE-573 |a DE-862 |a DE-703 |a DE-860 | ||
| 084 | |a SK 110 |0 (DE-625)143215: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 100 | 1 | |a Jung, Daniel |d 1981- |e Verfasser |0 (DE-588)1129609162 |4 aut | |
| 245 | 1 | 0 | |a Mathematik für Ingenieure |n Teil 2 |c von Daniel Jung ; Autor: Thorsten Schöning |
| 250 | |a 1. Auflage | ||
| 264 | 1 | |a Paderborn |b StudyHelp |c [2018]- | |
| 264 | 0 | |c [2020] | |
| 264 | 4 | |c © 2020 | |
| 300 | |a 146 Seiten |b Diagramme |c 30 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Auf der Seite des Impressums: inklusive Lernvideos, Aufgaben und Lösungen | ||
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ingenieurwissenschaften |0 (DE-588)4137304-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | 1 | |a Ingenieurwissenschaften |0 (DE-588)4137304-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Schöning, Thorsten |0 (DE-588)1211370968 |4 aut | |
| 773 | 0 | 8 | |w (DE-604)BV046744532 |g 2 |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031537484&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-031537484 | ||
Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 110 J95 -2 |
| DE-BY-FWS_katkey | 747020 |
| DE-BY-FWS_media_number | 083000523360 083000523331 |
| _version_ | 1806190509761232896 |
| adam_text | INHALT
1
LINEARE
ALGEBRA
...................................................................
9
1.1
MATRIZEN
................................................................................................................
9
1.1.1
BEZEICHNUNGEN
UND
NOTATIONEN
..........................................................................................
9
1.1.2
RECHENREGELN
.........................................................................................................................
11
1.1.3
SPEZIELLE
MATRIZEN
..................................................................................................................
13
1.1.4
SPEZIELLE
MATRIXSTRUKTUREN
.....................................................................................................
14
1.2
LINEARE
GLEICHUNGSSYSTEME
............................................................................
17
1.2.1
DEFINITION
................................................................................................................................
17
1.2.2
RECHENREGELN
.........................................................................................................................
17
1.2.3
LOESBARKEIT
EINES
LGS
.............................................................................................................
19
1.2.4
GAUSS-ALGORITHMUS
.................................................................................................................
21
1.2.5
ALTERNATIVE
LOESUNGSVERFAHREN
...............................................................................................
23
1.3
INVERSE
EINER
MATRIX
.........................................................................................
24
1.3.1
RECHENREGELN
........................................................................................................................
24
1.3.2
BERECHNUNG
DURCH
GAUSS-JORDAN-ALGORITHMUS
.....................................................................
25
1.3.3
INVERSE
EINER
2X2
UND
3X3-MATRIX
......................................................................................
25
1.4
VEKTORRAEUME
................................................................................
27
1.4.1
DEFINITION
................................................................................................................................
27
1.4.2
FAMILIE
VON
VEKTOREN
...........................................................................................................
30
1.4.3
LINEARKOMBINATION
................................................................................................................
30
1.4.4
UNTERVEKTORRAUM
...................................................................................................................
31
1.5
LINEARE
(UN)ABHAENGIGKEIT
.................................................................................
35
1.5.1
LINEARE
(UN)ABHAENGIGKEIT
-
DEFINITION
UND
PRUEFFORM
...........................................................
36
1.5.2
ERZEUGENDENSYSTEM
..............................................................................................................
38
1.5.3
BASIS
......................................................................................................................................
38
1.5.4
DIMENSION
.............................................................................................................................
36
1.5.5
KOORDINATEN
..........................................................................................................................
38
1.5.6
LINEARE
HUELLE
........................................................................................................................
39
1.5.7
BEISPIELE
ZUM
SCHAUBILD
.......................................................................................................
42
1.6
BASISTRANSFORMATIONEN
......................................................................................
46
1.6.1
SPEZIELLE
BASEN
...................................................................................................................
46
1.6.2
GRAM-SCHMIDT-VERFAHREN
......................................................................................................
47
1.6.3
BASISWECHSEL
........................................................................................................................
51
1.7
LINEARE
ABBILDUNGEN
........................................................................................
54
1.7.1
KERN
EINER
(ABBILDUNGS)MATRIX
..............................................................................................
55
1.7.2
BILD
EINER
(ABBILDUNGS)MATRIX
................................................................................................
56
1.7.3
DEFEKT
EINER
(ABBILDUNGS)MATRIX
...........................................................................................
58
1.7.4
RANG
EINER
(ABBILDUNGS)MATRIX
.............................................................................................
58
1.7.5
RANGVDIMENSIONSSATZ
.........................................................................................................
59
1.7.6
KLASSIFIZIERUNG
VON
LINEAREN
ABBILDUNGEN
(MORPHISMEN)
......................................................
60
6
INHALT
1.7.7
BASISWECHSEL
BEI
LINEAREN
ABBILDUNGEN
................................................................................
61
1.7.8
ABBILDUNGEN
DURCH
DREHMATRIZEN
/
ROTATIONSMATRIZEN
.........................................................
64
1.7.9
BEISPIEL
VON
KERN
BIS
MORPHISMEN
.........................................................................................
65
1.8
DETERMINANTE
......................................................................................................
67
1.8.1
BEDEUTUNG
DER
DETERMINANTE
.................................................................................................
67
1.8.2
RECHENREGELN
........................................................................................................................
67
1.8.3
BERECHNUNG
VON
DETERMINANTEN
...........................................................................................
68
1.8.4
ANWENDUNG
DETERMINANTEN
..................................................................................................
70
1.9
EIGENWERTE/-VEKTOREN/-RAEUME
...........................................................................
72
1.9.1
DEFINITION,
BEDEUTUNG
.............................................................................................................
72
1.9.2
EIGENWERTE
.............................................................................................................................
73
1.9.3
VIELFACHHEITEN
VON
EIGENWERTEN
...........................................................................................
74
1.9.4
EIGENVEKTOREN
........................................................................................................................
75
1.9.5
EIGENRAEUME
...........................................................................................................................
75
1.9.6
DIAGONALISIERBARKEIT
...............................................................................................................
76
1.10
DEFINITHEIT
............................................................................................................
78
1.10.1
DEFINITION
................................................................................................................................
78
1.10.2
NACHWEIS
PER
EIGENWERTE
.....................................................................................................
79
1.10.3
NACHWEIS
PER
HURWITZ-KRITERIUM/SYLVESTER-KRITERIUM/HAUPTMINOREN
....................................
79
1.11
ZUSAMMENHAENGENDE
EIGENSCHAFTEN
-
UEBERSICHT
..........................................
80
1.12
UEBUNGSAUFGABEN
-
LINEARE
ALGEBRA
................................................................
81
2
ANALYSIS
MEHRERER
VERAENDERLICHER
....................................
S?
2.1
FOLGEN
...................................................................................................................
88
2.2
STETIGKEIT
..............................................................................................................
88
2.3
DIFFERENTIATION,
ABLEITUNGEN
..............................................................................
93
2.3.1
DIFFERENZIERBARKEIT
.................................................................................................................
93
2.3.2
PARTIELLE
ABLEITUNG
..................................................................................................................
93
2.3.3
DIVERGENZ
..............................................................................................................................
96
2.3.4
ROTATION
...................................................................................................................................
96
2.3.5
JACOBI-MATRIX
.........................................................................................................................
97
2.3.6 GRADIENT
................................................................................................................................
98
2.3.7 HESSE-MATRIX
.........................................................................................................................
99
2.3.8 RICHTUNGSABLEITUNG
.............................................................................................................
100
2.3.9
ZUSAMMENHAENGE:
SCHAUBILD
DER
BEGRIFFE
...........................................................................
101
2.4
ANWENDUNGEN
DER
DIFFERENTIATION
..................................................................
101
2.4.1
TAYLORFUNKTION
.......................................................................................................................
101
2.4.2 TANGENTIALEBENEN
................................................................................................................
103
2.4.3
TOTALES
DIFFERENTIAL
................................................................................................................
103
2.4.4 EXTREMSTELLENBERECHNUNG
OHNE
NEBENBEDINGUNG
...............................................................
105
2.4.5 EXTREMSTELLENBERECHNUNG
MIT
NEBENBEDINGUNG
.................................................................
108
2.5
POTENTIALE
..........................................................................................................
113
2.5.1
EXISTENZ
EINES
POTENTIALS
-
INTEGRABILITAETSBEDINGUNGEN
.....................................................
113
2.5.2
POTENTIAL
BESTIMMEN
.............................................................................................................
114
2.6
UEBUNGSAUFGABEN
-
ANALYSIS
MEHRERER
VERAENDERLICHER
...............................
116
3
DIFFERENTIALGLEICHUNGEN
(DGL)
........................................
119
3.1
NOTATIONEN
........................................................................................................
120
3.2
TYPISIERUNGEN
...................................................................................................
121
3.2.1
TYPISIERUNG
DER
DGL
..........................................................................................................
121
INHALT
7
3.2.2
TYPISIERUNG
DER
LOESUNGSVARIANTEN
......................................................................................
124
3.3
UEBERGEORDNETE
LOESUNGSANSAETZE
...................................................................
125
3.3.1
EINORDNUNG
VON
LOESUNGSANSAETZEN
.......................................................................................
125
3.3.2
TDV
-
TRENNUNG
DER
VARIABLEN
/
TRENNUNG
DER
VERAENDERLICHEN
............................................
126
3.3.3
Y
H
:
EULER-ANSATZ
..................................................................................................................
127
3.3.4
Y
H
:
LOESUNGSFORMEL
(HOM)
......................................................................................................
129
3.3.5 SUPERPOSITION
VON
PARTIKULAEREN
LOESUNGEN
...........................................................................
129
3.3.6
Y
P
STOERGLIEDANSATZ
................................................................................................................
130
3.3.7
Y
P
.
VDK
-
VARIATION
DER
KONSTANTEN
.....................................................................................
132
3.3.8
Y
P
:
VDK
(LGS
VARIANTE)
........................................................................................................
132
3.3.9
Y
P
LOESUNGSFORMEL
(PART)
......................................................................................................
133
3.4
BEISPIELE:
LINEARE
DGL
ERSTER
ORDNUNG
.......................................................
134
3.5
BEISPIELE:
LINEARE
DGL
HOEHERER
ORDNUNG
MIT
KONSTANTEN
KOEFFIZIENTEN
..
136
3.6
BEISPIELE:
NICHT-LINEARE
DGL
ERSTER
ORDNUNG
..............................................
140
3.6.1
BERNOULLI-DGL
.......................................................................................................................
142
3.6.2
EULERHOMOGENE-DGL
...........................................................................................................
143
3.7
UEBUNGSAUFGABEN
-
DIFFERENTIALGLEICHUNGEN
.................................................
146
|
| any_adam_object | 1 |
| author | Jung, Daniel 1981- Schöning, Thorsten |
| author_GND | (DE-588)1129609162 (DE-588)1211370968 |
| author_facet | Jung, Daniel 1981- Schöning, Thorsten |
| author_role | aut aut |
| author_sort | Jung, Daniel 1981- |
| author_variant | d j dj t s ts |
| building | Verbundindex |
| bvnumber | BV046157502 |
| classification_rvk | SK 110 SK 950 |
| ctrlnum | (OCoLC)1120138248 (DE-599)BVBBV046157502 |
| discipline | Mathematik |
| edition | 1. Auflage |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV046157502 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-01T15:04:58Z |
| institution | BVB |
| isbn | 9783947506323 3947506325 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031537484 |
| oclc_num | 1120138248 |
| open_access_boolean | |
| owner | DE-83 DE-573 DE-862 DE-BY-FWS DE-703 DE-860 |
| owner_facet | DE-83 DE-573 DE-862 DE-BY-FWS DE-703 DE-860 |
| physical | 146 Seiten Diagramme 30 cm |
| publishDate | 2018 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | StudyHelp |
| record_format | marc |
| spellingShingle | Jung, Daniel 1981- Schöning, Thorsten Mathematik für Ingenieure Mathematik (DE-588)4037944-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4137304-2 (DE-588)4123623-3 |
| title | Mathematik für Ingenieure |
| title_auth | Mathematik für Ingenieure |
| title_exact_search | Mathematik für Ingenieure |
| title_full | Mathematik für Ingenieure Teil 2 von Daniel Jung ; Autor: Thorsten Schöning |
| title_fullStr | Mathematik für Ingenieure Teil 2 von Daniel Jung ; Autor: Thorsten Schöning |
| title_full_unstemmed | Mathematik für Ingenieure Teil 2 von Daniel Jung ; Autor: Thorsten Schöning |
| title_short | Mathematik für Ingenieure |
| title_sort | mathematik fur ingenieure |
| topic | Mathematik (DE-588)4037944-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| topic_facet | Mathematik Ingenieurwissenschaften Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031537484&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV046744532 |
| work_keys_str_mv | AT jungdaniel mathematikfuringenieureteil2 AT schoningthorsten mathematikfuringenieureteil2 |