Oscillations and waves:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 495 - 511 |
| Physical Description: | XIV, 523 S. Ill., graph. Darst. |
| ISBN: | 354062001X |
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MARC
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| 016 | 7 | |a 950918075 |2 DE-101 | |
| 020 | |a 354062001X |c Pp. : DM 98.00 |9 3-540-62001-X | ||
| 035 | |a (OCoLC)247383269 | ||
| 035 | |a (DE-599)BVBBV011515095 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
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| 044 | |a gw |c DE | ||
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| 082 | 0 | |a 530.12/4 | |
| 084 | |a UF 5000 |0 (DE-625)145595: |2 rvk | ||
| 084 | |a PHY 013f |2 stub | ||
| 100 | 1 | |a Kneubühl, Fritz Kurt |d 1931-1999 |e Verfasser |0 (DE-588)115520015 |4 aut | |
| 245 | 1 | 0 | |a Oscillations and waves |c Fritz K. Kneubühl |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
| 300 | |a XIV, 523 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 495 - 511 | ||
| 650 | 0 | 7 | |a Welle |0 (DE-588)4065310-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schwingung |0 (DE-588)4053999-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schwingungsgleichung |0 (DE-588)4180567-7 |2 gnd |9 rswk-swf |
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| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Schwingungsgleichung |0 (DE-588)4180567-7 |D s |
| 689 | 2 | |5 DE-604 | |
| 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=007750067&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007750067 | |
Record in the Search Index
| _version_ | 1807323547049132032 |
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| adam_text |
CONTENTS
1
INTRODUCTION
.
1
1.1
TOPICS
.
1
1.2
HELPFUL
NOTES
.
4
2
FREE
OSCILLATIONS
.
5
2.1
SURVEY
.
5
2.2
HARMONIC
OSCILLATORS
.
6
2.2.1
UNDAMPED
HARMONIC
OSCILLATORS
.
6
2.2.2
HARMONIC
OSCILLATIONS
.
9
2.2.3
PHASE
DIAGRAMS
.
12
2.2.4
HARMONIC
OSCILLATORS
WITH
DAMPING
AND
AMPLIFICATION
.
14
2.2.5
FREQUENCY
SPECTRA
.
20
2.2.6
LINEAR
SPRING-MASS
SYSTEMS
.
23
2.2.7
LINEAR
ELECTRIC
CIRCUITS
.
25
2.2.8
EQUIVALENT
NONLINEAR
OSCILLATORS
.
27
2.3
MODULATED
LINEAR
OSCILLATORS
.
29
2.3.1
REPRESENTATIONS
.
29
2.3.2
GENERAL
SOLUTIONS
.
31
2.3.3
ZEROS
AND
OSCILLATORY
BEHAVIOR
.
34
2.3.4
CHIRP
OSCILLATORS
.
35
2.3.5
APERIODICALLY
MODULATED
LINEAR
OSCILLATORS
.
37
2.3.6
OSCILLATORS
WITH
STEP
OR
PULSE
MODULATION
.
42
2.3.7
PARAMETRIC
LINEAR
OSCILLATORS
.
47
2.3.8
SINGULARITIES
AND
APPROXIMATIONS
.
65
2.4
OSCILLATORS
WITH
RELAYS
.
77
2.4.1
SWITCHING
FUNCTIONS
.
78
2.4.2
OSCILLATORS
WITH
DRY
FRICTION
.
79
2.4.3
OSCILLATORS
WITH
DRAG
.
82
2.4.4
OSCILLATORS
WITH
CONSTANT
RESTORING
FORCE
.
84
2.4.5
OSCILLATORS
WITH
CONSTANT
RESTORING
FORCE
AND
DEAD
ZONE
.
85
2.4.6
OSCILLATORS
WITH
HYSTERESIS
.
88
2.5
NONLINEAR
LIENARD
OSCILLATORS
.
89
2.5.1
GENERAL
PROPERTIES
.
90
2.5.2
DUFFING
OSCILLATORS
.
91
2.5.3
SIMPLE
PENDULUM
.
98
X
2.5.4
SMITH
OSCILLATORS
.
101
2.5.5
VAN
DER
POL
OSCILLATOR
.
103
3
FORCED
OSCILLATIONS
.
ILL
3.1
EXTERNAL
FORCES
.
ILL
3.2
EXCITATION
OF
HARMONIC
OSCILLATORS
.
112
3.2.1
TRANSIENTS
.
113
3.2.2
REAL
HARMONIC
EXCITATION
.
113
3.2.3
COMPLEX
HARMONIC
EXCITATION
.
116
3.2.4
EXCEPTIONAL
SUB-AND
ULTRAHARMONICS
.
117
3.2.5
GENERAL
PERIODIC
EXCITATION
.
120
3.2.6
BROAD-BAND
EXCITATION
.
120
3.2.7
IMPULSE
OR
SHOCK
EXCITATION
.
121
3.2.8
TRANSIENTS
AFTER
SWITCHING
ON
.
123
3.3
EXCITATION
OF
MODULATED
LINEAR
OSCILLATORS
.
126
3.3.1
STATIONARY
MOTION
AND
GREEN
FUNCTIONS
.
127
3.3.2
EXCITATION
OF
SPECIFIC
OSCILLATORS
.
128
3.3.3
FEEDBACK
.
131
3.4
EXCITATION
OF
NONLINEAR
LIENARD
OSCILLATORS
.
133
3.4.1
LAGRANGE
STABILITY
.
133
3.4.2
PERIODIC
EXCITATION
OF
DUFFING
OSCILLATORS
.
134
3.4.3
HARMONIC
EXCITATION
OF
THE
VAN
DER
POL
OSCILLATOR
.
141
4
KINEMATICS
OF
SYSTEMS
.
147
4.1
SURVEY
.
147
4.1.1
STANDARD
SYSTEMS
.
147
4.1.2
AUTONOMOUS
SYSTEMS
.
148
4.1.3
LINEAR
SYSTEMS
.
149
4.1.4
LINEARIZATION
OF
AUTONOMOUS
SYSTEMS
.
151
4.2
TWO-DIMENSIONAL
AUTONOMOUS
SYSTEMS
IN
GENERAL
.
152
4.2.1
DESCRIPTION
IN
CARTESIAN
COORDINATES
.
152
4.2.2
DESCRIPTION
IN
POLAR
COORDINATES
.
153
4.2.3
CLASSIFICATION
OF
SYSTEMS
AND
FLOWS
.
153
4.2.4
IDEAL
FLOWS
.
156
4.2.5
HAMILTONIAN
SYSTEMS
.
169
4.2.6
GRADIENT
SYSTEMS
AND
FLOWS
.
177
4.3
TWO-DIMENSIONAL
LINEAR
AUTONOMOUS
SYSTEMS
.
183
4.3.1
REPRESENTATIONS
.
183
4.3.2
ASSOCIATED
DIFFERENTIAL
EQUATIONS
.
185
4.3.3
STABILITY
.
188
4.3.4
ANALYSIS
OF
THE
CRITICAL
POINT
.
190
4.3.5
PROPAGATORS
.
195
4.4
TWO-DIMENSIONAL
QUADRATIC
AUTONOMOUS
SYSTEMS
.
198
4.4.1
CLASSIFICATION
.
198
4.4.2
TYPE
I
QUADRATIC
SYSTEMS
.
200
XI
4.4.3
TYPE
II
QUADRATIC
SYSTEMS
.
209
4.4.4
TYPE
III
QUADRATIC
SYSTEMS
.
216
4.5
LIMIT
CYCLES
OF
TWO-DIMENSIONAL
AUTONOMOUS
NONLINEAR
SYSTEMS
.
223
4.5.1
LIMIT
CYCLES
OF
AXIALLY
SYMMETRIC
SYSTEMS
.
223
4.5.2
EXISTENCE
OF
LIMIT
CYCLES
.
231
4.6
STABILITY
CRITERIA
OF
LYAPUNOV
.
232
4.6.1
CONSERVATIVE
FIELD
OF
FORCE
.
233
4.6.2
LYAPUNOV
FUNCTIONS
AND
STABILITY
.
234
4.6.3
THE
HAMILTON
FUNCTION
AS
LYAPUNOV
FUNCTION
.
236
4.7
POPULATION
DYNAMICS
.
238
4.7.1
SINGLE
POPULATIONS
.
239
4.7.2
THE
LOTKA-VOL
TERRA
MODEL
.
240
4.8
CONSERVATIVE
LINEAR
MECHANICAL
SYSTEMS
.
243
4.8.1
LAGRANGE
MECHANICS
.
244
4.8.2
OSCILLATIONS
.
244
4.8.3
MOLECULAR
VIBRATIONS
.
246
4.9
TIME-DEPENDENT
LINEAR
SYSTEMS
.
247
4.9.1
HOMOGENOUS
SYSTEMS
OF
ARBITRARY
DIMENSIONS
.
247
4.9.2
STABILITY
OF
HOMOGENEOUS
SYSTEMS
.
252
4.9.3
TWO-DIMENSIONAL
HOMOGENEOUS
SYSTEMS
.
253
4.9.4
INHOMOGENEOUS
SYSTEMS
.
257
4.10
THREE-DIMENSIONAL
SYSTEMS
AND
FLOWS
.
258
4.10.1
CONCEPTS
OF
FLUID
KINEMATICS
.
259
4.10.2
GRADIENT
SYSTEMS
AS
POTENTIAL
FLOWS
.
267
4.10.3
FLOWS
WITHOUT
SOURCES
OF
SINKS
.
270
4.10.4
DECOMPOSITION
OF
VELOCITY
FIELDS
.
273
4.10.5
THREE
AND
HIGHER
DIMENSIONAL
D'ALEMBERT
SYSTEMS
.
274
5
TRANSFER
SYSTEMS
.
276
5.1
LINEAR
TIME-INVARIANT
SYSTEMS
.
276
5.1.1
BASIC
CONCEPTS
.
276
5.1.2
SYSTEM
OPERATORS
OF
LTI
SYSTEMS
.
277
5.1.3
IMPUL
SE
RESPONSE
FUNCTIONS
.
278
5.1.4
TRANSIENTS
.
280
5.1.5
RESPONSE
EVALUATION
BY
LAPLACE
TRANSFORMATION
.
282
5.1.6
FOURIER
ANALYSIS
.
282
5.1.7
AVERAGES
AND
CORRELATIONS
.
284
5.1.8
DIFFERENTIAL
TRANSFER
EQUATIONS
.
287
5.1.9
NONLINEAR
TIME-INVARIANT
SYSTEMS
.
289
5.2
CIRCUITS
.
289
5.2.1
FEEDBACK-CONTROL
SYSTEMS
.
290
5.2.2
RESONANT
OSCILLATING
CIRCUITS
.
291
5.3
DELAY
SYSTEMS
.
294
5.3.1
NORMALIZED
DELAY
SYSTEM
.
294
XN
5.3.2
DELAY
SYSTEMS
IN
CIRCUITS
.
295
5.3.3
NONLINEAR
DELAY
SYSTEMS
.
298
6
INSTABILITY
AND
CHAOS
.
300
6.1
BIFURCATION
.
300
6.1.1
BIFURCATION
IN
AUTONOMOUS
SYSTEMS
.
300
6.1.2
BIFURCATION
IN
ONE
DIMENSION
.
302
6.1.3
SADDLE-NODE
BIFURCATION
.
303
6.1.4
TRANSCRITICAL
BIFURCATION
.
306
6.1.5
PITCHFORK
BIFURCATION
.
308
6.1.6
ROTATING
PENDUL
UM
.
311
6.1.7
HOPF
BIFURCATION
.
314
6.2
DETERMINISTIC
CHAOS
.
317
6.2.1
CRITERIA
FOR
CHAOS
.
319
6.2.2
ROUTES
TO
CHAOS
.
320
6.3
LORENZ
MODEL
.
322
6.3.1
STABILITY
CONSIDERATIONS
.
323
6.3.2
STRANGE
LORENZ
ATTRACTOR
.
325
6.4
LOGISTIC
MAP
.
326
7
LINEAR
WAVES
.
331
7.1
CLASSIFICATION
OF
WAVES
.
331
7.1.1
SCALAR
AND
VECTORIAL
WAVES
.
331
7.1.2
LONGITUDINAL
AND
TRANSVERSAL
WAVES
.
334
7.1.3
EQUIVALENCE
OF
SCALAR
AND
LONGITUDINAL
WAVES
.
340
7.1.4
LINEAR
WAVES
.
341
7.2
HARMONIC
WAVES
.
342
7.2.1
DESCRIPTION
.
342
7.2.2
DISPERSION
RELATIONS
.
344
7.2.3
DIFFERENTIAL
OPERATORS
.
347
7.2.4
HARMONIC
ELECTROMAGNETIC
WAVES
IN
VACUUM
.
349
7.3
WAVE
VELOCITIES
AND
DISPERSION
.
356
7.3.1
PHASE
VELOCITY
.
358
7.3.2
GROUP
OR
ENVELOPE
VELOCITY
.
359
7.3.3
PHASE
DISPERSION
.
360
7.3.4
GROUP
DISPERSION
.
362
7.3.5
SURFACE
WAVES
OF
LIQUIDS
.
363
7.3.6
ENVELOPE
EQUATIONS
.
365
7.4
LINEAR
WAVES
IN
HOMOGENEOUS
ISOTROPIC
MEDIA
.
368
7.4.1
HERTZ
EQUATION
.
369
7.4.2
REDUCED
HERTZ
EQUATION
.
370
7.4.3
LINEAR
KLEIN-GORDON
EQUATION
.
371
7.4.4
TELEGRAPH
EQUATION
.
374
7.4.5
LINEAR
DIFFUSION
EQUATION
.
377
7.4.6
LINEARIZED
KORTEWEG-DE
VRIES
EQUATION
.
379
XM
7.4.7
LINEAR
SCHRODINGER
EQUATION
.
380
7.5
ELECTROMAGNETIC
WAVES
IN
LINEAR
MEDIA
.
382
7.5.1
CHARACTERIZATION
OF
THE
MEDIA
.
382
7.5.2
DISPERSION
OF
HARMONIC
WAVES
.
385
7.5.3
TRANSIENT
WAVES
.
389
7.6
LINEAR
WAVES
IN
PERIODIC
MEDIA
AND
STRUCTURES
.
391
7.6.1
INFINITE
CHAINS
WITH
IDENTICAL
SPRINGS
AND
MASSES
.
391
7.6.2
INFINITE
CHAINS
WITH
IDENTICAL
SPRINGS
AND
ALTERNATING
MASSES
.
394
7.6.3
ELECTROMAGNETIC
WAVES
IN
PERIODIC
MEDIA
.
398
7.6.4
WAVE
MECHANICS
OF
A
PARTICLE
IN
A
PERIODIC
POTENTIAL
.
408
8
NONLINEAR
WAVES
.
413
8.1
WAVE
EQUATIONS
AND
SOLITARY
WAVES
.
413
8.2
NONLINEAR
WAVES
WITHOUT
DISPERSION
.
416
8.3
NONLINEAR
DIFFUSION
.
418
8.4
KORTEWEG-DE
VRIES
EQUATION
.
420
8.4.1
CONSERVATION
LAWS
.
421
8.4.2
TRAVELING
WAVES
.
421
8.4.3
KORTEWEG-DE
VRIES
SOLITONS
.
423
8.4.4
CNOIDAL
KORTEWEG-DE
VRIES
WAVES
.
425
8.4.5
GENERALIZED
KORTEWEG-DE
VRIES
EQUATION
.
426
8.5
NONLINEAR
KLEIN-GORDON
EQUATIONS
.
427
8.5.1
TRAVELING
WAVES
.
429
8.5.2
SINE-GORDON
SOLITONS
.
430
8.5.3
CNOIDAL
SINE-GORDON
WAVES
.
433
8.6
NONLINEAR
SCHRODINGER
EQUATION
.
435
8.6.1
NONLINEAR
KERR
MEDIA
.
436
8.6.2
SOLITONS
IN
KERR
MEDIA
.
439
8.6.3
KERR
MEDIA
WITH
GAIN
.
441
8.7
MAXWELL-BLOCH
EQUATIONS
.
442
8.8
TODA
CHAIN
.
447
8.8.1
TODA
SOLITONS
.
448
8.8.2
CNOIDAL
TODA
WAVES
.
449
9
STANDING
WAVES
.
451
9.1
WAVE
FORM
AND
BOUNDARY
CONDITIONS
.
452
9.2
FREE
VIBRATIONS
OF
A
STRING
.
453
9.3
FREE
STANDING
WAVES
ON
MEMBRANES
.
456
9.3.1
MODES
OF
A
RECTANGULAR
MEMBRANE
.
457
9.3.2
MODES
OF
A
CIRCULAR
MEMBRANE
.
458
9.4
FREE
ACOUSTIC
STANDING
WAVES
IN
CAVITIES
.
460
9.4.1
TRAVELING
AND
STANDING
SPHERICAL
WAVES
.
460
9.4.2
ACOUSTIC
MODES
OF
A
SPHERICAL
CAVITY
.
462
9.5
STURM-LIOUVILLE
WAVE
PATTERNS
.
466
XIV
9.5.1
STURM-LIOUVILLE
SYSTEMS
.
467
9.5.2
EIGENVALUES
AND
EIGENFUNCTIONS
.
469
9.6
FREE
NONLINEAR
STANDING
WAVES
.
471
9.6.1
GRADIENT
DOMINATED
HERTZ
WAVES
.
471
9.6.2
EULER-PAINLEVE
WAVES
.
473
9.7
FORCED
STANDING
WAVES
.
474
9.7.1
FORCED
WAVES
ON
A
STRING
.
474
9.7.2
FORCED
WAVES
ON
A
TELEGRAPH
LINE
.
475
9.7.3
FORCED
GRADIENT
DOMINATED HERTZ
WAVES
.
476
9.7.4
FORCED
BIOCHE
WAVES
.
477
A
APPENDIX
.
479
A.L
FOURIER
SERIES
.
479
A.
1.1
GENERAL
RULES
.
479
A.
1.2
REAL
PERIODIC
FUNCTIONS
.
480
A.2
FOURIER
TRANSFORMATION
.
484
A.2.1
GENERAL
RULES
.
484
A.2.2
REAL
FUNCTIONS
.
485
A.3
LAPLACE
TRANSFORMATION
.
487
A.3.1
GENERAL
RULES
.
487
A.
3.2
HEAVISIDE
AND
DIRAC
FUNCTIONS
.
488
A.
3.3
REAL
FUNCTIONS
.
489
A.4
CONVOLUTION
(FALTUNG)
.
490
A.4.
1
GENERAL
RULES
.
490
A.4.
2
HEAVISIDE
UNIT
STEP
.
492
A.4.3
SPECIAL
REAL
FUNCTIONS
.
493
AAA
HILBERT
TRANSFORMATION
.
494
REFERENCES
.
495
B
BOOKS
.
495
J
PUBLICATIONS
IN
JOURNALS
.
507
INDEX
.
513 |
| any_adam_object | 1 |
| author | Kneubühl, Fritz Kurt 1931-1999 |
| author_GND | (DE-588)115520015 |
| author_facet | Kneubühl, Fritz Kurt 1931-1999 |
| author_role | aut |
| author_sort | Kneubühl, Fritz Kurt 1931-1999 |
| author_variant | f k k fk fkk |
| building | Verbundindex |
| bvnumber | BV011515095 |
| classification_rvk | UF 5000 |
| classification_tum | PHY 013f |
| ctrlnum | (OCoLC)247383269 (DE-599)BVBBV011515095 |
| dewey-full | 530.12/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12/4 |
| dewey-search | 530.12/4 |
| dewey-sort | 3530.12 14 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV011515095 |
| illustrated | Illustrated |
| indexdate | 2024-08-14T01:14:06Z |
| institution | BVB |
| isbn | 354062001X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007750067 |
| oclc_num | 247383269 |
| open_access_boolean | |
| owner | DE-29T DE-19 DE-BY-UBM DE-703 DE-20 DE-91G DE-BY-TUM DE-706 DE-634 DE-83 DE-11 |
| owner_facet | DE-29T DE-19 DE-BY-UBM DE-703 DE-20 DE-91G DE-BY-TUM DE-706 DE-634 DE-83 DE-11 |
| physical | XIV, 523 S. Ill., graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| spelling | Kneubühl, Fritz Kurt 1931-1999 Verfasser (DE-588)115520015 aut Oscillations and waves Fritz K. Kneubühl Berlin [u.a.] Springer 1997 XIV, 523 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 495 - 511 Welle (DE-588)4065310-9 gnd rswk-swf Schwingung (DE-588)4053999-4 gnd rswk-swf Schwingungsgleichung (DE-588)4180567-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Schwingung (DE-588)4053999-4 s DE-604 Welle (DE-588)4065310-9 s Schwingungsgleichung (DE-588)4180567-7 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007750067&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kneubühl, Fritz Kurt 1931-1999 Oscillations and waves Welle (DE-588)4065310-9 gnd Schwingung (DE-588)4053999-4 gnd Schwingungsgleichung (DE-588)4180567-7 gnd |
| subject_GND | (DE-588)4065310-9 (DE-588)4053999-4 (DE-588)4180567-7 (DE-588)4123623-3 |
| title | Oscillations and waves |
| title_auth | Oscillations and waves |
| title_exact_search | Oscillations and waves |
| title_full | Oscillations and waves Fritz K. Kneubühl |
| title_fullStr | Oscillations and waves Fritz K. Kneubühl |
| title_full_unstemmed | Oscillations and waves Fritz K. Kneubühl |
| title_short | Oscillations and waves |
| title_sort | oscillations and waves |
| topic | Welle (DE-588)4065310-9 gnd Schwingung (DE-588)4053999-4 gnd Schwingungsgleichung (DE-588)4180567-7 gnd |
| topic_facet | Welle Schwingung Schwingungsgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007750067&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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