Distribution theory: with applications in engineering and physics
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2013
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XII, 381 S. graph. Darst. 25 cm |
| ISBN: | 352741083X 9783527410835 |
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
PREFACE XI
1 INTRODUCTION TO THE DISTRIBUTION THEORY 1
1.1 SHORT HISTORY 1
1.2 FUNDAMENTAL CONCEPTS AND FORMULAE 2 1.2.1 NORMED VECTOR SPACES:
METRIC SPACES 3 1.2.2 SPACES O F TEST FUNCTIONS 6 1.2.2.1 THE SPACE )
M ( Q ) 9 1.2.2.2 THE SPACE () 10 1.2.2.3 THE SPACE 11 1.2.2.4 THE
SPACE ) (THE SCHWARTZ SPACE) 11 1.2.2.5 THE SPACE S (THE SPACE
FUNCTIONS WHICH DECREASE RAPIDLY) 14 1.2.3 SPACES O F DISTRIBUTIONS 15
1.2.3.1 EQUALITY O F TWO DISTRIBUTIONS: SUPPORT O F A DISTRIBUTION 20
1.2.4 CHARACTERIZATION THEOREMS O F DISTRIBUTIONS 27 1.3 OPERATIONS WITH
DISTRIBUTIONS 31 1.3.1 THE CHANGE O F VARIABLES IN DISTRIBUTIONS 31
1.3.2 TRANSLATION, SYMMETRY AND HOMOTHETY O F DISTRIBUTIONS 36 1.3.3
DIFFERENTIATION O F DISTRIBUTIONS 40
1.3.3.1 PROPERTIES O F THE DERIVATIVE OPERATOR 45 1.3.4 THE FUNDAMENTAL
SOLUTION O F A LINEAR DIFFERENTIAL OPERATOR 58 1.3.5 THE DERIVATION O F
THE HOMOGENEOUS DISTRIBUTIONS 62 1.3.6 DIRAC REPRESENTATIVE SEQUENCES:
CRITERIA FOR THE REPRESENTATIVE DIRAC
SEQUENCES 69
1.3.7 DISTRIBUTIONS DEPENDING ON A PARAMETER 81 1.3.7.1 DIFFERENTIATION
O F DISTRIBUTIONS DEPENDING ON A PARAMETER 81 1.3.7.2 INTEGRATION O F
DISTRIBUTIONS DEPENDING ON A PARAMETER 84 1.3.8 DIRECT PRODUCT AND
CONVOLUTION PRODUCT O F FUNCTIONS AND
DISTRIBUTIONS 88
1.3.8.1 PROPERTIES OF THE DIRECT PRODUCT 90 1.3.8.2 THE CONVOLUTION
PRODUCT OF DISTRIBUTIONS 92 1.3.8.3 THE CONVOLUTION O F DISTRIBUTIONS
DEPENDING ON A PARAMETER: PROPERTIES 102
HTTP://D-NB.INFO/1027115888
IMAGE 2
VI | CONTENTS
1.3.8.4 THE PARTIAL CONVOLUTION PRODUCT FOR FUNCTIONS AND DISTRIBUTIONS
105
1.3.9 PARTIAL CONVOLUTION PRODUCT O F FUNCTIONS 111
2 INTEGRAL TRANSFORMS O F DISTRIBUTIONS 113 2.1 FOURIER SERIES AND
SERIES OF DISTRIBUTIONS 113 2.1.1 SEQUENCES AND SERIES OF DISTRIBUTIONS
113 2.1.2 EXPANSION O F DISTRIBUTIONS INTO FOURIER SERIES 116 2.1.3
EXPANSION O F SINGULAR DISTRIBUTIONS INTO FOURIER SERIES 128 2.2 FOURIER
TRANSFORMS O F FUNCTIONS AND DISTRIBUTIONS 129 2.2.1 FOURIER TRANSFORMS
O F FUNCTIONS 129
2.2.2 FOURIER TRANSFORM AND THE CONVOLUTION PRODUCT 131 2.2.3 PARTIAL
FOURIER TRANSFORM O F FUNCTIONS 132 2.2.4 FOURIER TRANSFORM O F
DISTRIBUTIONS FROM THE SPACES S' AND )'(R") 133 2.2.4.1 PROPERTIES O F
THE FOURIER TRANSFORM 136
2.2.4.2 FOURIER TRANSFORM O F THE DISTRIBUTIONS FROM THE SPACE 0'(R")
139 2.2.4.3 FOURIER TRANSFORM AND THE PARTIAL CONVOLUTION PRODUCT 144
2.3 LAPLACE TRANSFORMS O F FUNCTIONS AND DISTRIBUTIONS 145 2.3.1 LAPLACE
TRANSFORMS OF FUNCTIONS 146 2.3.2 LAPLACE TRANSFORMS OF DISTRIBUTIONS
149
3 VARIATIONAL CALCULUS AND DIFFERENTIAL EQUATIONS IN DISTRIBUTIONS 151
3.1 VARIATIONAL CALCULUS IN DISTRIBUTIONS 151 3.1.1 EQUATIONS O F THE
EULER-POISSON TYPE 158 3.2 ORDINARY DIFFERENTIAL EQUATIONS 160 3.3
CONVOLUTION EQUATIONS 166 3.3.1 CONVOLUTION ALGEBRAS 166 3.3.2
CONVOLUTION ALGEBRA S)' + : CONVOLUTION EQUATIONS IN ' + 170 3.4 THE
CAUCHY PROBLEM FOR LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT
COEFFICIENTS 174
3.5 PARTIAL DIFFERENTIAL EQUATIONS: FUNDAMENTAL SOLUTIONS AND SOLVING
THE CAUCHY PROBLEM 177 3.5.1 FUNDAMENTAL SOLUTION FOR THE LONGITUDINAL
VIBRATIONS O F VISCOELASTIC BARS O F MAXWELL TYPE 180 3.6 WAVE EQUATION
AND THE SOLUTION O F THE CAUCHY PROBLEM 184 3.7 HEAT EQUATION AND CAUCHY
PROBLEM SOLUTION 187 3.8 POISSON EQUATION: FUNDAMENTAL SOLUTIONS 189 3.9
GREEN'S FUNCTIONS: METHODS O F CALCULATION 190 3.9.1 HEAT CONDUCTION
EQUATION 190 3.9.1.1 GENERALIZED POISSON EQUATION 194 3.9.2 GREEN'S
FUNCTION FOR THE VIBRATING STRING 197
4 REPRESENTATION IN DISTRIBUTIONS O F MECHANICAL AND PHYSICAL QUANTITIES
201 4.1 REPRESENTATION OF CONCENTRATED FORCES 201 4.2 REPRESENTATION O F
CONCENTRATED MOMENTS 206 4.2.1 CONCENTRATE MOMENT O F LINEAR DIPOLE TYPE
208
IMAGE 3
CONTENTS | VII
4.2.2 ROTATIONAL CONCENTRATED MOMENT (CENTER O F ROTATION) 210
4.2.3 CONCENTRATED MOMENT O F PLANE DIPOLE TYPE (CENTER O F DILATATION
OR CONTRACTION) 212 4.3 REPRESENTATION IN DISTRIBUTIONS O F THE SHEAR
FORCES AND THE BENDING MOMENTS 213
4.3.1 CONCENTRATED FORCE OF MAGNITUDE P APPLIED AT THE POINT C E [A, B]
217 4.3.2 CONCENTRATED MOMENT O F MAGNITUDE M APPLIED AT THE POINT C E
[A, B] 217 4.3.3 DISTRIBUTED FORCES O F INTENSITY Q E !}",.([, B]) 218
4.4 REPRESENTATION BY DISTRIBUTIONS O F THE MOMENTS O F A MATERIAL
SYSTEM 220
4.5 REPRESENTATION I N DISTRIBUTIONS O F ELECTRICAL QUANTITIES 225 4.5.1
VOLUME AND SURFACE POTENTIAL O F THE ELECTROSTATIC FIELD 225 4.5.2
ELECTROSTATIC FIELD 228 4.5.3 ELECTRIC POTENTIAL O F SINGLE AND DOUBLE
LAYERS 232 4.6 OPERATIONAL FORM O F THE CONSTITUTIVE LAW O F
ONE-DIMENSIONAL
VISCOELASTIC SOLIDS 235
5 APPLICATIONS O F THE DISTRIBUTION THEORY IN MECHANICS 241 5.1
NEWTONIAN MODEL O F MECHANICS 241 5.2 THE MOTION O F A HEAVY MATERIAL
POINT IN AIR 243 5.3 LINEAR OSCILLATOR 246
5.3.1 THE CAUCHY PROBLEM AND THE PHENOMENON O F RESONANCE 246 5.4
TWO-POINT PROBLEM 249
5.5 BENDING O F THE STRAIGHT BARS 250
6 APPLICATIONS O F THE DISTRIBUTION THEORY TO THE MECHANICS O F THE
LINEAR ELASTIC BODIES 253 6.1 THE MATHEMATICAL MODEL O F THE LINEAR
ELASTIC BODY 253 6.2 EQUATIONS O F THE ELASTICITY THEORY 256 6.3
GENERALIZED SOLUTION IN SD'(M 2 ) REGARDING THE PLANE ELASTIC
PROBLEMS 258
6.4 GENERALIZED SOLUTION IN 0'(R) O F THE STATIC PROBLEM O F THE
ELASTIC HALF-PLANE 264 6.5 GENERALIZED SOLUTION, IN DISPLACEMENTS, FOR
THE STATIC PROBLEM O F THE ELASTIC SPACE 268
7 APPLICATIONS O F THE DISTRIBUTION THEORY TO LINEAR VISCOELASTIC BODIES
273 7.1 THE MATHEMATICAL MODEL O F A LINEAR VISCOELASTIC SOLID 273 7.2
MODELS O F ONE-DIMENSIONAL VISCOELASTIC SOLIDS 275 7.3 VISCOELASTICITY
THEORY EQUATIONS: CORRESPONDENCE PRINCIPLE 281 7.3.1 VISCOELASTICITY
THEORY EQUATIONS 281 7.3.2 CORRESPONDENCE PRINCIPLE 283
8 APPLICATIONS O F THE DISTRIBUTION THEORY IN ELECTRICAL ENGINEERING 285
8.1 STUDY O F THE RLC CIRCUIT: CAUCHY PROBLEM 285 8.2 COUPLED
OSCILLATING CIRCUIT: CAUCHY PROBLEM 290
IMAGE 4
VIII | CONTENTS
8.3 ADMITTANCE AND IMPEDANCE O F THE RLC CIRCUIT 294
8.4 QUADRUPOLES 295
9 APPLICATIONS O F THE DISTRIBUTION THEORY IN THE STUDY O F ELASTIC BARS
301 9.1 LONGITUDINAL VIBRATIONS O F ELASTIC BARS 301 9.1.1 EQUATIONS O F
MOTION EXPRESSED IN DISPLACEMENTS AND IN STRESSES: FORMULATION O F THE
PROBLEMS WITH BOUNDARY-INITIAL CONDITIONS 301
9.1.2 FORCED LONGITUDINAL VIBRATIONS O F A BAR WITH BOUNDARY CONDITIONS
EXPRESSED IN DISPLACEMENTS 303 9.1.3 FORCED VIBRATIONS O F A BAR WITH
BOUNDARY CONDITIONS EXPRESSED IN STRESSES 306 9.2 TRANSVERSE VIBRATIONS
O F ELASTIC BARS 308 9.2.1 DIFFERENTIAL EQUATION IN DISTRIBUTIONS OF
TRANSVERSE VIBRATIONS O F ELASTIC
BARS 308
9.2.2 FREE VIBRATIONS O F AN INFINITE BAR 311 9.2.3 FORCED TRANSVERSE
VIBRATIONS O F THE BARS 312 9.2.4 BENDING O F ELASTIC BARS ON ELASTIC
FOUNDATION 315 9.3 TORSIONAL VIBRATION O F THE ELASTIC BARS 331 9.3.1
DIFFERENTIAL EQUATION O F TORSIONAL VIBRATIONS O F THE ELASTIC BARS WITH
CIRCULAR CROSS-SECTION 331 9.3.2 THE ANALOGY BETWEEN LONGITUDINAL
VIBRATIONS AND TORSIONAL VIBRATIONS O F ELASTIC BARS 335 9.3.3 TORSIONAL
VIBRATION O F FREE BARS EMBEDDED AT ONE END AND FREE AT THE
OTHER END 336
9.3.4 FORCED TORSIONAL VIBRATIONS O F A BAR EMBEDDED AT THE ENDS 338
10 APPLICATIONS O F THE DISTRIBUTION THEORY IN THE STUDY O F
VISCOELASTIC BARS 343 10.1 THE EQUATIONS O F THE LONGITUDINAL VIBRATIONS
O F THE VISCOELASTIC BARS IN THE DISTRIBUTIONS SPACE ' + 343 10.2
LONGITUDINAL VIBRATIONS O F MAXWELL TYPE VISCOELASTIC BARS:
SOLUTION IN THE DISTRIBUTIONS SPACE )' + 345 10.3 STEADY-STATE
LONGITUDINAL VIBRATIONS FOR THE MAXWELL BAR 347 10.4 QUASI-STATIC
PROBLEMS O F VISCOELASTIC BARS 349 10.4.1 BENDING O F THE VISCOELASTIC
BARS 350 10.4.2 BENDING O F A VISCOELASTIC BAR O F KELVIN-VOIGT TYPE 352
10.4.3 BENDING O F A VISCOELASTIC BAR O F MAXWELL TYPE 352 10.5
TORSIONAL VIBRATIONS EQUATION O F VISCOELASTIC BARS IN THE DISTRIBUTIONS
SPACE JD^_ 354
10.6 TRANSVERSE VIBRATIONS O F VISCOELASTIC BARS ON VISCOELASTIC
FOUNDATION 357 10.6.1 THE GENERALIZED EQUATION IN DISTRIBUTIONS SPACE
D'(K 2 ) OF THE TRANSVERSE VIBRATIONS O F VISCOELASTIC BARS ON
VISCOELASTIC
FOUNDATION 357
10.6.2 GENERALIZED CAUCHY PROBLEM SOLUTION FOR TRANSVERSE VIBRATIONS O F
THE ELASTIC BARS ON KELVIN-VOIGT TYPE VISCOELASTIC FOUNDATION 359
IMAGE 5
CONTENTS | IX
10.6.2.1 PARTICULAR CASES 363
11 APPLICATIONS O F THE DISTRIBUTION THEORY IN PHYSICS 365 11.1
APPLICATIONS O F THE DISTRIBUTION THEORY IN ACOUSTICS 365 11.1.1 DOPPLER
EFFECT FOR A ONE-DIMENSIONAL SOUND SOURCE 365 11.1.2 DOPPLER EFFECT IN
THE PRESENCE O F WIND 367 11.2 APPLICATIONS OF THE DISTRIBUTION THEORY
IN OPTICS 371 11.2.1 THE PHENOMENON O F DIFFRACTION AT INFINITY 371
11.2.2 DIFFRACTION O F FRESNEL TYPE 374
REFERENCES 377
INDEX 379 |
| any_adam_object | 1 |
| author | Teodorescu, Petre P. 1929- Kecs, Wilhelm W. Toma, Antonela |
| author_GND | (DE-588)133443086 |
| author_facet | Teodorescu, Petre P. 1929- Kecs, Wilhelm W. Toma, Antonela |
| author_role | aut aut aut |
| author_sort | Teodorescu, Petre P. 1929- |
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| building | Verbundindex |
| bvnumber | BV041042630 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)843406317 (DE-599)DNB1027115888 |
| dewey-full | 515.782 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.782 |
| dewey-search | 515.782 |
| dewey-sort | 3515.782 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV041042630 |
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| indexdate | 2024-08-03T00:40:19Z |
| institution | BVB |
| isbn | 352741083X 9783527410835 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026020007 |
| oclc_num | 843406317 |
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| owner | DE-29T DE-19 DE-BY-UBM DE-11 DE-83 |
| owner_facet | DE-29T DE-19 DE-BY-UBM DE-11 DE-83 |
| physical | XII, 381 S. graph. Darst. 25 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Wiley-VCH |
| record_format | marc |
| spelling | Teodorescu, Petre P. 1929- Verfasser (DE-588)133443086 aut Distribution theory with applications in engineering and physics Petre P. Teodorescu ; Wilhelm W. Kecs and Antonela Toma Weinheim Wiley-VCH 2013 XII, 381 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Literaturangaben Distributionstheorie (DE-588)4150254-1 gnd rswk-swf Lehrbuch gnd rswk-swf Distributionstheorie (DE-588)4150254-1 s Lehrbuch f DE-604 Kecs, Wilhelm W. Verfasser aut Toma, Antonela Verfasser aut Erscheint auch als Online-Ausgabe, PDF 978-3-527-65364-5 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4166018&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026020007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Teodorescu, Petre P. 1929- Kecs, Wilhelm W. Toma, Antonela Distribution theory with applications in engineering and physics Distributionstheorie (DE-588)4150254-1 gnd |
| subject_GND | (DE-588)4150254-1 |
| title | Distribution theory with applications in engineering and physics |
| title_auth | Distribution theory with applications in engineering and physics |
| title_exact_search | Distribution theory with applications in engineering and physics |
| title_full | Distribution theory with applications in engineering and physics Petre P. Teodorescu ; Wilhelm W. Kecs and Antonela Toma |
| title_fullStr | Distribution theory with applications in engineering and physics Petre P. Teodorescu ; Wilhelm W. Kecs and Antonela Toma |
| title_full_unstemmed | Distribution theory with applications in engineering and physics Petre P. Teodorescu ; Wilhelm W. Kecs and Antonela Toma |
| title_short | Distribution theory |
| title_sort | distribution theory with applications in engineering and physics |
| title_sub | with applications in engineering and physics |
| topic | Distributionstheorie (DE-588)4150254-1 gnd |
| topic_facet | Distributionstheorie Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4166018&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026020007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT teodorescupetrep distributiontheorywithapplicationsinengineeringandphysics AT kecswilhelmw distributiontheorywithapplicationsinengineeringandphysics AT tomaantonela distributiontheorywithapplicationsinengineeringandphysics |