Functional equations and modelling in science and engineering:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1992
|
| Schriftenreihe: | Pure and applied mathematics
161 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 328 S. graph. Darst. |
| ISBN: | 082478717X |
Internformat
MARC
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| 245 | 1 | 0 | |a Functional equations and modelling in science and engineering |c Enrique Castillo ; Maria Reyes Ruiz-Cobo |
| 264 | 1 | |a New York [u.a.] |b Dekker |c 1992 | |
| 300 | |a XV, 328 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 161 | |
| 650 | 4 | |a Modèles mathématiques | |
| 650 | 4 | |a Équations fonctionnelles | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Functional equations | |
| 650 | 4 | |a Mathematical models | |
| 650 | 0 | 7 | |a Funktionalgleichung |0 (DE-588)4018923-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804119665127981056 |
|---|---|
| adam_text | Contents
Preface v
List of figures xiii
List of tables xv
1 Introduction and motivation 1
1.1 Introduction 1
1.2 Aim of the book 2
1.3 Organization of the book 2
1.4 Basic concepts and definitions 3
1.5 Exercises 9
2 Equations for one function of one variable 11
2.1 Introduction 11
2.2 Homogeneous functions 12
2.3 A general type of equation 18
2.4 Cauchy s equations 23
2.5 Jensen s equation 31
2.6 Generalizations of Cauchy s equations 32
2.7 D Alembert s functional equation 38
2.8 Linear difference equations 38
2.8.1 Solution of the homogeneous equation 38
2.8.2 Particular solution of the complete equation 39
2.9 Exercises 44
3 Equations with several functions in one variable 45
3.1 Introduction 45
3.2 Pexider s equations 46
3.3 Other generalizations 49
ix
x CONTENTS
n
3.4 Equations of the form £ fk(x)9k{y) = 0 52
k=l
3.5 Other equations 61
3.6 Exercises 69
4 Equations for one function of several variables 71
4.1 Introduction 71
4.2 Generalizations of Cauchy s and Jensen s equations 71
4.3 Other equations 76
4.4 Application to iterative methods 79
4.5 Exercises 80
5 Equations with functions of several variables 81
5.1 Introduction 81
5.2 Generalization of Pexider s and Jensen s equations 81
5.3 Generalization of Sincov s equation 84
5.4 A general equation 86
5.5 The associativity equation 94
5.6 The transitivity equation 96
5.7 The bisymmetry equation 99
5.8 The transformation equation 100
5.9 Exercises 103
6 Functional equations and differential equations 105
6.1 Introduction 105
6.2 From functional equations to differential equations 106
6.2.1 Reduction to ordinary differential equations 106
6.2.2 Reduction to partial differential equations 122
6.3 From differential equations to functional equations 147
6.4 Exercises 154
7 Vector and matrix equations 155
7.1 Introduction 155
7.2 Cauchy s equation 155
7.3 Pexider s equation 157
7.4 Sincov s equation and generalizations 158
7.5 Exercises 165
8 Miscellaneous applications 167
8.1 Introduction 167
8.2 Laws of science 168
8.3 Taxation functions 178
8.3.1 Restrictions to be imposed on taxation functions . . 179
CONTENTS xi
8.3.2 Compatible tax functions 185
8.4 A statistical model for lifetime analysis 192
8.4.1 Theoretical derivation of the proposed model .... 193
8.5 Nomograms and probability papers 199
8.5.1 Nomograms , 199
8.5.2 Probability papers 208
8.6 Fundamental formula for polyhedra 212
8.7 Price and advertising policy 222
8.8 Price and quantity levels 226
8.9 Price indices 229
8.10 Estimation of a multinomial model 233
8.11 Interest rates 236
8.12 Exercises 238
Bibliography 239
Index 325
|
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| discipline | Mathematik |
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| id | DE-604.BV005454438 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:29:48Z |
| institution | BVB |
| isbn | 082478717X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003412474 |
| oclc_num | 25550487 |
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| owner | DE-384 DE-703 DE-521 DE-11 |
| owner_facet | DE-384 DE-703 DE-521 DE-11 |
| physical | XV, 328 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Castillo, Enrique 1946- Verfasser (DE-588)124179266 aut Functional equations and modelling in science and engineering Enrique Castillo ; Maria Reyes Ruiz-Cobo New York [u.a.] Dekker 1992 XV, 328 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 161 Modèles mathématiques Équations fonctionnelles Mathematisches Modell Functional equations Mathematical models Funktionalgleichung (DE-588)4018923-5 gnd rswk-swf Funktionalgleichung (DE-588)4018923-5 s DE-604 Reyes Ruiz-Cobo, Maria Verfasser aut Pure and applied mathematics 161 (DE-604)BV000001885 161 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003412474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Castillo, Enrique 1946- Reyes Ruiz-Cobo, Maria Functional equations and modelling in science and engineering Pure and applied mathematics Modèles mathématiques Équations fonctionnelles Mathematisches Modell Functional equations Mathematical models Funktionalgleichung (DE-588)4018923-5 gnd |
| subject_GND | (DE-588)4018923-5 |
| title | Functional equations and modelling in science and engineering |
| title_auth | Functional equations and modelling in science and engineering |
| title_exact_search | Functional equations and modelling in science and engineering |
| title_full | Functional equations and modelling in science and engineering Enrique Castillo ; Maria Reyes Ruiz-Cobo |
| title_fullStr | Functional equations and modelling in science and engineering Enrique Castillo ; Maria Reyes Ruiz-Cobo |
| title_full_unstemmed | Functional equations and modelling in science and engineering Enrique Castillo ; Maria Reyes Ruiz-Cobo |
| title_short | Functional equations and modelling in science and engineering |
| title_sort | functional equations and modelling in science and engineering |
| topic | Modèles mathématiques Équations fonctionnelles Mathematisches Modell Functional equations Mathematical models Funktionalgleichung (DE-588)4018923-5 gnd |
| topic_facet | Modèles mathématiques Équations fonctionnelles Mathematisches Modell Functional equations Mathematical models Funktionalgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003412474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
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