Mathematical methods for system theory:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1998
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 553 S. |
| ISBN: | 9810233345 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | MAFHEMAFICAL MEFHODS FOR SYSTEM THEORQ F GENTILI L MENINI A TORNAMBE L
ZACCARIAN UNIVERSITAE DI ROMA, ITALY VFE WORLD SCIENTIFIC IM SINGAPORE *
NEW JERSEY * LONDON * HONG KONG CONTENTS PREFACE V NOTATIONS XIII 1
DISCRETE PROBABILITY SPACES 1 1.1 BASIC NOTIONS OF DISCRETE PROBABILITY
SPACES 1 1.2 HINTS ON CONTINUOUS PROBABILITY SPACES 27 1.3 SOME USEFUL
RESULTS 37 1.4 APPLICATIONS 49 1.4.1 GEOMETRIE DISTRIBUTION 49 1.4.2
EXPONENTIAL DISTRIBUTION 52 1.4.3 BINOMIAL DISTRIBUTION 54 1.4.4 ERLANG
DISTRIBUTION 57 1.5 PROBLEMS 58 BIBLIOGRAPHY 61 2 BASICS OF ABSTRACT
ALGEBRA 63 2.1 BASIC NOTIONS OF SEMIGROUPS 63 2.2 GROUPS OF ORDER 1, 2,
3 AND 4 82 2.2.1 GROUPS OF ORDER 1 82 2.2.2 GROUPS OF ORDER 2 82 2.2.3
GROUPS OF ORDER 3 83 2.2.4 GROUPS OF ORDER 4 84 2.3 BASIC NOTIONS OF
BINARY RELATIONS 86 2.4 EQUIVALENCE RELATIONS 99 IX X CONTENTS 2.4.1
EQUIVALENCE RELATIONS ON A SINGLETON 100 2.4.2 EQUIVALENCE RELATIONS ON
A SET HAVING TWO ELEMENTS . 101 2.4.3 EQUIVALENCE RELATIONS ON A SET
HAVING THREE ELEMENTS 102 2.5 PARTIALLY ORDERED SETS 105 2.5.1 PARTIALLY
ORDERED SETS HAVING TWO ELEMENTS 105 2.5.2 PARTIALLY ORDERED SETS HAVING
THREE ELEMENTS 107 2.6 PROBLEMS 122 BIBLIOGRAPHY 123 3 GRAPHS AND
ALGORITHMS 125 3.1 BASIC NOTIONS 125 3.2 REPRESENTATIONS OF GRAPHS AND
SOME RESULTS 143 3.3 PROBLEMS 161 BIBLIOGRAPHY 161 4 GEOMETRY OF 1R 163
4.1 GEOMETRIE APPLICATIONS IN LR * 163 4.2 CONVEX SETS 177 4.3 EXTREME
POINTS AND SUPPORTING HYPERPLANES 187 4.4 PROBLEMS 194 BIBLIOGRAPHY 196
5 LINEAR ALGEBRAIC EQUATIONS 197 5.1 BASIC NOTATIONS 197 5.2 LINEAR
DEPENDENCE AND INDEPENDENCE OF VECTORS 198 5.3 LINEAR EQUATIONS 210 5.4
PROBLEMS 219 BIBLIOGRAPHY 220 6 DIFFERENCE AND DIFFERENTIAL EQUATIONS
221 6.1 BASIC DEFINITIONS AND RESULTS 221 6.2 LINEAR TIME-INVARIANT
DIFFERENCE AND DIFFERENTIAL EQUATIONS . 227 6.3 ORBITS OF PLANAR SYSTEMS
251 6.3.1 LINEAR TIME-INVARIANT SYSTEMS 252 6.3.2 NON-LINEAR
TIME-INVARIANT SYSTEMS 259 6.3.3 THE METHOD OF ISOCLINES 263 6.4
BIFURCATION POINTS 268 6.5 SOLUTION OF LINEAR TIME-INVARIANT EQUATIONS
USING Z AND LA- PLACE TRANSFORMS 270 6.6 AFFINE TIME-INVARIANT
DIFFERENCE AND DIFFERENTIAL EQUATIONS . . 274 CONTENTS XI 6.6.1
DIFFERENCE EQUATIONS 275 6.6.2 DIFFERENTIAL EQUATIONS 277 6.6.3 AFFINE
SPACE OF SOLUTIONS 278 6.7 STEADY-STATE SOLUTION 280 6.7.1 DIFFERENTIAL
EQUATIONS 281 6.7.2 DIFFERENCE EQUATIONS 296 6.7.3 SCALAR EQUATIONS 308
6.8 PROBLEMS 318 BIBLIOGRAPHY 318 7 THE Z-TRANSFORM 321 7.1 DEFINITIONS
AND PROPERTIES 321 7.2 BASIC RESULTS ON Z-TRANSFORM 328 7.3 REMARKABLE
Z-TRANSFORMS 337 7.4 THE INVERSE Z-TRANSFORM 345 7.4.1 INVERSE
TRANSFORMATION BY POLYNOMIAL DIVISION 346 7.4.2 INVERSE TRANSFORMATION
BY PARTIAL FRACTIONS 350 7.5 APPLICATIONS 354 7.6 PROBLEMS 363
BIBLIOGRAPHY 363 8 THE LAPLACE TRANSFORM 371 8.1 DEFINITIONS AND
PROPERTIES 371 8.2 BASIC RESULTS ON LAPLACE TRANSFORM 380 8.3 REMARKABLE
LAPLACE TRANSFORMS 390 8.4 THE INVERSE LAPLACE TRANSFORM 400 8.4.1
INVERSE TRANSFORMATION BY POLYNOMIAL DIVISION 400 8.4.2 INVERSE
TRANSFORMATION BY PARTIAL FRACTIONS 404 8.5 APPLICATIONS 407 8.6
PROBLEMS 414 BIBLIOGRAPHY 415 9 NORMS 421 9.1 VECTOR SPACES 421 9.2
NORMED VECTOR SPACES 444 9.2.1 NORMS OF N-DIMENSIONAL COMPLEX VECTORS
447 9.2.2 NORMS OF COMPLEX-VALUED SCALAR FUNCTIONS 451 9.2.3 NORMS OF
COMPLEX-VALUED VECTOR FUNCTIONS 455 9.2.4 NORMS OF LAPLACE TRANSFORMABLE
FUNCTIONS 456 XII CONTENTS 9.2.5 NORM OF THE SOLUTIONS OF LINEAR
DIFFERENTIAL EQUATIONS . 464 9.2.6 NORMS OF Z-TRANSFORMABLE FUNCTIONS
469 9.2.7 NORM OF THE SOLUTIONS OF LINEAR DIFFERENCE EQUATIONS . 477 9.3
COMPATIBLE AND INDUCED NORMS 481 9.4 NORMS OF MATRICES 488 9.4.1 THE [1,
L]-NORM OF MATRICES 488 9.4.2 THE [2, 2]-NORM OF MATRICES 491 9.4.3 THE
[MAX, MAX]-NORM OF MATRICES 493 9.5 PROBLEMS 496 BIBLIOGRAPHY 496 A
SOLUTIONS OF SELECTED EXERCISES 497 B ANSWERS TO PROBLEMS 533 SUBJECT
INDEX 547
|
| adam_txt |
MAFHEMAFICAL MEFHODS FOR SYSTEM THEORQ F GENTILI L MENINI A TORNAMBE L
ZACCARIAN UNIVERSITAE DI ROMA, ITALY VFE WORLD SCIENTIFIC IM SINGAPORE *
NEW JERSEY * LONDON * HONG KONG CONTENTS PREFACE V NOTATIONS XIII 1
DISCRETE PROBABILITY SPACES 1 1.1 BASIC NOTIONS OF DISCRETE PROBABILITY
SPACES 1 1.2 HINTS ON CONTINUOUS PROBABILITY SPACES 27 1.3 SOME USEFUL
RESULTS 37 1.4 APPLICATIONS 49 1.4.1 GEOMETRIE DISTRIBUTION 49 1.4.2
EXPONENTIAL DISTRIBUTION 52 1.4.3 BINOMIAL DISTRIBUTION 54 1.4.4 ERLANG
DISTRIBUTION 57 1.5 PROBLEMS 58 BIBLIOGRAPHY 61 2 BASICS OF ABSTRACT
ALGEBRA 63 2.1 BASIC NOTIONS OF SEMIGROUPS 63 2.2 GROUPS OF ORDER 1, 2,
3 AND 4 82 2.2.1 GROUPS OF ORDER 1 82 2.2.2 GROUPS OF ORDER 2 82 2.2.3
GROUPS OF ORDER 3 83 2.2.4 GROUPS OF ORDER 4 84 2.3 BASIC NOTIONS OF
BINARY RELATIONS 86 2.4 EQUIVALENCE RELATIONS 99 IX X CONTENTS 2.4.1
EQUIVALENCE RELATIONS ON A SINGLETON 100 2.4.2 EQUIVALENCE RELATIONS ON
A SET HAVING TWO ELEMENTS . 101 2.4.3 EQUIVALENCE RELATIONS ON A SET
HAVING THREE ELEMENTS 102 2.5 PARTIALLY ORDERED SETS 105 2.5.1 PARTIALLY
ORDERED SETS HAVING TWO ELEMENTS 105 2.5.2 PARTIALLY ORDERED SETS HAVING
THREE ELEMENTS 107 2.6 PROBLEMS 122 BIBLIOGRAPHY 123 3 GRAPHS AND
ALGORITHMS 125 3.1 BASIC NOTIONS 125 3.2 REPRESENTATIONS OF GRAPHS AND
SOME RESULTS 143 3.3 PROBLEMS 161 BIBLIOGRAPHY 161 4 GEOMETRY OF 1R" 163
4.1 GEOMETRIE APPLICATIONS IN LR * 163 4.2 CONVEX SETS 177 4.3 EXTREME
POINTS AND SUPPORTING HYPERPLANES 187 4.4 PROBLEMS 194 BIBLIOGRAPHY 196
5 LINEAR ALGEBRAIC EQUATIONS 197 5.1 BASIC NOTATIONS 197 5.2 LINEAR
DEPENDENCE AND INDEPENDENCE OF VECTORS 198 5.3 LINEAR EQUATIONS 210 5.4
PROBLEMS 219 BIBLIOGRAPHY 220 6 DIFFERENCE AND DIFFERENTIAL EQUATIONS
221 6.1 BASIC DEFINITIONS AND RESULTS 221 6.2 LINEAR TIME-INVARIANT
DIFFERENCE AND DIFFERENTIAL EQUATIONS . 227 6.3 ORBITS OF PLANAR SYSTEMS
251 6.3.1 LINEAR TIME-INVARIANT SYSTEMS 252 6.3.2 NON-LINEAR
TIME-INVARIANT SYSTEMS 259 6.3.3 THE METHOD OF ISOCLINES 263 6.4
BIFURCATION POINTS 268 6.5 SOLUTION OF LINEAR TIME-INVARIANT EQUATIONS
USING Z AND LA- PLACE TRANSFORMS 270 6.6 AFFINE TIME-INVARIANT
DIFFERENCE AND DIFFERENTIAL EQUATIONS . . 274 CONTENTS XI 6.6.1
DIFFERENCE EQUATIONS 275 6.6.2 DIFFERENTIAL EQUATIONS 277 6.6.3 AFFINE
SPACE OF SOLUTIONS 278 6.7 STEADY-STATE SOLUTION 280 6.7.1 DIFFERENTIAL
EQUATIONS 281 6.7.2 DIFFERENCE EQUATIONS 296 6.7.3 SCALAR EQUATIONS 308
6.8 PROBLEMS 318 BIBLIOGRAPHY 318 7 THE Z-TRANSFORM 321 7.1 DEFINITIONS
AND PROPERTIES 321 7.2 BASIC RESULTS ON Z-TRANSFORM 328 7.3 REMARKABLE
Z-TRANSFORMS 337 7.4 THE INVERSE Z-TRANSFORM 345 7.4.1 INVERSE
TRANSFORMATION BY POLYNOMIAL DIVISION 346 7.4.2 INVERSE TRANSFORMATION
BY PARTIAL FRACTIONS 350 7.5 APPLICATIONS 354 7.6 PROBLEMS 363
BIBLIOGRAPHY 363 8 THE LAPLACE TRANSFORM 371 8.1 DEFINITIONS AND
PROPERTIES 371 8.2 BASIC RESULTS ON LAPLACE TRANSFORM 380 8.3 REMARKABLE
LAPLACE TRANSFORMS 390 8.4 THE INVERSE LAPLACE TRANSFORM 400 8.4.1
INVERSE TRANSFORMATION BY POLYNOMIAL DIVISION 400 8.4.2 INVERSE
TRANSFORMATION BY PARTIAL FRACTIONS 404 8.5 APPLICATIONS 407 8.6
PROBLEMS 414 BIBLIOGRAPHY 415 9 NORMS 421 9.1 VECTOR SPACES 421 9.2
NORMED VECTOR SPACES 444 9.2.1 NORMS OF N-DIMENSIONAL COMPLEX VECTORS
447 9.2.2 NORMS OF COMPLEX-VALUED SCALAR FUNCTIONS 451 9.2.3 NORMS OF
COMPLEX-VALUED VECTOR FUNCTIONS 455 9.2.4 NORMS OF LAPLACE TRANSFORMABLE
FUNCTIONS 456 XII CONTENTS 9.2.5 NORM OF THE SOLUTIONS OF LINEAR
DIFFERENTIAL EQUATIONS . 464 9.2.6 NORMS OF Z-TRANSFORMABLE FUNCTIONS
469 9.2.7 NORM OF THE SOLUTIONS OF LINEAR DIFFERENCE EQUATIONS . 477 9.3
COMPATIBLE AND INDUCED NORMS 481 9.4 NORMS OF MATRICES 488 9.4.1 THE [1,
L]-NORM OF MATRICES 488 9.4.2 THE [2, 2]-NORM OF MATRICES 491 9.4.3 THE
[MAX, MAX]-NORM OF MATRICES 493 9.5 PROBLEMS 496 BIBLIOGRAPHY 496 A
SOLUTIONS OF SELECTED EXERCISES 497 B ANSWERS TO PROBLEMS 533 SUBJECT
INDEX 547 |
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| index_date | 2024-07-02T22:32:13Z |
| indexdate | 2024-07-09T21:23:43Z |
| institution | BVB |
| isbn | 9810233345 |
| language | English |
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| spelling | Mathematical methods for system theory F. Gentili ... Singapore [u.a.] World Scientific 1998 XXII, 553 S. txt rdacontent n rdamedia nc rdacarrier System analysis Systemtheorie (DE-588)4058812-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Systemtheorie (DE-588)4058812-9 s Mathematik (DE-588)4037944-9 s DE-604 Gentili, Federico Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016838292&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematical methods for system theory System analysis Systemtheorie (DE-588)4058812-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4058812-9 (DE-588)4037944-9 (DE-588)4123623-3 |
| title | Mathematical methods for system theory |
| title_auth | Mathematical methods for system theory |
| title_exact_search | Mathematical methods for system theory |
| title_exact_search_txtP | Mathematical methods for system theory |
| title_full | Mathematical methods for system theory F. Gentili ... |
| title_fullStr | Mathematical methods for system theory F. Gentili ... |
| title_full_unstemmed | Mathematical methods for system theory F. Gentili ... |
| title_short | Mathematical methods for system theory |
| title_sort | mathematical methods for system theory |
| topic | System analysis Systemtheorie (DE-588)4058812-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | System analysis Systemtheorie Mathematik Lehrbuch |
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