Comprehensive mathematics for computer scientists: 2 Calculus and ODEs, splines, probability, Fourier and wavelet theory, fractals and neural networks, categories and lambda calculus
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 355 S. Ill., graph. Darst. |
| ISBN: | 3540208615 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text |
GUERINO MAZZOLA * GERARD MILMEISTER JODY WEISSMANN COMPREHENSIVE
MATHEMATICS FOR COMPUTER SCIENTISTS 2 CALCULUS AND ODES, SPLINES,
PROBABILITY, FOURIER AND WAVELET THEORY, FRACTALS AND NEURAL NETWORKS,
CATEGORIES AND LAMBDA CALCULUS WITH 114 FIGURES 4Y SPRINGER CONTENTS III
TOPOLOGY AND CALCULUS 1 27 LIMITS AND TOPOLOGY 3 27.1 INTRODUCTION 3
27.2 TOPOLOGIES ON REAL VECTOR SPACES 4 27.3 CONTINUITY 14 27.4 SERIES
21 27.5 EULER'S FORMULA FOR POLYHEDRA AND KURATOWSKI'S THEOREM 30 28
DIFFERENTIABILITY 37 28.1 INTRODUCTION 37 28.2 DIFFERENTIATION 39 28.3
TAYLOR'S FORMULA 53 29 INVERSE AND IMPLICIT FUNCTIONS 59 29.1
INTRODUCTION 59 29.2 THE INVERSE FUNCTION THEOREM 60 29.3 THE IMPLICIT
FUNCTION THEOREM 64 30 INTEGRATION 73 30.1 INTRODUCTION 73 30.2
PARTITIONS AND THE INTEGRAL 74 30.3 MEASURE AND INTEGRABILITY 81 31 THE
FUNDAMENTAL THEOREM OF CALCULUS AND FUBINI'S THEOREM 87 31.1
INTRODUCTION 87 31.2 THE FUNDAMENTAL THEOREM OF CALCULUS 88 31.3
FUBINI'S THEOREM ON ITERATED INTEGRATION 92 32 VECTOR FIELDS 97 32.1
INTRODUCTION 97 32.2 VECTOR FIELDS 98 VIII CONTENTS 33 FIXPOINTS 105
33.1 INTRODUCTION 105 33.2 CONTRACTIONS 105 34 MAIN THEOREM OF ODES 113
34.1 INTRODUCTION 113 34.2 CONSERVATIVE AND TIME-DEPENDENT ORDINARY
DIFFERENTIAL EQUATIONS: THE LOCAL SETUP 114 34.3 THE FUNDAMENTAL
THEOREM: LOCAL VERSION 115 34.4 THE SPECIAL CASE OF A LINEAR ODE 117
34.5 THE FUNDAMENTAL THEOREM: GLOBAL VERSION 119 35 THIRD ADVANCED TOPIC
125 35.1 INTRODUCTION 125 35.2 NUMERICS OF ODES 125 35.3 THE EULER
METHOD ." 129 35.4 RUNGE-KUTTA METHODS 131 IV SELECTED HIGHER SUBJECTS
137 36 CATEGORIES 139 36.1 INTRODUCTION 139 36.2 WHAT CATEGORIES ARE 140
36.3 EXAMPLES 143 36.4 FUNCTORS AND NATURAL TRANSFORMATIONS 147 36.5
LIMITS AND COLIMITS 153 36.6 ADJUNCTION 159 37 SPLINES 161 37.1
INTRODUCTION 161 37.2 PRELIMINARIES ON SIMPLEXES 161 37.3 WHAT ARE
SPLINES? 164 37.4 LAGRANGE INTERPOLATION 168 37.5 BEZIER CURVES 171 37.6
TENSOR PRODUCT SPHNES 176 37.7B-SPLINES 179 38 FOURIER THEORY 183 38.1
INTRODUCTION 183 38.2 SPACES OF PERIODIC FUNCTIONS 185 38.3
ORTHOGONALITY 188 CONTENTS IX 38.4 FOURIER'S THEOREM 191 38.5
RESTATEMENT IN TERMS OF THE SINE AND COSINE FUNCTIONS. 194 38.6 FINITE
FOURIER SERIES AND FAST FOURIER TRANSFORM 200 38.7FAST FOURIER TRANSFORM
(FFT) 204 38.8 THE FOURIER TRANSFORM 209 39 WAVELETS 215 39.1
INTRODUCTION 215 39.2 THE HILBERT SPACE L 2 (K) 217 39.3 FRAMES AND
ORTHONORMAL WAVELET BASES 221 39.4THE FAST HAAR WAVELET TRANSFORM 225 40
FRACTALS 231 40.1 INTRODUCTION 231 40.2 HAUSDORFF-METRIC SPACES 232 40.3
CONTRACTIONS ON HAUSDORFF-METRIC SPACES 236 40.4 FRACTAL DIMENSION 242
41 NEURAL NETWORKS 253 41.1 INTRODUCTION 253 41.2 FORMAL NEURONS 254
41.3 NEURAL NETWORKS 264 41.4 MULTI-LAYERED PERCEPTRONS 269 41.5 THE
BACK-PROPAGATION ALGORITHM 272 42 PROBABILITY THEORY 279 42.1
INTRODUCTION 279 42.2 EVENT SPACES AND RANDOM VARIABLES 279 42.3
PROBABILITY SPACES 283 42.4 DISTRIBUTION FUNCTIONS 290 42.5 EXPECTATION
AND VARIANCE 299 42.6 INDEPENDENCE AND THE CENTRAL LIMIT THEOREM 306
42.7 A REMARK ON INFERENTIAL STATISTICS 310 43 LAMBDA CALCULUS 313 43.1
INTRODUCTION 313 43.2 THE LAMBDA LANGUAGE 314 43.3 SUBSTITUTION 316 43.4
ALPHA-EQUIVALENCE 318 43.5 BETA-REDUCTION 320 43.6 THE A-CALCULUS AS A
PROGRAMMING LANGUAGE 326 CONTENTS 43.7 RECURSIVE FUNCTIONS 328 43.8
REPRESENTATION OF PARTIAL RECURSIVE FUNCTIONS 331 A FURTHER READING 335
B BIBLIOGRAPHY 337 INDEX 341 |
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| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik |
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| indexdate | 2024-07-20T07:39:29Z |
| institution | BVB |
| isbn | 3540208615 |
| language | English |
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| spelling | Mazzola, Guerino 1947- Verfasser (DE-588)120861437 aut Comprehensive mathematics for computer scientists 2 Calculus and ODEs, splines, probability, Fourier and wavelet theory, fractals and neural networks, categories and lambda calculus Guerino Mazzola ; Gérard Milmeister ; Jody Weissmann Berlin [u.a.] Springer 2005 X, 355 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Informatik Mathematik Computer science Mathematics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Milmeister, Gérard 1971- Verfasser (DE-588)1120930758 aut Weissmann, Jody Verfasser aut (DE-604)BV019431205 2 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013326490&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazzola, Guerino 1947- Milmeister, Gérard 1971- Weissmann, Jody Comprehensive mathematics for computer scientists Informatik Mathematik Computer science Mathematics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4001865-9 |
| title | Comprehensive mathematics for computer scientists |
| title_auth | Comprehensive mathematics for computer scientists |
| title_exact_search | Comprehensive mathematics for computer scientists |
| title_full | Comprehensive mathematics for computer scientists 2 Calculus and ODEs, splines, probability, Fourier and wavelet theory, fractals and neural networks, categories and lambda calculus Guerino Mazzola ; Gérard Milmeister ; Jody Weissmann |
| title_fullStr | Comprehensive mathematics for computer scientists 2 Calculus and ODEs, splines, probability, Fourier and wavelet theory, fractals and neural networks, categories and lambda calculus Guerino Mazzola ; Gérard Milmeister ; Jody Weissmann |
| title_full_unstemmed | Comprehensive mathematics for computer scientists 2 Calculus and ODEs, splines, probability, Fourier and wavelet theory, fractals and neural networks, categories and lambda calculus Guerino Mazzola ; Gérard Milmeister ; Jody Weissmann |
| title_short | Comprehensive mathematics for computer scientists |
| title_sort | comprehensive mathematics for computer scientists calculus and odes splines probability fourier and wavelet theory fractals and neural networks categories and lambda calculus |
| topic | Informatik Mathematik Computer science Mathematics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Informatik Mathematik Computer science Mathematics Wahrscheinlichkeitstheorie Analysis |
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