Complex variables and transform calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Southampton [u.a.]
Computational Mechanics Publ.
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 322 S. graph. Darst. |
| ISBN: | 1853124915 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | COMPLEX VARIABLES AND TRANSFORM CALCULUS BY M.RAHMAN TECHNICAL
UNIVERSITY OF NOVA SCOTIA CANADA NIEDER3ACKS. STAATS.U.UNIV.. BIBLIOTHEK
GOTTEN GEN COMPUTATIONAL MECHANICS PUBLICATIONS SOUTHAMPTON UK AND
BOSTON USA CONTENTS PREFACE V 1 COMPLEX NUMBERS, ANALYTIC FUNCTIONS OF A
COMPLEX VARIABLE 1 1.1 INTRODUCTION 1 1.2 ALGEBRAIC PROPERTIES,
CARTESIAN AND POLAR COORDINATES 1 1.3 FUNCTIONS OF A COMPLEX VARIABLE,
LIMITS AND CONTINUITY 13 1.4 ANALYTIC FUNCTIONS, CAUCHY-RIEMANN
EQUATIONS AND LAPLACE S EQUATION 19 1.5 ELEMENTARY FUNCTIONS OF Z:
EXPONENTIAL, TRIGONOMETRIC, HYPERBOLIC AND LOGARITHMIC FUNCTIONS 31 2
COMPLEX INTEGRATION 43 2.1 INTRODUCTION V . 43 2.2 THE CAUCHY-GOURSAT
THEOREM 46 2.3 APPLICATIONS 53 3 SERIES EXPANSION 72 3.1 POWER SERIES 72
3.2 TAYLOR SERIES 77 3.2.1 TAYLOR SERIES OF ELEMENTARY FUNCTIONS 79 3.3
LAURENT SERIES 84 4 THE THEORY OF RESIDUES 93 4.1 INTRODUCTION 93 4.1.1
ISOLATED SINGULAR POINT 93 4.1.2 POLES , 93 4.1.3 ESSENTIAL SINGULAR
POINTS 93 4.1.4 REMOVABLE SINGULARITY 94 4.1.5 BRANCH POINTS AND BRANCH
CUTS 94 4.2 DEFINITION OF THE RESIDUE 95 4.3 RESIDUE THEOREM * . . 97
4.4 EVALUATION OF REAL INTEGRALS 107 4.4.1 EVALUATION OF IMPROPER
INTEGRALS 107 4.4.2 IMPROPER INTEGRALS INVOLVING TRIGONOMETRIC FUNCTIONS
ILL 4.4.3 DEFINITE INTEGRALS OF TRIGONOMETRIC FUNCTIONS 113 4.4.4
INTEGRATION AROUND A BRANCH POINT 117 THE THEORY OF TRANSFORM CALCULUS
AND APPLICATIONS 133 5.1 FOURIER SERIES 133 5.1.1 INTRODUCTION 133 5.1.2
FOURIER SERIES AND FOURIER COEFFICIENTS 134 5.1.3 COMPLEX FORM OF
FOURIER SERIES 136 5.1.4 HALF-RANGE FOURIER SINE AND COSINE SERIES 138
5.1.5 PARSEVAL S IDENTITY 140 5.2 FOURIER INTEGRAL AND TRANSFORM 142
5.2.1 RELATIONSHIP BETWEEN FOURIER AND LAPLACE TRANSFORMS 147 5.2.2
CONVOLUTION INTEGRAL AND CONVOLUTION THEOREM 149 5.2.3 CONVOLUTION
INTEGRALS FROM FOURIER TO LAPLACE 149 5.3 LAPLACE TRANSFORMS 151 5.3.1
INTRODUCTION 151 5.3.2 DEFINITION OF LAPLACE TRANSFORM 152 5.3.3
THEOREMS ON LAPLACE TRANSFORMS 153 5.3.4 LAPLACE TRANSFORMS OF SPECIAL
FUNCTIONS 155 5.3.5 SOME SPECIALLY IMPORTANT THEOREMS 162 5.4 THE UNIT
STEP FUNCTION AND THE DIRAC DELTA FUNCTION 164 5.4.1 THE UNIT STEP
FUNCTION AND ITS TRANSFORM 164 5.4.2 THE DIRAC DELTA FUNCTION 164 5.4.3
PROPERTIES OF GENERALIZED FUNCTIONS 167 5.5 THE HEAVISIDE EXPANSION
THEOREMS FOR FINDING INVERSES 170 5.5.1 LAPLACE TRANSFORM OF A PERIODIC
FUNCTION 173 5.6 TRANSFER FUNCTION, IMPULSE RESPONSE AND INDICIA!
RESPONSE 176 5.6.1 SIGNIFICANCE OF CONVOLUTION THEOREM 177 5.6.2
SIGNIFICANCE OF DUHAMEL S THEOREM 178 5.7 COMPLEX INVERSION INTEGRALS
182 5.8 STABILITY CRITERIA 193 5.8.1 THE NYQUIST CRITERION 200 5.8.2
APPLICATIONS 208 CONFORMAL MAPPING 212 6.1 INTRODUCTION 212 6.2 SOME
SIMPLE MAPPING 214 6.3 CONFORMAL MAPPING 216 6.4 THE BILINEAR
TRANSFORMATION 224 6.5 THE SCHWARZ-CHRISTOFFEL TRANSFORMATION 245 6.6
APPLICATIONS 247 APPLICATIONS TO PHYSICAL PROBLEMS 259 7.1 INTRODUCTION
. . . . V 259 7.2 APPLICATIONS TO FLUID FLOW 259 7.2.1 TWO DIMENSIONAL
FLOW 259 7.2.2 THE COMPLEX POTENTIAL 263 7.2.3 SINGULARITIES IN TWO
DIMENSIONAL FLOW 264 7.2.4 CIRCULATION AROUND A CURVE 267 7.2.5.
CONFORMAL MAPPING IN HYDRODYNAMICS 272 7.2.6 LIFT FORCE 276 7.2.7
APPLICATIONS 278 7.3 APPLICATIONS TO HEAT FLOW 287 7.3.1 HEAT FLUX IN
TWO DIMENSION 287 7.4 APPLICATIONS TO ELECTROSTATIC POTENTIALS 293
ANALYTIC CONTINUATION 303 8.1 INTRODUCTION 303 8.2 NATURAL BOUNDARY OF
AN ANALYTIC FUNCTION 306 8.3 GENERALIZATION OF ANALYTIC CONTINUATION 308
8.4 SOME IMPORTANT THEOREMS 311 BIBLIOGRAPHY 314 ANSWERS TO ODD-NUMBERED
EXERCISES 316 INDEX 323
|
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:30:08Z |
| institution | BVB |
| isbn | 1853124915 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008547493 |
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| physical | 322 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Computational Mechanics Publ. |
| record_format | marc |
| spelling | Rahman, Matiur Verfasser aut Complex variables and transform calculus by M. Rahman Southampton [u.a.] Computational Mechanics Publ. 1997 322 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CALCULUS nasat COMPLEX VARIABLES nasat INTEGRAL TRANSFORMATIONS nasat Functions of complex variables Transformations (Mathematics) Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008547493&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rahman, Matiur Complex variables and transform calculus CALCULUS nasat COMPLEX VARIABLES nasat INTEGRAL TRANSFORMATIONS nasat Functions of complex variables Transformations (Mathematics) Komplexe Variable (DE-588)4164905-9 gnd |
| subject_GND | (DE-588)4164905-9 |
| title | Complex variables and transform calculus |
| title_auth | Complex variables and transform calculus |
| title_exact_search | Complex variables and transform calculus |
| title_full | Complex variables and transform calculus by M. Rahman |
| title_fullStr | Complex variables and transform calculus by M. Rahman |
| title_full_unstemmed | Complex variables and transform calculus by M. Rahman |
| title_short | Complex variables and transform calculus |
| title_sort | complex variables and transform calculus |
| topic | CALCULUS nasat COMPLEX VARIABLES nasat INTEGRAL TRANSFORMATIONS nasat Functions of complex variables Transformations (Mathematics) Komplexe Variable (DE-588)4164905-9 gnd |
| topic_facet | CALCULUS COMPLEX VARIABLES INTEGRAL TRANSFORMATIONS Functions of complex variables Transformations (Mathematics) Komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008547493&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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