Applied complex variables for scientists and engineers:
This book is an introduction to complex variable methods for scientists and engineers. It begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2002
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents Inhaltsverzeichnis |
| Zusammenfassung: | This book is an introduction to complex variable methods for scientists and engineers. It begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. One feature that will appeal to scientists is the high proportion of the book devoted to applications of the material to physical problems. These include detailed treatments of potential theory, hydrodynamics, electrostatics, gravitation and the uses of the Laplace transform for partial differential equations. The text contains some 300 stimulating exercises of high quality, with solutions given to many of them. It will be highly suitable for students wishing to learn the elements of complex analysis in an applied context. |
| Beschreibung: | Includes index. |
| Beschreibung: | xi, 392 p. ill. : 24 cm |
| ISBN: | 0521803020 0521004624 |
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| 245 | 1 | 0 | |a Applied complex variables for scientists and engineers |c Yue Kuen Kwok |
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| 500 | |a Includes index. | ||
| 520 | 3 | |a This book is an introduction to complex variable methods for scientists and engineers. It begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. One feature that will appeal to scientists is the high proportion of the book devoted to applications of the material to physical problems. These include detailed treatments of potential theory, hydrodynamics, electrostatics, gravitation and the uses of the Laplace transform for partial differential equations. The text contains some 300 stimulating exercises of high quality, with solutions given to many of them. It will be highly suitable for students wishing to learn the elements of complex analysis in an applied context. | |
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Datensatz im Suchindex
| _version_ | 1804129298262523904 |
|---|---|
| adam_text | APPLIED COMPLEX VARIABLES FOR SCIENTISTS AND ENGINEERS YUE KUEN KWOK
HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY CAMBRIDGE UNIVERSITY
PRESS CONTENTS PREFACE PAGE IX 1 COMPLEX NUMBERS 1 1.1 COMPLEX NUMBERS
AND THEIR REPRESENTATIONS 1 1.2 ALGEBRAIC PROPERTIES OF COMPLEX NUMBERS
5 1.2.1 DE MOIVRE S THEOREM 7 1.3 GEOMETRIC PROPERTIES OF COMPLEX
NUMBERS 13 1.3.1 NTH ROOTS OF UNITY 16 1.3.2 SYMMETRY WITH RESPECT TO A
CIRCLE 17 1.4 SOME TOPOLOGICAL DEFINITIONS 22 1.5 COMPLEX INFINITY AND
THE RIEMANN SPHERE 26 1.5.1 THE RIEMANN SPHERE AND STEREOGRAPHIC
PROJECTION 27 1.6 APPLICATIONS TO ELECTRICAL CIRCUITS 29 1.7 PROBLEMS 33
2 ANALYTIC FUNCTIONS 40 2.1 FUNCTIONS OF A COMPLEX VARIABLE 40 2.1.1
VELOCITY OF FLUID FLOW EMANATING FROM A SOURCE 42 2.1.2 MAPPING
PROPERTIES OF COMPLEX FUNCTIONS 44 2.1.3 DEFINITIONS OF EXPONENTIAL AND
TRIGONOMETRIC FUNCTIONS 47 2.2 LIMIT AND CONTINUITY OF COMPLEX FUNCTIONS
48 2.2.1 LIMIT OF A COMPLEX FUNCTION 48 2.2.2 CONTINUITY OF A COMPLEX
FUNCTION 50 2.3 DIFFERENTIATION OF COMPLEX FUNCTIONS 52 2.3.1 COMPLEX
VELOCITY AND ACCELERATION 54 2.4 CAUCHY-RIEMANN RELATIONS 55 2.4.1
CONJUGATE COMPLEX VARIABLES 60 2.5 ANALYTICITY 61 VI CONTENTS 2.6
HARMONIC FUNCTIONS 63 2.6.1 HARMONIC CONJUGATE 65 2.6.2 STEADY STATE
TEMPERATURE DISTRIBUTION 69 2.6.3 POISSON S EQUATION 73 2.7 PROBLEMS 74
3 EXPONENTIAL, LOGARITHMIC AND TRIGONOMETRIC FUNCTIONS 81 3.1
EXPONENTIAL FUNCTIONS 81 3.1.1 DEFINITION FROM THE FIRST PRINCIPLES 82
3.1.2 MAPPING PROPERTIES OF THE COMPLEX EXPONENTIAL FUNCTION 84 3.2
TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS 85 .3.2.1 MAPPING PROPERTIES OF
THE COMPLEX SINE FUNCTION 90 3.3 LOGARITHMIC FUNCTIONS 92 3.3.1 HEAT
SOURCE 94 3.3.2 TEMPERATURE DISTRIBUTION IN THE UPPER HALF-PLANE 96 3.4
INVERSE TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS 99 3.5 GENERALIZED
EXPONENTIAL AND POWER FUNCTIONS 102 3.6 BRANCH POINTS, BRANCH CUTS AND
RIEMANN SURFACES 105 3.6.1 JOUKOWSKI MAPPING 109 3.7 PROBLEMS 112 4
COMPLEX INTEGRATION 118 4.1 FORMULATIONS OF COMPLEX INTEGRATION 118
4.1.1 DEFINITE INTEGRAL OF A COMPLEX-VALUED FUNCTION OF A REAL VARIABLE
119 4.1.2 COMPLEX INTEGRALS AS LINE INTEGRALS 120 4.2 CAUCHY S INTEGRAL
THEOREM 127 4.3 CAUCHY S INTEGRAL FORMULA AND ITS CONSEQUENCES 136 4.3.1
DERIVATIVES OF CONTOUR INTEGRALS 138 4.3.2 MORERA S THEOREM 142 4.3.3
CONSEQUENCES OF THE CAUCHY INTEGRAL FORMULA 142 4.4 POTENTIAL FUNCTIONS
OF CONSERVATIVE FIELDS 147 4.4.1 VELOCITY POTENTIAL AND STREAM FUNCTION
OF FLUID FLOWS 147 4.4.2 ELECTROSTATIC FIELDS 160 4.4.3 GRAVITATIONAL
FIELDS 164 4.5 PROBLEMS 169 5 TAYLOR AND LAURENT SERIES 177 5.1 COMPLEX
SEQUENCES AND SERIES 177 5.1.1 CONVERGENCE OF COMPLEX SEQUENCES 177
CONTENTS VII 5.1.2 INFINITE SERIES OF COMPLEX NUMBERS 179 5.1.3
CONVERGENCE TESTS OF COMPLEX SERIES 180 5.2 SEQUENCES AND SERIES OF
COMPLEX FUNCTIONS 183 5.2.1 CONVERGENCE OF SERIES OF COMPLEX FUNCTIONS
184 5.2.2 POWER SERIES 186 5.3 TAYLOR SERIES 190 5.4 LAURENT SERIES 196
5.4.1 POTENTIAL FLOW PAST AN OBSTACLE 205 5.5 ANALYTIC CONTINUATION 208
5.5.1 REFLECTION PRINCIPLE 211 5.6 PROBLEMS 212 SINGULARITIES AND
CALCULUS OF RESIDUES 221 6.1 CLASSIFICATION OF SINGULAR POINTS 221 6.2
RESIDUES AND THE RESIDUE THEOREM 227 6.2.1 COMPUTATIONAL FORMULAS FOR
EVALUATING RESIDUES 228 6.3 EVALUATION OF REAL INTEGRALS BY RESIDUE
CALCULUS 232 6.3.1 INTEGRALS OF TRIGONOMETRIC FUNCTIONS OVER [0, 2N] 232
6.3.2 INTEGRALS OF RATIONAL FUNCTIONS 234 6.3.3 INTEGRALS INVOLVING
MULTI-VALUED FUNCTIONS 236 6.3.4 MISCELLANEOUS TYPES OF INTEGRAL 239 6.4
FOURIER TRANSFORMS 243 6.4.1 FOURIER INVERSION FORMULA 244 6.4.2
EVALUATION OF FOURIER INTEGRALS 248 6.5 CAUCHY PRINCIPAL VALUE OF AN
IMPROPER INTEGRAL 251 6.6 HYDRODYNAMICS IN POTENTIAL FLUID FLOWS 258
6.6.1 BLASIUS LAWS OF HYDRODYNAMIC FORCE AND MOMENT 258 6.6.2
KUTTA-JOUKOWSKI S LIFTING FORCE THEOREM 262 6.7 PROBLEMS 263 BOUNDARY
VALUE PROBLEMS AND INITIAL-BOUNDARY VALUE PROBLEMS 272 7.1 INTEGRAL
FORMULAS OF HARMONIC FUNCTIONS 273 7.1.1 POISSON INTEGRAL FORMULA 273
7.1.2 SCHWARZ INTEGRAL FORMULA 280 7.1.3 NEUMANN PROBLEMS 285 7.2 THE
LAPLACE TRANSFORM AND ITS INVERSION 287 7.2.1 BROMWICH INTEGRALS 291 7.3
INITIAL-BOUNDARY VALUE PROBLEMS 298 7.3.1 HEAT CONDUCTION 298 7.3.2
LONGITUDINAL OSCILLATIONS OF AN ELASTIC THIN ROD 303 7.4 PROBLEMS 308
VIII CONTENTS 8 CONFORMAL MAPPINGS AND APPLICATIONS 319 8.1 CONFORMAL
MAPPINGS 319 8.1.1 INVARIANCE OF THE LAPLACE EQUATION 326 8.1.2
HODOGRAPH TRANSFORMATIONS 332 8.2 BILINEAR TRANSFORMATIONS 335 8.2.1
CIRCLE-PRESERVING PROPERTY 338 8.2.2 SYMMETRY-PRESERVING PROPERTY 341
8.2.3 SOME SPECIAL BILINEAR TRANSFORMATIONS 350 8.3 SCHWARZ-CHRISTOFFEL
TRANSFORMATIONS 358 8.4 PROBLEMS 368 ANSWERS TO PROBLEMS 311 INDEX 389
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.9 |
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| discipline | Mathematik |
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| spelling | Kwok, Yue-Kuen 1957- Verfasser (DE-588)136047629 aut Applied complex variables for scientists and engineers Yue Kuen Kwok 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2002 xi, 392 p. ill. : 24 cm txt rdacontent n rdamedia nc rdacarrier Includes index. This book is an introduction to complex variable methods for scientists and engineers. It begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. One feature that will appeal to scientists is the high proportion of the book devoted to applications of the material to physical problems. These include detailed treatments of potential theory, hydrodynamics, electrostatics, gravitation and the uses of the Laplace transform for partial differential equations. The text contains some 300 stimulating exercises of high quality, with solutions given to many of them. It will be highly suitable for students wishing to learn the elements of complex analysis in an applied context. Functions of complex variables Textbooks Funktionentheorie (DE-588)4018935-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Funktionentheorie (DE-588)4018935-1 s DE-604 http://www.loc.gov/catdir/description/cam021/2001018485.html Publisher description http://www.loc.gov/catdir/toc/cam026/2001018485.html Table of contents GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009875421&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kwok, Yue-Kuen 1957- Applied complex variables for scientists and engineers Functions of complex variables Textbooks Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4123623-3 |
| title | Applied complex variables for scientists and engineers |
| title_auth | Applied complex variables for scientists and engineers |
| title_exact_search | Applied complex variables for scientists and engineers |
| title_full | Applied complex variables for scientists and engineers Yue Kuen Kwok |
| title_fullStr | Applied complex variables for scientists and engineers Yue Kuen Kwok |
| title_full_unstemmed | Applied complex variables for scientists and engineers Yue Kuen Kwok |
| title_short | Applied complex variables for scientists and engineers |
| title_sort | applied complex variables for scientists and engineers |
| topic | Functions of complex variables Textbooks Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Functions of complex variables Textbooks Funktionentheorie Lehrbuch |
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