Function of one complex variable:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Liverpool
World Academic Press, World Acad. Union
2005
|
| Series: | Textbook of mathematical science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 214 S. graph. Darst. |
| ISBN: | 1846261627 |
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Record in the Search Index
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| adam_text | TEXTBOOK OF MATHEMATICAL SCIENCE ISBN: 1-84626-162-7 FUNCTION OF ONE
COMPLEX VARIABLE SHU WEN, DONGDONG WANG SUB GOTTINGEN 7 219 715 033
PUBLISHED BY WORLD ACADEMIC PRESS, WORLD ACADEMIC UNION, 2005 WWW .
WORLD ACADEMIC PRESS . COM CONTENTS CHAPTER 1 COMPLEX NUMBERS 1.1 THE
CONCEPT AND THE COMPUTATION OF THE COMPLEX NUMBERS . . . 1 1.2 BASIC
ALGEBRAIC PROPERTIES 2 1.3 MODULI 3 1.4 COMPLEX CONJUGATES 5 1.5
EXPONENTIAL FORM 7 1.6 ROOTS OF COMPLEX NUMBERS 11 1.7 REGIONS IN THE
COMPLEX PLANE 14 EXERCISE 1 15 CHAPTER 2 ANALYTIC FUNCTIONS 2.1
FUNCTIONS OF A COMPLEX VARIABLE 18 2.2 MAPPINGS 19 2.3 LIMITS FOR
COMPLEX FUNCTION 20 2.4 LIMITS ABOUT THE POINT AT INFINITY 24 2.5
CONTINUITY FOR COMPLEX FUNCTION 26 2.6 DERIVATIVES 27 2.7 CAUCHY-RIEMANN
EQUATIONS 31 2.8 SUFFICIENT CONDITIONS FOR DIFFERENTIABILITY 33 2.9
ANALYTIC FUNCTIONS 36 2.10 HARMONIC FUNCTIONS 38 2.11 UNIQUENESS FOR
ANALYTIC FUNCTIONS 40 EXERCISE 2 41 CHAPTER 3 ELEMENTARY FUNCTIONS 3.1
THE EXPONENTIAL FUNCTION 44 3.2 THE LOGARITHMIC FUNCTION 45 3.3 BRANCHES
AND DERIVATIVES OF LOGARITHMS FUNCTION 46 3.4 SOME IDENTITIES INVOLVING
LOGARITHMS FUNCTION 47 3.5 COMPLEX EXPONENTS 49 3.6 TRIGONOMETRIC
FUNCTIONS 50 3.7 HYPERBOLIC FUNCTIONS 52 EXERCISE 3 53 CHAPTER 4
INTEGRALS 4.1 DERIVATIVES OF FUNCTIONS W(T) 55- 4.2 DEFINITE INTEGRALS
OF FUNCTIONS W(X) 56 4.3 CONTOURS. 57 4.4 CONTOUR INTEGRALS 59 4.5 UPPER
BOUNDS FOR MODULI OF CONTOUR INTEGRALS 62 4.6 ANTIDERIVATIVES 63 4.7
CAUCHY-GOURSAT THEOREM 67 4.8 SIMPLY AND MULTIPLY CONNECTED DOMAINS 69
4.9 CAUCHY INTEGRAL FORMULAS 72 4.10 DERIVATIVES OF ANALYTIC FUNCTIONS
74 4.11 LIOUVILLE S THEOREM AND THE FUNDAMENTAL THEOREM OF ALGEBRA . .
77 4.12 MAXIMUM MODULUS PRINCIPLE 80 EXERCISE 4 83 CHAPTER 5 SERIES 5.1
CONVERGENCE OF SEQUENCES 87 5.2 CONVERGENCE OF SERIES 89 5.3 TAYLOR
SERIES 91 5.4 LAURENT SERIES 96 5.5 ABSOLUTE AND UNIFORM CONVERGENCE OF
POWER SERIES 102 5.6 CONTINUITY OF SUMS OF POWER SERIES 105 5.7
INTEGRATION AND DIFFERENTIATION OF POWER SERIES 106 5.8 UNIQUENESS OF
SERIES REPRESENTATIONS 109 5.9 MULTIPLICATION AND DIVISION OF POWER
SERIES ILL EXERCISE 5 11 3 CHAPTER 6 RESIDUES AND POLES 6.1 RESIDUES. .
117 6.2 CAUCHY S RESIDUE THEOREM 120 6.3 THE THREE TYPES OF ISOLATED
SINGULAR POINTS 123 6.4 RESIDUES AT POLES 125 6.5 ZEROS OF ANALYTIC
FUNCTIONS 128 6.6 ZEROS AND POLES 130 6.7 BEHAVIOR OF NEAR ISOLATED
SINGULAR POINTS 132 EXERCISE 6 135 CHAPTER 7 APPLICATIONS OF RESIDUES
7.1 EVALUATION OF IMPROPER INTEGRALS 137 7.2 JORDAN S LEMMA 141 7.3
INDENTED PATHS 143 7.4 AN INDENTATION AROUND A BRANCH POINT 145 7.5
INTEGRATION ALONG A BRANCH CUT 147 7.6 DEFINITE INTEGRALS INVOLVING
SINES AND COSINES 149 7.7 ARGUMENT PRINCIPLE 150 7.8 ROUCHE S THEOREM .
. . , 153 7.9 INVERSE LAPLACE TRANSFORM 154 EXERCISE 7 161 CHAPTER 8
MAPPING BY ELEMENTARY FUNCTIONS 8.1 LINEAR TRANSFORMATIONS 164 8.2 THE
TRANSFORMATION W=L/Z 165 8.3 MAPPING BY 1/Z 166 8.4 LINEAR FRACTIONAL
TRANSFORMATIONS 169 8.5 AN IMPLICIT FORM 171 8.6 MAPPINGS OF THE UPPER
HALF PLANE 173 8.7 THE TRANSFORMATION W=E Z 176 8.8 THE TRANSFORMATION
W=SINZ 177 8.9 MAPPINGS BY Z 2 AND BRANCHES OF Z 1/2 179 EXERCISE 8 183
CHAPTER 9 CONFORMAL MAPPING 9.1 PRESERVATION OF ANGLES 185 9.2 SCALE
FACTORS 187 9.3 LOCAL INVERSES 188 9.4 HARMONIC CONJUGATES 190 9.5
TRANSFORMATIONS OF HARMONIC FUNCTIONS 191 9.6 TRANSFORMATIONS OF
BOUNDARY CONDITIONS 193 EXERCISE 9 195 APPENDIXE 1. PROOF FOR
CAUCHY-GOURSAT THEOREM 197 APPENDIXE 2. ANSWER FOR EXERCISE 202
APPENDIXE 3. VOCABULARY 207 VII
|
| adam_txt |
TEXTBOOK OF MATHEMATICAL SCIENCE ISBN: 1-84626-162-7 FUNCTION OF ONE
COMPLEX VARIABLE SHU WEN, DONGDONG WANG SUB GOTTINGEN 7 219 715 033
PUBLISHED BY WORLD ACADEMIC PRESS, WORLD ACADEMIC UNION, 2005 WWW .
WORLD ACADEMIC PRESS . COM CONTENTS CHAPTER 1 COMPLEX NUMBERS 1.1 THE
CONCEPT AND THE COMPUTATION OF THE COMPLEX NUMBERS . . . 1 1.2 BASIC
ALGEBRAIC PROPERTIES 2 1.3 MODULI 3 1.4 COMPLEX CONJUGATES 5 1.5
EXPONENTIAL FORM 7 1.6 ROOTS OF COMPLEX NUMBERS 11 1.7 REGIONS IN THE
COMPLEX PLANE 14 EXERCISE 1 15 CHAPTER 2 ANALYTIC FUNCTIONS 2.1
FUNCTIONS OF A COMPLEX VARIABLE 18 2.2 MAPPINGS 19 2.3 LIMITS FOR
COMPLEX FUNCTION 20 2.4 LIMITS ABOUT THE POINT AT INFINITY 24 2.5
CONTINUITY FOR COMPLEX FUNCTION 26 2.6 DERIVATIVES 27 2.7 CAUCHY-RIEMANN
EQUATIONS 31 2.8 SUFFICIENT CONDITIONS FOR DIFFERENTIABILITY 33 2.9
ANALYTIC FUNCTIONS 36 2.10 HARMONIC FUNCTIONS 38 2.11 UNIQUENESS FOR
ANALYTIC FUNCTIONS 40 EXERCISE 2 41 CHAPTER 3 ELEMENTARY FUNCTIONS 3.1
THE EXPONENTIAL FUNCTION 44 3.2 THE LOGARITHMIC FUNCTION 45 3.3 BRANCHES
AND DERIVATIVES OF LOGARITHMS FUNCTION 46 3.4 SOME IDENTITIES INVOLVING
LOGARITHMS FUNCTION 47 3.5 COMPLEX EXPONENTS 49 3.6 TRIGONOMETRIC
FUNCTIONS 50 3.7 HYPERBOLIC FUNCTIONS 52 EXERCISE 3 53 CHAPTER 4
INTEGRALS 4.1 DERIVATIVES OF FUNCTIONS W(T) 55- 4.2 DEFINITE INTEGRALS
OF FUNCTIONS W(X) 56 4.3 CONTOURS. 57 4.4 CONTOUR INTEGRALS 59 4.5 UPPER
BOUNDS FOR MODULI OF CONTOUR INTEGRALS 62 4.6 ANTIDERIVATIVES 63 4.7
CAUCHY-GOURSAT THEOREM 67 4.8 SIMPLY AND MULTIPLY CONNECTED DOMAINS 69
4.9 CAUCHY INTEGRAL FORMULAS 72 4.10 DERIVATIVES OF ANALYTIC FUNCTIONS
74 4.11 LIOUVILLE'S THEOREM AND THE FUNDAMENTAL THEOREM OF ALGEBRA . .
77 4.12 MAXIMUM MODULUS PRINCIPLE 80 EXERCISE 4 83 CHAPTER 5 SERIES 5.1
CONVERGENCE OF SEQUENCES 87 5.2 CONVERGENCE OF SERIES 89 5.3 TAYLOR
SERIES 91 5.4 LAURENT SERIES 96 5.5 ABSOLUTE AND UNIFORM CONVERGENCE OF
POWER SERIES 102 5.6 CONTINUITY OF SUMS OF POWER SERIES 105 5.7
INTEGRATION AND DIFFERENTIATION OF POWER SERIES 106 5.8 UNIQUENESS OF
SERIES REPRESENTATIONS 109 5.9 MULTIPLICATION AND DIVISION OF POWER
SERIES ILL EXERCISE 5 11 3 CHAPTER 6 RESIDUES AND POLES 6.1 RESIDUES. .
117 6.2 CAUCHY'S RESIDUE THEOREM 120 6.3 THE THREE TYPES OF ISOLATED
SINGULAR POINTS 123 6.4 RESIDUES AT POLES 125 6.5 ZEROS OF ANALYTIC
FUNCTIONS 128 6.6 ZEROS AND POLES 130 6.7 BEHAVIOR OF NEAR ISOLATED
SINGULAR POINTS 132 EXERCISE 6 135 CHAPTER 7 APPLICATIONS OF RESIDUES
7.1 EVALUATION OF IMPROPER INTEGRALS 137 7.2 JORDAN'S LEMMA 141 7.3
INDENTED PATHS 143 7.4 AN INDENTATION AROUND A BRANCH POINT 145 7.5
INTEGRATION ALONG A BRANCH CUT 147 7.6 DEFINITE INTEGRALS INVOLVING
SINES AND COSINES 149 7.7 ARGUMENT PRINCIPLE 150 7.8 ROUCHE'S THEOREM .
. . , 153 7.9 INVERSE LAPLACE TRANSFORM 154 EXERCISE 7 161 CHAPTER 8
MAPPING BY ELEMENTARY FUNCTIONS 8.1 LINEAR TRANSFORMATIONS 164 8.2 THE
TRANSFORMATION W=L/Z 165 8.3 MAPPING BY 1/Z 166 8.4 LINEAR FRACTIONAL
TRANSFORMATIONS 169 8.5 AN IMPLICIT FORM 171 8.6 MAPPINGS OF THE UPPER
HALF PLANE 173 8.7 THE TRANSFORMATION W=E Z 176 8.8 THE TRANSFORMATION
W=SINZ 177 8.9 MAPPINGS BY Z 2 AND BRANCHES OF Z 1/2 179 EXERCISE 8 183
CHAPTER 9 CONFORMAL MAPPING 9.1 PRESERVATION OF ANGLES 185 9.2 SCALE
FACTORS 187 9.3 LOCAL INVERSES 188 9.4 HARMONIC CONJUGATES 190 9.5
TRANSFORMATIONS OF HARMONIC FUNCTIONS 191 9.6 TRANSFORMATIONS OF
BOUNDARY CONDITIONS 193 EXERCISE 9 195 APPENDIXE 1. PROOF FOR
CAUCHY-GOURSAT THEOREM 197 APPENDIXE 2. ANSWER FOR EXERCISE 202
APPENDIXE 3. VOCABULARY 207 VII |
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| author | Wen, Shu Wang, Dongdong |
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| dewey-full | 515.93 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| index_date | 2024-07-02T16:00:12Z |
| indexdate | 2024-07-09T20:45:51Z |
| institution | BVB |
| isbn | 1846261627 |
| language | English |
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| physical | VII, 214 S. graph. Darst. |
| publishDate | 2005 |
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| publisher | World Academic Press, World Acad. Union |
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| spelling | Wen, Shu Verfasser aut Function of one complex variable Shu Wen ; Dongdong Wang Liverpool World Academic Press, World Acad. Union 2005 VII, 214 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Textbook of mathematical science Functions of complex variables Komplexe Funktion (DE-588)4217733-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Komplexe Funktion (DE-588)4217733-9 s DE-604 Wang, Dongdong Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015052113&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wen, Shu Wang, Dongdong Function of one complex variable Functions of complex variables Komplexe Funktion (DE-588)4217733-9 gnd |
| subject_GND | (DE-588)4217733-9 (DE-588)4151278-9 |
| title | Function of one complex variable |
| title_auth | Function of one complex variable |
| title_exact_search | Function of one complex variable |
| title_exact_search_txtP | Function of one complex variable |
| title_full | Function of one complex variable Shu Wen ; Dongdong Wang |
| title_fullStr | Function of one complex variable Shu Wen ; Dongdong Wang |
| title_full_unstemmed | Function of one complex variable Shu Wen ; Dongdong Wang |
| title_short | Function of one complex variable |
| title_sort | function of one complex variable |
| topic | Functions of complex variables Komplexe Funktion (DE-588)4217733-9 gnd |
| topic_facet | Functions of complex variables Komplexe Funktion Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015052113&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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