Complex variables for scientists and engineers:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Macmillan [u.a.]
1990
|
| Ausgabe: | 2. ed., 1. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 586 S. |
| ISBN: | 0023905611 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV021897317 | ||
| 003 | DE-604 | ||
| 005 | 20040301000000.0 | ||
| 007 | t | ||
| 008 | 910508s1990 |||| 00||| eng d | ||
| 020 | |a 0023905611 |9 0-02-390561-1 | ||
| 035 | |a (OCoLC)19885827 | ||
| 035 | |a (DE-599)BVBBV021897317 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-706 | ||
| 050 | 0 | |a QA331.7 | |
| 082 | 0 | |a 515/.9 |2 20 | |
| 100 | 1 | |a Paliouras, John D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Complex variables for scientists and engineers |c John D. Paliouras ; Douglas S. Meadows |
| 250 | |a 2. ed., 1. print. | ||
| 264 | 1 | |a New York |b Macmillan [u.a.] |c 1990 | |
| 300 | |a XIII, 586 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Analyse mathématique |2 ram | |
| 650 | 7 | |a Fonctions d'une variable complexe |2 ram | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 0 | 7 | |a Komplexe Funktion |0 (DE-588)4217733-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Komplexe Variable |0 (DE-588)4164905-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Komplexe Funktion |0 (DE-588)4217733-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Komplexe Variable |0 (DE-588)4164905-9 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Meadows, Douglas S. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015112500&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015112500 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804135842502934528 |
|---|---|
| adam_text | Contents
Preface vii
PART I FOUNDATIONS OF COMPLEX VARIABLES
Chapter 1 Complex Numbers 3
Section 1 Complex Numbers and Their Algebra 4
2 Geometry of Complex Numbers 10
Appendix 1 Part A: A Formal Look at Complex Numbers 26
Part B: Stereographic Projection 30
Chapter 2 Complex Functions 33
Section 3 Preliminaries 34
4 Definition and Elementary Geometry of a Complex
Function 38
5 Limits, Continuity 47
6 Differentiation 54
7 The Cauchy Riemann Equations 61
8 Elementary Complex Functions: Definitions and Basic
Properties 66
9 Analytic Functions; Domains of Analyticity 85
Appendix 2 Proofs of Theorems 90
Chapter 3 Harmonic Functions with Applications 96
Section 10 Harmonic Functions 97
11 Applications to Fluid Flow 108
12 Applications to Electrostatics 123
Appendix 3 Part A: The Equations of Fluid Flow 136
Part B: Basic Laws of Electrostatics 144
xi
xii Contents
Chapter 4 Complex Integration 158
Section 13 Paths; Connectedness 159
14 Line Integrals 166
15 The Complex Integral 177
Appendix 4 Proofs of Theorems 189
Chapter 5 Cauchy Theory of Integration 193
Section 16 Integrals of Analytic Functions; Cauchy s Theorem 194
17 The Annulus Theorem and Its Extension 204
18 The Cauchy Integral Formulas; Morera s Theorem 211
Appendix 5 Part A: Proofs of Theorems 219
Part B: Proof of the Cauchy Integral Theorem 224
Part C: The Winding Number and the Generalized
Cauchy Theorems 241
Chapter 6 Complex Power Series 248
Section 19 Sequences and Series of Complex Numbers 249
20 Power Series 260
21 Power Series as Analytic Functions 266
22 Analytic Functions as Power Series 274
Appendix 6 Part A: Proofs of Theorems 288
Part B: More on Sequences and Series;
The Cauchy Hadamard Theorem 291
Chapter 7 Laurent Series; Residues 298
Section 23 Laurent Series 299
24 Singularities and Zeros of an Analytic Function 308
25 Theory of Residues 317
26 Evaluation of Certain Real Integrals by Use of
Residues 325
Appendix 7 Proof of Laurent s Theorem; Uniqueness of Taylor and
Laurent Expansions 339
PART II FURTHER THEORY AND APPLICATIONS OF
COMPLEX VARIABLES
Chapter 8 Mapping Properties of Analytic Functions 345
Section 27 Algebraic Functions 346
28 Transcendental Functions 380
29 Behavior of Functions at Infinity 403
Appendix 8 Part A: Riemann Surfaces of Multivalued Functions 410
Part B: Integration Involving Branch Points 418
Contents xiii
Chapter 9 Conformal Mapping with Applications 424
Section 30 Conformality and Analytic Functions 425
31 Laplace s Equation 437
32 Applications to Boundary Value Problems 459
33 Applications to Aerodynamics 484
34 The Schwarz Christoffel Integral 497
Appendix 9 Univalent Functions 525
Chapter 10 Further Theoretical Results 529
Section 35 The Maximum Modulus Principle 530
36 Liouville s Theorem; The Fundamental Theorem of
Algebra 536
37 Behavior of Functions Near Isolated Singularities 540
38 Analytic Continuation and the Schwarz Reflection
Principle 544
Bibliography 555
Answers to Selected Exercises 557
Index 577
|
| adam_txt |
Contents
Preface vii
PART I FOUNDATIONS OF COMPLEX VARIABLES
Chapter 1 Complex Numbers 3
Section 1 Complex Numbers and Their Algebra 4
2 Geometry of Complex Numbers 10
Appendix 1 Part A: A Formal Look at Complex Numbers 26
Part B: Stereographic Projection 30
Chapter 2 Complex Functions 33
Section 3 Preliminaries 34
4 Definition and Elementary Geometry of a Complex
Function 38
5 Limits, Continuity 47
6 Differentiation 54
7 The Cauchy Riemann Equations 61
8 Elementary Complex Functions: Definitions and Basic
Properties 66
9 Analytic Functions; Domains of Analyticity 85
Appendix 2 Proofs of Theorems 90
Chapter 3 Harmonic Functions with Applications 96
Section 10 Harmonic Functions 97
11 Applications to Fluid Flow 108
12 Applications to Electrostatics 123
Appendix 3 Part A: The Equations of Fluid Flow 136
Part B: Basic Laws of Electrostatics 144
xi
xii Contents
Chapter 4 Complex Integration 158
Section 13 Paths; Connectedness 159
14 Line Integrals 166
15 The Complex Integral 177
Appendix 4 Proofs of Theorems 189
Chapter 5 Cauchy Theory of Integration 193
Section 16 Integrals of Analytic Functions; Cauchy's Theorem 194
17 The Annulus Theorem and Its Extension 204
18 The Cauchy Integral Formulas; Morera's Theorem 211
Appendix 5 Part A: Proofs of Theorems 219
Part B: Proof of the Cauchy Integral Theorem 224
Part C: The Winding Number and the Generalized
Cauchy Theorems 241
Chapter 6 Complex Power Series 248
Section 19 Sequences and Series of Complex Numbers 249
20 Power Series 260
21 Power Series as Analytic Functions 266
22 Analytic Functions as Power Series 274
Appendix 6 Part A: Proofs of Theorems 288
Part B: More on Sequences and Series;
The Cauchy Hadamard Theorem 291
Chapter 7 Laurent Series; Residues 298
Section 23 Laurent Series 299
24 Singularities and Zeros of an Analytic Function 308
25 Theory of Residues 317
26 Evaluation of Certain Real Integrals by Use of
Residues 325
Appendix 7 Proof of Laurent's Theorem; Uniqueness of Taylor and
Laurent Expansions 339
PART II FURTHER THEORY AND APPLICATIONS OF
COMPLEX VARIABLES
Chapter 8 Mapping Properties of Analytic Functions 345
Section 27 Algebraic Functions 346
28 Transcendental Functions 380
29 Behavior of Functions at Infinity 403
Appendix 8 Part A: Riemann Surfaces of Multivalued Functions 410
Part B: Integration Involving Branch Points 418
Contents xiii
Chapter 9 Conformal Mapping with Applications 424
Section 30 Conformality and Analytic Functions 425
31 Laplace's Equation 437
32 Applications to Boundary Value Problems 459
33 Applications to Aerodynamics 484
34 The Schwarz Christoffel Integral 497
Appendix 9 Univalent Functions 525
Chapter 10 Further Theoretical Results 529
Section 35 The Maximum Modulus Principle 530
36 Liouville's Theorem; The Fundamental Theorem of
Algebra 536
37 Behavior of Functions Near Isolated Singularities 540
38 Analytic Continuation and the Schwarz Reflection
Principle 544
Bibliography 555
Answers to Selected Exercises 557
Index 577 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Paliouras, John D. Meadows, Douglas S. |
| author_facet | Paliouras, John D. Meadows, Douglas S. |
| author_role | aut aut |
| author_sort | Paliouras, John D. |
| author_variant | j d p jd jdp d s m ds dsm |
| building | Verbundindex |
| bvnumber | BV021897317 |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331.7 |
| callnumber-search | QA331.7 |
| callnumber-sort | QA 3331.7 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)19885827 (DE-599)BVBBV021897317 |
| dewey-full | 515/.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.9 |
| dewey-search | 515/.9 |
| dewey-sort | 3515 19 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed., 1. print. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01637nam a2200433zc 4500</leader><controlfield tag="001">BV021897317</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20040301000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">910508s1990 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0023905611</subfield><subfield code="9">0-02-390561-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)19885827</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021897317</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-706</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA331.7</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.9</subfield><subfield code="2">20</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Paliouras, John D.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Complex variables for scientists and engineers</subfield><subfield code="c">John D. Paliouras ; Douglas S. Meadows</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed., 1. print.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York</subfield><subfield code="b">Macmillan [u.a.]</subfield><subfield code="c">1990</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 586 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analyse mathématique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Fonctions d'une variable complexe</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions of complex variables</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Komplexe Funktion</subfield><subfield code="0">(DE-588)4217733-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Komplexe Variable</subfield><subfield code="0">(DE-588)4164905-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Komplexe Funktion</subfield><subfield code="0">(DE-588)4217733-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Komplexe Variable</subfield><subfield code="0">(DE-588)4164905-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Meadows, Douglas S.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015112500&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-015112500</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV021897317 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:04:27Z |
| indexdate | 2024-07-09T20:46:56Z |
| institution | BVB |
| isbn | 0023905611 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015112500 |
| oclc_num | 19885827 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | XIII, 586 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Macmillan [u.a.] |
| record_format | marc |
| spelling | Paliouras, John D. Verfasser aut Complex variables for scientists and engineers John D. Paliouras ; Douglas S. Meadows 2. ed., 1. print. New York Macmillan [u.a.] 1990 XIII, 586 S. txt rdacontent n rdamedia nc rdacarrier Analyse mathématique ram Fonctions d'une variable complexe ram Functions of complex variables Komplexe Funktion (DE-588)4217733-9 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Komplexe Funktion (DE-588)4217733-9 s DE-604 Komplexe Variable (DE-588)4164905-9 s 1\p DE-604 Meadows, Douglas S. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015112500&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Paliouras, John D. Meadows, Douglas S. Complex variables for scientists and engineers Analyse mathématique ram Fonctions d'une variable complexe ram Functions of complex variables Komplexe Funktion (DE-588)4217733-9 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| subject_GND | (DE-588)4217733-9 (DE-588)4164905-9 |
| title | Complex variables for scientists and engineers |
| title_auth | Complex variables for scientists and engineers |
| title_exact_search | Complex variables for scientists and engineers |
| title_exact_search_txtP | Complex variables for scientists and engineers |
| title_full | Complex variables for scientists and engineers John D. Paliouras ; Douglas S. Meadows |
| title_fullStr | Complex variables for scientists and engineers John D. Paliouras ; Douglas S. Meadows |
| title_full_unstemmed | Complex variables for scientists and engineers John D. Paliouras ; Douglas S. Meadows |
| title_short | Complex variables for scientists and engineers |
| title_sort | complex variables for scientists and engineers |
| topic | Analyse mathématique ram Fonctions d'une variable complexe ram Functions of complex variables Komplexe Funktion (DE-588)4217733-9 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| topic_facet | Analyse mathématique Fonctions d'une variable complexe Functions of complex variables Komplexe Funktion Komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015112500&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT paliourasjohnd complexvariablesforscientistsandengineers AT meadowsdouglass complexvariablesforscientistsandengineers |