Complex variables and applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
McGraw-Hill
c2009
|
| Ausgabe: | 8th ed. |
| Schriftenreihe: | Brown and Churchill series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XI, 468 S. |
| ISBN: | 9780073051949 0073051942 |
Internformat
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| 245 | 1 | 0 | |a Complex variables and applications |c James Ward Brown ; Ruel V. Churchill |
| 250 | |a 8th ed. | ||
| 264 | 1 | |a Boston [u.a.] |b McGraw-Hill |c c2009 | |
| 300 | |a XI, 468 S. | ||
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| 490 | 0 | |a Brown and Churchill series | |
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Datensatz im Suchindex
| _version_ | 1804137316027990016 |
|---|---|
| adam_text | CONTENTS
Preface
1
Complex Numbers
Sums and Products
1
Basic Algebraic Properties
3
Further Properties
5
Vectors and Moduli
9
Complex Conjugates
13
Exponential Form
16
Products and Powers in Exponential Form
18
Arguments of Products and Quotients
20
Roots of Complex Numbers
24
Examples
27
Regions in the Complex Plane
31
2
Analytic Functions
35
Functions of a Complex Variable
35
Mappings
38
Mappings by the Exponential Function
42
Limits
45
Theorems on Limits
48
VI
CONTENTS
Limits Involving the Point at Infinity
50
Continuity
53
Derivatives
56
Differentiation Formulas
60
Cauchy-Riemann Equations
63
Sufficient Conditions for Differentiability
66
Polar Coordinates
68
Analytic Functions
73
Examples
75
Harmonic Functions
78
Uniquely Determined Analytic Functions
83
Reflection Principle
85
3
Elementary Functions
89
The Exponential Function
89
The Logarithmic Function
93
Branches and Derivatives of Logarithms
95
Some Identities Involving Logarithms
98
Complex Exponents
101
Trigonometric Functions
104
Hyperbolic Functions
109
Inverse Trigonometric and Hyperbolic Functions
112
4
Integrals
117
Derivatives of Functions wit)
117
Definite Integrals of Functions w(t)
119
Contours
122
Contour Integrals
127
Some Examples
129
Examples with Branch Cuts
133
Upper Bounds for Moduli of Contour Integrals
137
Antiderivatives 142
Proof of the Theorem
146
Cauchy-Goursat Theorem
150
Proof of the Theorem
152
CONTENTS
VU
Simply Connected Domains
156
Multiply Connected Domains
158
Cauchy Integral Formula
164
An Extension of the Cauchy Integral Formula
165
Some Consequences of the Extension
168
Liouville s Theorem and the Fundamental Theorem of Algebra
172
Maximum Modulus Principle
175
5
Series
181
Convergence of Sequences
181
Convergence of Series
184
Taylor Series
189
Proof of Taylor
s
Theorem
190
Examples
192
Laurent Series
197
Proof of Laurent s Theorem
199
Examples
202
Absolute and Uniform Convergence of Power Series
208
Continuity of Sums of Power Series
211
Integration and Differentiation of Power Series
213
Uniqueness of Series Representations
217
Multiplication and Division of Power Series
222
6
Residues and Poles
229
Isolated Singular Points
229
Residues
231
Cauchy s Residue Theorem
234
Residue at Infinity
237
The Three Types of Isolated Singular Points
240
Residues at Poles
244
Examples
245
Zeros of Analytic Functions
249
Zeros and Poles
252
Behavior of Functions Near Isolated Singular Points
257
VIU
CONTENTS
7
Applications
of Residues
261
Evaluation of Improper Integrals
261
Example
264
Improper Integrals from Fourier Analysis
269
Jordan s Lemma
272
Indented Paths
277
An Indentation Around a Branch Point
280
Integration Along a Branch Cut
283
Definite Integrals Involving Sines and Cosines
288
Argument Principle
291
Rouché s
Theorem
294
Inverse Laplace Transforms
298
Examples
301
8
Mapping by Elementary Functions
311
Linear Transformations
311
The Transformation
w
=
l/z
313
Mappings by l/z
315
Linear Fractional Transformations
319
An Implicit Form
322
Mappings of the Upper Half Plane
325
The Transformation
w
=
sin
z
330
Mappings by z2 and Branches of zl/2
336
Square Roots of Polynomials
341
Riemann Surfaces
347
Surfaces for Related Functions
351
9
Conformai
Mapping
355
Preservation of Angles
355
Scale Factors
358
Local Inverses
360
Harmonic Conjugates
363
Transformations of Harmonic Functions
365
Transformations of Boundary Conditions
367
CONTENTS
IX
10 Applications
of
Conformai
Mapping
373
Steady Temperatures
373
Steady Temperatures in a Half Plane
375
A Related Problem
377
Temperatures in a Quadrant
379
Electrostatic Potential
385
Potential in a Cylindrical Space
386
Two-Dimensional Fluid Flow
391
The Stream Function
393
Flows Around a Corner and Around a Cylinder
395
11
The Schwarz-Christoffel Transformation
403
Mapping the Real Axis Onto a Polygon
403
Schwarz-Christoffel Transformation
405
Triangles and Rectangles
408
Degenerate Polygons
413
Huid
Flow in a Channel Through a Slit
417
Flow in a Channel With an Offset
420
Electrostatic Potential About an Edge of a Conducting Plate
422
12
Integral Formulas of the
Poisson Type
429
Poisson
Integral Formula
429
Dirichlet Problem for a Disk
432
Related Boundary Value Problems
437
Schwarz
Integral Formula
440
Dirichlet Problem for a Half Plane
441
Neumann Problems
445
Appendixes
449
Bibliography
449
Table of Transformations of Regions
452
Index
461
|
| adam_txt |
CONTENTS
Preface
1
Complex Numbers
Sums and Products
1
Basic Algebraic Properties
3
Further Properties
5
Vectors and Moduli
9
Complex Conjugates
13
Exponential Form
16
Products and Powers in Exponential Form
18
Arguments of Products and Quotients
20
Roots of Complex Numbers
24
Examples
27
Regions in the Complex Plane
31
2
Analytic Functions
35
Functions of a Complex Variable
35
Mappings
38
Mappings by the Exponential Function
42
Limits
45
Theorems on Limits
48
VI
CONTENTS
Limits Involving the Point at Infinity
50
Continuity
53
Derivatives
56
Differentiation Formulas
60
Cauchy-Riemann Equations
63
Sufficient Conditions for Differentiability
66
Polar Coordinates
68
Analytic Functions
73
Examples
75
Harmonic Functions
78
Uniquely Determined Analytic Functions
83
Reflection Principle
85
3
Elementary Functions
89
The Exponential Function
89
The Logarithmic Function
93
Branches and Derivatives of Logarithms
95
Some Identities Involving Logarithms
98
Complex Exponents
101
Trigonometric Functions
104
Hyperbolic Functions
109
Inverse Trigonometric and Hyperbolic Functions
112
4
Integrals
117
Derivatives of Functions wit)
117
Definite Integrals of Functions w(t)
119
Contours
122
Contour Integrals
127
Some Examples
129
Examples with Branch Cuts
133
Upper Bounds for Moduli of Contour Integrals
137
Antiderivatives 142
Proof of the Theorem
146
Cauchy-Goursat Theorem
150
Proof of the Theorem
152
CONTENTS
VU
Simply Connected Domains
156
Multiply Connected Domains
158
Cauchy Integral Formula
164
An Extension of the Cauchy Integral Formula
165
Some Consequences of the Extension
168
Liouville's Theorem and the Fundamental Theorem of Algebra
172
Maximum Modulus Principle
175
5
Series
181
Convergence of Sequences
181
Convergence of Series
184
Taylor Series
189
Proof of Taylor'
s
Theorem
190
Examples
192
Laurent Series
197
Proof of Laurent's Theorem
199
Examples
202
Absolute and Uniform Convergence of Power Series
208
Continuity of Sums of Power Series
211
Integration and Differentiation of Power Series
213
Uniqueness of Series Representations
217
Multiplication and Division of Power Series
222
6
Residues and Poles
229
Isolated Singular Points
229
Residues
231
Cauchy's Residue Theorem
234
Residue at Infinity
237
The Three Types of Isolated Singular Points
240
Residues at Poles
244
Examples
245
Zeros of Analytic Functions
249
Zeros and Poles
252
Behavior of Functions Near Isolated Singular Points
257
VIU
CONTENTS
7
Applications
of Residues
261
Evaluation of Improper Integrals
261
Example
264
Improper Integrals from Fourier Analysis
269
Jordan's Lemma
272
Indented Paths
277
An Indentation Around a Branch Point
280
Integration Along a Branch Cut
283
Definite Integrals Involving Sines and Cosines
288
Argument Principle
291
Rouché's
Theorem
294
Inverse Laplace Transforms
298
Examples
301
8
Mapping by Elementary Functions
311
Linear Transformations
311
The Transformation
w
=
l/z
313
Mappings by l/z
315
Linear Fractional Transformations
319
An Implicit Form
322
Mappings of the Upper Half Plane
325
The Transformation
w
=
sin
z
330
Mappings by z2 and Branches of zl/2
336
Square Roots of Polynomials
341
Riemann Surfaces
347
Surfaces for Related Functions
351
9
Conformai
Mapping
355
Preservation of Angles
355
Scale Factors
358
Local Inverses
360
Harmonic Conjugates
363
Transformations of Harmonic Functions
365
Transformations of Boundary Conditions
367
CONTENTS
IX
10 Applications
of
Conformai
Mapping
373
Steady Temperatures
373
Steady Temperatures in a Half Plane
375
A Related Problem
377
Temperatures in a Quadrant
379
Electrostatic Potential
385
Potential in a Cylindrical Space
386
Two-Dimensional Fluid Flow
391
The Stream Function
393
Flows Around a Corner and Around a Cylinder
395
11
The Schwarz-Christoffel Transformation
403
Mapping the Real Axis Onto a Polygon
403
Schwarz-Christoffel Transformation
405
Triangles and Rectangles
408
Degenerate Polygons
413
Huid
Flow in a Channel Through a Slit
417
Flow in a Channel With an Offset
420
Electrostatic Potential About an Edge of a Conducting Plate
422
12
Integral Formulas of the
Poisson Type
429
Poisson
Integral Formula
429
Dirichlet Problem for a Disk
432
Related Boundary Value Problems
437
Schwarz
Integral Formula
440
Dirichlet Problem for a Half Plane
441
Neumann Problems
445
Appendixes
449
Bibliography
449
Table of Transformations of Regions
452
Index
461 |
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| id | DE-604.BV023072285 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:33:32Z |
| indexdate | 2024-07-09T21:10:21Z |
| institution | BVB |
| isbn | 9780073051949 0073051942 |
| language | English |
| lccn | 2007043490 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016275421 |
| oclc_num | 176648981 |
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| physical | XI, 468 S. |
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| spelling | Brown, James Ward 1934- Verfasser (DE-588)136655386 aut Complex variables and applications James Ward Brown ; Ruel V. Churchill 8th ed. Boston [u.a.] McGraw-Hill c2009 XI, 468 S. txt rdacontent n rdamedia nc rdacarrier Brown and Churchill series Includes bibliographical references and index Funções de uma variável complexa (análise;textos elementares) larpcal Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 Funktion Mathematik (DE-588)4071510-3 s 1\p DE-604 Mehrere komplexe Variable (DE-588)4169285-8 s 2\p DE-604 Churchill, Ruel Vance 1899-1987 Verfasser (DE-588)115367608 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016275421&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brown, James Ward 1934- Churchill, Ruel Vance 1899-1987 Complex variables and applications Funções de uma variável complexa (análise;textos elementares) larpcal Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4169285-8 (DE-588)4071510-3 |
| title | Complex variables and applications |
| title_auth | Complex variables and applications |
| title_exact_search | Complex variables and applications |
| title_exact_search_txtP | Complex variables and applications |
| title_full | Complex variables and applications James Ward Brown ; Ruel V. Churchill |
| title_fullStr | Complex variables and applications James Ward Brown ; Ruel V. Churchill |
| title_full_unstemmed | Complex variables and applications James Ward Brown ; Ruel V. Churchill |
| title_short | Complex variables and applications |
| title_sort | complex variables and applications |
| topic | Funções de uma variável complexa (análise;textos elementares) larpcal Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| topic_facet | Funções de uma variável complexa (análise;textos elementares) Functions of complex variables Funktionentheorie Mehrere komplexe Variable Funktion Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016275421&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT brownjamesward complexvariablesandapplications AT churchillruelvance complexvariablesandapplications |