An introduction to complex analysis: classical and modern approaches
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2005
|
| Schriftenreihe: | Modern analysis series
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 460 S. graph. Darst. |
| ISBN: | 1584884789 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV019819841 | ||
| 003 | DE-604 | ||
| 005 | 20110211 | ||
| 007 | t | ||
| 008 | 050524s2005 d||| |||| 00||| eng d | ||
| 020 | |a 1584884789 |9 1-584-88478-9 | ||
| 035 | |a (OCoLC)55535023 | ||
| 035 | |a (DE-599)BVBBV019819841 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-824 |a DE-91G |a DE-20 |a DE-703 |a DE-83 | ||
| 050 | 0 | |a QA300 | |
| 082 | 0 | |a 515 |2 22 | |
| 084 | |a SK 700 |0 (DE-625)143253: |2 rvk | ||
| 084 | |a MAT 260f |2 stub | ||
| 084 | |a 30-01 |2 msc | ||
| 100 | 1 | |a Tutschke, Wolfgang |d 1934- |e Verfasser |0 (DE-588)137687273 |4 aut | |
| 245 | 1 | 0 | |a An introduction to complex analysis |b classical and modern approaches |c Wolfgang Tutschke ; Harkrishan L. Vasudeva |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2005 | |
| 300 | |a XVI, 460 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Modern analysis series |v 7 | |
| 650 | 7 | |a Analyse (wiskunde) |2 gtt | |
| 650 | 4 | |a Mathematical analysis | |
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Funktionentheorie |0 (DE-588)4018935-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Vasudeva, Harkrishan L. |e Verfasser |4 aut | |
| 830 | 0 | |a Modern analysis series |v 7 |w (DE-604)BV019876740 |9 7 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013145128&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-013145128 | ||
Datensatz im Suchindex
| _version_ | 1804133322099523584 |
|---|---|
| adam_text | Contents
1
Preliminaries
1
1.1
The field of complex numbers
................. 1
1.1.1
Introduction
....................... 1
1.1.2
Complex numbers as pairs of real numbers
...... 1
1.1.3
Solvability of z*
= -1 ................. 3
1.1.4
Definition of complex numbers using equivalence classes
of polynomials
...................... 4
1.2
The complex plane
........................ 6
1.2.1
Geometrical interpretation of complex numbers
.... 6
1.2.2
Absolute value. Conjugate complex numbers
..... 6
1.2.3
Interpretation of complex numbers as vectors
..... 7
1.2.4
Trigonometric form of complex numbers
........ 9
1.2.5
Geometrical interpretation of the product of complex
numbers
.......................... 9
1.2.6
Powers and roots of complex numbers
......... 10
1.2.7
Some special sets in the complex plane
......... 11
1.2.8
Examples
......................... 12
1.3
Metric spaces
........................... 14
1.3.1
The concept of a metric space
.............. 14
1.3.2
Open sets
......................... 16
1.3.3
Convergence
....................... 18
1.3.4
Closed subsets
...................... 18
1.3.5
Definition of some more terms
............. 20
1.3.6
Completeness
....................... 22
1.3.7
Compact sets
....................... 24
1.3.8
Coverings
......................... 25
1.3.9
Examples
......................... 27
1.4
Mappings and functions. Continuity
.............. 28
VIU
1.4.1
Basic
definitions.....................
28
1.4.2
The extended complex plane. Spherical distance
... 31
1.4.3
Limits of functions
.................... 34
1.4.4
Continuous functions
................... 35
1.4.5
Curves
........................... 38
1.4.6
Connectivity
....................... 39
1.4.7
Sequences of functions
.................. 40
1.4.8
Infinite series
....................... 45
1.4.9
Power series
........................ 57
1.4.10
The complex exponential and trigonometric functions
67
1.4.11
Logarithm and its Riemann Surface
.......... 75
1.4.12
Remark on the concept of a topological space
..... 80
1.4.13
Examples
......................... 81
1.5
Exercises to Chapter
1 ..................... 82
2
The classical approach
87
2.1
Ordinary complex differentiation
................ 87
2.1.1
Complex differentiability
................. 87
2.1.2
Rules of differentiation
.................. 90
2.1.3
The Cauchy-Riemann system
.............. 90
2.1.4
Holomorphic functions
.................. 94
2.1.5
Differentiation of Power Series
............. 96
2.1.6
Differentiation of inverse functions
........... 100
2.2
Preliminaries of the Integral Calculus
............. 102
2.2.1
Line integrals of real valued functions
......... 102
2.2.2
The Green-Gauss Integral Theorem
.......... 104
2.2.3
Line integrals of complex valued functions
....... 106
2.3
Complex Integral Theorems
.................. 112
2.3.1
Cauchy s Integral Theorem
............... 113
2.3.2
Cauchy s Integral Formula
................ 115
2.4
Exercises to Chapter
2 ..................... 116
їх
3
An alternative approach
121
3.1
Partial complex differentiations
................. 121
3.1.1
Linearization of functions of one real variable
..... 121
3.1.2
Linearization of functions depending on several real
variables
.......................... 121
3.1.3
Linearization of functions depending on one complex
variable
.......................... 122
3.1.4
Definition of partial complex derivatives
........ 122
3.1.5
Differentiability rules for partial complex derivatives
. 123
3.2
Complex Green-Gauss Integral Theorems
*.......... 123
3.3
Generalized Cauchy Integral Formula
* ............ 125
3.3.1
Application of complex version of the Green-Gauss For¬
mula to functions having isolated singularities
..... 125
3.3.2
The limit of the domain integral. Schmidt s Inequality
125
3.3.3
The limit of the line integral
.............. 128
3.3.4
An integral representation formula for continuously dif-
ferentiable functions
................... 128
3.4
The classical Cauchy Integral Formula
* ........... 129
3.4.1
Another approach to Cauchy s Integral Formula
. . . 129
3.4.2
A second proof of Cauchy s Integral Theorem
..... 129
3.5
Comparison
* .......................... 130
3.5.1
Partial complex derivatives of functions having an ordi¬
nary complex derivative
................. 130
3.5.2
Ordinary complex differentiability of solutions of the
Cauchy-Riemann system
................. 130
3.6
Exercises to Chapter
3 ..................... 131
4
Local properties
135
4.1
Existence of higher order derivatives
.............. 135
4.1.1
A method for proving local properties of holomorphic
functions
......................... 135
4.1.2
The holomorphy of
Une
integrals with respect to com¬
plex parameters
...................... 135
4.1.3
Cauchy s Integral Formula for the derivatives of a holo¬
morphic function
..................... 137
4.2
Local power series representation
................ 138
4.2.1
Power series representation of the Cauchy kernel
. . . 138
χ
4.2.2
Local power series for holomorphic functions
ала
an in¬
tegral representation of the coefficients
......... 139
4.2.3
Cauchy s estimate of the coefficients
.......... 142
4.2.4
The power series of the product of two holomorphic
functions
......................... 142
4.2.5
Division of power series
................. 143
4.3
Distribution of zeros
....................... 144
4.4
The
Weierstrass
Convergence Theorem
............ 145
4.4.1
Statement of the problem
................ 145
4.4.2
Formulation and proof
.................. 145
4.4.3
Termwise differentiability
................ 146
4.5
Connexion with plane Potential Theory
............ 147
4.5.1
Holomorphic functions as solutions of the Laplace equa¬
tion
............................ 147
4.5.2
Representation of the Laplace operator by partial com¬
plex differentiations
................... 148
4.6
Complex Integral Theorems revisited
* ............ 148
4.6.1
Goursat s Theorem
.................... 149
4.6.2
G.
Fichera s
proof of the Goursat Theorem
...... 152
4.6.3
A measure-theoretic approach to Cauchy s Integral The¬
orem
............................ 155
4.6.4
Consequences of Complex Integral Theorems under
weaker assumptions
................... 163
4.7
Exercises to Chapter
4 ..................... 163
5
Global properties
169
5.1
Analytic continuation
...................... 169
5.1.1
Definition of analytic continuation
........... 169
5.1.2
The Unique Continuation Theorem
........... 170
5.1.3
The uniqueness of analytic continuation
........ 171
5.1.4
Analytic continuation of the limit
fonction
of a power
series
........................... 172
5.1.5
Analytic continuation across a curve
.......... 180
5.1.6
Global behaviour of holomorphic functions with non-
isolated wo-points
.................... 181
5.2
Maximum Modulus Principle (Maximum Principle)
..... 182
Xl
5.2.1
The basic statement
................... 182
5.2.2
Holomorphic functions with constant modulus
.... 182
5.2.3
Mean Value Property of holomorphic functions
.... 183
5.2.4
Proof of the Maximum Modulus Principle
....... 183
5.2.5
A Maximum Modulus Principle for bounded domains
184
5.2.6
The Minimum Modulus Principle (Minimum Principle)
184
5.3
Entire functions
......................... 186
5.3.1
Definition and basic properties
............. 186
5.3.2
Liouville s Theorem
................... 187
5.3.3
Functions of polynomial growth
............. 187
5.4
Fundamental Theorem of Algebra
............... 188
5.4.1
Statement of the problem
................ 188
5.4.2
Proofs of the Fundamental Theorem of Algebra using
complex analysis
..................... 189
5.4.3
Special case: Existence of the roots of complex numbers
192
5.4.4
Argand s proof of the Fundamental Theorem of Algebra
193
5.4.5
Additional proofs of the Fundamental Theorem of Al¬
gebra
........................... 195
5.4.6
Factorization of polynomials
............... 195
5.5
Exercises to Chapter
5 ..................... 195
β
Isolated singularities
199
6.1
Classification
........................... 199
6.1.1
Definition of isolated singularities
............ 199
6.1.2
Removable singularities
................. 199
6.1.3
Poles
............................ 201
6.1.4
Essential singularities
.................. 202
6.2
Laurent series
.......................... 202
6.2.1
Holomorphic functions in an annulus
.......... 202
6.2.2
Holomorphic functions in a punctured disk
...... 205
6.3
Characterization by the principal part
............. 206
6.4
Meromorphic functions
..................... 208
6.5
Behaviour at essential singularities
............... 210
6.6
Behaviour at infinity
...................... 211
xii
6.7
Partial fractions
of rational functions
............. 213
6.7.1
An application of the Division Algorithm
....... 213
6.7.2
Representation of rational functions by partial fractions
214
6.8
Meromorphic functions on the Sphere
............. 216
6.9
Exercises to Chapter
6 ..................... 217
7
Homotopy
223
7.1
Statement of the problem
.................... 223
7.2
Homotopic curves
........................ 225
7.3
Path independent line integrals
................. 227
7.4
Simply connected domains
................... 229
7.4.1
The concept of simple connectedness
.......... 229
7.4.2
Cauchy s Integral Theorem in homotopy formulation
. 229
7.4.3
Monodromy Theorem
.................. 230
7.5
Solution of first order systems
................. 232
7.5.1
A property of path independent line integrals
..... 232
7.5.2
Local solution of first order systems
.......... 233
7.5.3
Global solutions of first order systems
......... 234
7.6
Conjugate solutions
....................... 234
7.7
Inversion of complex differentiation
.............. 235
7.8
Morera s
Theorem
........................ 237
7.9
Potentials of vector fields
.................... 238
7.9.1
The concept of a potential
................ 238
7.9.2
Some physical interpretations of vector fields
..... 239
7.9.3
Curl-free and source-free vector fields
......... 240
7.10
Exercises to Chapter
7 ..................... 241
8
Residue theory
245
8.1
Statement of the problem
.................... 245
8.2
Winding numbers
........................ 245
8.3
The integration of principal parts
............... 246
8.3.1
Tennwise integration
................... 246
8.3.2
A complex version of the Fundamental Theorem of Dif¬
ferential and Integral Calculus
............. 247
XIU
8.3.3 Integration
of meromorphic functions with first order
poles
............................ 249
8.4
Residue Theorem
........................ 249
8.5
Calculation of residues
..................... 251
8.5.1
The case of first order poles
............... 252
8.5.2
The case of poles of order
к
> 2............ 253
8.5.3
Determination of residues using Laurent series
.... 253
8.6
Exercises to Chapter
8 ..................... 254
9
Applications of residue calculus
257
9.1
Total number of zeros and poles
................ 257
9.1.1
Representation by a boundary integral
......... 257
9.1.2
A proof of Fundamental Theorem of Algebra based on
a boundary integral representation
........... 258
9.1.3
Rouché s
Theorem
.................... 259
9.1.4
Another proof of Fundamental Theorem of Algebra us¬
ing
Rouché s
Theorem
.................. 259
9.2
Evaluation of definite integrals
................. 260
9.2.1
Evaluation of integrals involving certain periodic func¬
tions between the limits
0
and
2π
........... 260
9.2.2
Evaluation of improper real integrals
.......... 263
9.2.3
Integrals involving many-valued functions
....... 273
9.3
Sum of certain series
...................... 277
9.4
Exercises to Chapter
9 ..................... 280
10
Mapping properties
287
10.1
Continuously differentiable mappings
............. 287
10.1.1
Invertible linear mappings. The general case
..... 287
10.1.2
The exceptional case
................... 290
10.1.3
Calculation of the angle of rotation
........... 291
10.1.4
Orientation-preserving mappings
............ 292
10.2
Conformai
mappings
...................... 293
10.2.1
Conformai
mappings by holomorphic functions
.... 293
10.2.2
Behaviour at zeros of the derivative
.......... 294
10.2.3
Inversion of multivalent functions
* .......... 295
10.2.4
Another proof of the local existence of the inverse func¬
tion
*...........................
296
10.2.5
Domain
invariance
* .................. 296
10.2.6
Behaviour of the Cauchy-Riemann system under con-
formal mappings
* ................... 297
10.2.7
Conformai
equivalence
* ................ 297
10.2.8
Quasiconformal mappings
* .............. 297
10.3
Examples of
conformai
mappings
................ 299
10.3.1
Some elementary
conformai
mappings
......... 299
10.3.2
The
Möbius
fractional linear transformations
..... 302
10.3.3
Mappings of the unit disk onto itself
.......... 307
10.3.4
Complex plane onto itself
................ 313
10.3.5
Schwarz
Reflection Principle
.............. 314
10.4
Univalent
functions
* ...................... 316
10.4.1
Definition and basic properties
............. 316
10.4.2
Bieberbach s conjecture
................. 316
10.4.3
Univalent
functions outside the unit disk
........ 317
10.4.4
Proof of Bieberbach s conjecture for
аг
........ 318
10.4.5
Koebe s Covering Theorem
............... 320
10.4.6
Limits of
univalent
functions
.............. 320
10.5
Riemann s Mapping Theorem
* ................ 321
10.5.1
Statement of the problem
................ 321
10.5.2
Outline of the proof; extremal problems in classes of
holomorphic functions
.................. 322
10.5.3
Proof of Riemann s Mapping Theorem
......... 322
10.5.4
Summary of the solution of the main problems of Con-
formal Mappings
..................... 326
10.6
Construction of flow
Unes
*................... 328
10.6.1
The level curves of real and imaginary parts of holomor¬
phic functions
....................... 328
10.6.2
Construction of curl-free and source-free vector fields in
the plane
......................... 328
10.6.3
Flow lines
......................... 329
10.6.4
Examples of the construction of flow
Unes
....... 330
10.7
Exercises to Chapter
10..................... 332
11
Special
functions
339
11.1
Prescribed principal parts
.................... 339
11.2
Prescribed zeros
......................... 346
11.3
Infinite products
*........................ 348
11.3.1
Statement of the the problem
.............. 348
11.3.2
Infinite products of complex numbers
......... 349
11.3.3
Infinite products of complex-valued functions
..... 355
11.3.4
Derivatives of infinite products
............. 359
11.4
Weierstrass
products
* ..................... 362
11.4.1
Statement of the problem
................ 362
11.4.2
Entire functions without zeros
............. 363
11.4.3
Weierstrass
Primary Factors
............... 364
11.4.4
Preliminaries for the application of
Weierstrass
Pri¬
mary Factors
....................... 366
11.4.5
The
Weierstrass
Factorization Theorem
........ 367
11.4.6
Some examples
...................... 368
11.5
Gamma function
*........................ 369
11.5.1
Definition of the gamma function
............ 369
11.5.2
Functional equation of the gamma function
...... 372
11.5.3
Some elementary properties of the gamma function
. . 372
11.5.4
An integral representation of the gamma function in the
right half-plane
...................... 375
11.5.5
A partial fraction representation of the gamma function
379
11.6
The Riemann
zeta
function
* ................. 381
11.6.1
Definition of Riemann s
zeta
function
......... 381
11.6.2
Connexion between
zeta
function and prime numbers
382
11.6.3
Analytic continuation of the Riemann
zeta
function
. 383
11.6.4
Relationship between gamma function and
zeta
function
386
11.7
EDiptic functions
* ....................... 388
11.7.1
Weierstrass
zeta
function
................ 388
11.7.2
Weierstrass p-function
................. 390
11.7.3
Periods of meromorphic functions
............ 393
11.7.4
Properties of elliptic functions
............. 400
XVI
11.7.5
Construction
of elliptic functions with prescribed prin¬
cipal parts
......................... 406
11.7.6
Related topics
...................... 408
11.8
Exercises to Chapter
11..................... 416
12
Boundary value problems
425
12.1
Preliminaries
........................... 425
12.1.1
Harmonic functions and the Dirichlet problem
.... 425
12.1.2
Maximum Principle
................... 426
12.2
The
Poisson
Integral Formula
................. 428
12.2.1
Derivation of Poisson s Integral Formula
........ 428
12.2.2
Construction of solutions of the Laplace equation by
Poisson s Integral Formula
................ 430
12.2.3
Preliminaries for the proof of Theorem
101...... 431
12.2.4
Proof of Theorem
101.................. 432
12.2.5
Examples
......................... 433
12.2.6
Poisson
kernel and its conjugate
............ 435
12.3
Cauchy Type Integrals
* .................... 436
12.3.1
Statement of the problem
................ 436
12.3.2
Cauchy Type Integrals with constant density
..... 437
12.3.3
Cauchy Type Integrals with Holder-continuous density
440
12.3.4
The Plemelj Formulae
.................. 444
12.4
Desired holomorphic functions
*................ 447
12.4.1
The
Schwarz
problem
.................. 447
12.4.2
Solution of the
Schwarz
problem in a disk
....... 448
12.4.3
The Riemann boundary value problem
......... 449
12.5
Exercises to Chapter
12..................... 450
References
455
Index
457
|
| any_adam_object | 1 |
| author | Tutschke, Wolfgang 1934- Vasudeva, Harkrishan L. |
| author_GND | (DE-588)137687273 |
| author_facet | Tutschke, Wolfgang 1934- Vasudeva, Harkrishan L. |
| author_role | aut aut |
| author_sort | Tutschke, Wolfgang 1934- |
| author_variant | w t wt h l v hl hlv |
| building | Verbundindex |
| bvnumber | BV019819841 |
| callnumber-first | Q - Science |
| callnumber-label | QA300 |
| callnumber-raw | QA300 |
| callnumber-search | QA300 |
| callnumber-sort | QA 3300 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 700 |
| classification_tum | MAT 260f |
| ctrlnum | (OCoLC)55535023 (DE-599)BVBBV019819841 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01635nam a2200421 cb4500</leader><controlfield tag="001">BV019819841</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20110211 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">050524s2005 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1584884789</subfield><subfield code="9">1-584-88478-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)55535023</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV019819841</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA300</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 700</subfield><subfield code="0">(DE-625)143253:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 260f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">30-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Tutschke, Wolfgang</subfield><subfield code="d">1934-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)137687273</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">An introduction to complex analysis</subfield><subfield code="b">classical and modern approaches</subfield><subfield code="c">Wolfgang Tutschke ; Harkrishan L. Vasudeva</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton [u.a.]</subfield><subfield code="b">Chapman & Hall/CRC</subfield><subfield code="c">2005</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 460 S.</subfield><subfield code="b">graph. Darst.</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="490" ind1="1" ind2=" "><subfield code="a">Modern analysis series</subfield><subfield code="v">7</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analyse (wiskunde)</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionentheorie</subfield><subfield code="0">(DE-588)4018935-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Funktionentheorie</subfield><subfield code="0">(DE-588)4018935-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Vasudeva, Harkrishan L.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Modern analysis series</subfield><subfield code="v">7</subfield><subfield code="w">(DE-604)BV019876740</subfield><subfield code="9">7</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</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=013145128&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:BVB01-013145128</subfield></datafield></record></collection> |
| id | DE-604.BV019819841 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:06:52Z |
| institution | BVB |
| isbn | 1584884789 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013145128 |
| oclc_num | 55535023 |
| open_access_boolean | |
| owner | DE-824 DE-91G DE-BY-TUM DE-20 DE-703 DE-83 |
| owner_facet | DE-824 DE-91G DE-BY-TUM DE-20 DE-703 DE-83 |
| physical | XVI, 460 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Modern analysis series |
| series2 | Modern analysis series |
| spelling | Tutschke, Wolfgang 1934- Verfasser (DE-588)137687273 aut An introduction to complex analysis classical and modern approaches Wolfgang Tutschke ; Harkrishan L. Vasudeva Boca Raton [u.a.] Chapman & Hall/CRC 2005 XVI, 460 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Modern analysis series 7 Analyse (wiskunde) gtt Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 Vasudeva, Harkrishan L. Verfasser aut Modern analysis series 7 (DE-604)BV019876740 7 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013145128&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tutschke, Wolfgang 1934- Vasudeva, Harkrishan L. An introduction to complex analysis classical and modern approaches Modern analysis series Analyse (wiskunde) gtt Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 |
| title | An introduction to complex analysis classical and modern approaches |
| title_auth | An introduction to complex analysis classical and modern approaches |
| title_exact_search | An introduction to complex analysis classical and modern approaches |
| title_full | An introduction to complex analysis classical and modern approaches Wolfgang Tutschke ; Harkrishan L. Vasudeva |
| title_fullStr | An introduction to complex analysis classical and modern approaches Wolfgang Tutschke ; Harkrishan L. Vasudeva |
| title_full_unstemmed | An introduction to complex analysis classical and modern approaches Wolfgang Tutschke ; Harkrishan L. Vasudeva |
| title_short | An introduction to complex analysis |
| title_sort | an introduction to complex analysis classical and modern approaches |
| title_sub | classical and modern approaches |
| topic | Analyse (wiskunde) gtt Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Analyse (wiskunde) Mathematical analysis Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013145128&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019876740 |
| work_keys_str_mv | AT tutschkewolfgang anintroductiontocomplexanalysisclassicalandmodernapproaches AT vasudevaharkrishanl anintroductiontocomplexanalysisclassicalandmodernapproaches |