An introduction to complex analysis and geometry:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2010
|
| Schriftenreihe: | Pure and applied undergraduate texts
12 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022617073&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 163 S. graph. Darst. |
| ISBN: | 9780821852743 |
Internformat
MARC
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| 010 | |a 2010029859 | ||
| 020 | |a 9780821852743 |c alk. paper |9 978-0-8218-5274-3 | ||
| 035 | |a (OCoLC)734071192 | ||
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| 100 | 1 | |a D'Angelo, John P. |d 1951- |e Verfasser |0 (DE-588)143370472 |4 aut | |
| 245 | 1 | 0 | |a An introduction to complex analysis and geometry |c John P. D'Angelo |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2010 | |
| 300 | |a XI, 163 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied undergraduate texts |v 12 | |
| 490 | 0 | |a The Sally series | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Sequences (Mathematics) | |
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Lehrbuch |0 (DE-588)4123623-3 |D s |
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| 830 | 0 | |a Pure and applied undergraduate texts |v 12 |w (DE-604)BV035489189 |9 12 | |
| 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=022617073&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-022617073 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 939-12 |
|---|---|
| DE-BY-TUM_katkey | 1946142 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040071432941 |
| _version_ | 1821933296169254912 |
| adam_text | Contents
Preface
vii
Chapter
1.
From the Real Numbers to the Complex Numbers
1
1.
Introduction
1
2.
Number systems
1
3.
Inequalities and ordered fields
7
4.
The complex numbers
15
5.
Alternative definitions of
С
17
6.
A glimpse at metric spaces
21
Chapter
2.
Complex Numbers
25
1.
Complex conjugation
25
2.
Existence of square roots
27
3.
Limits
30
4.
Convergent infinite series
32
5.
Uniform convergence and consequences
35
6.
The unit circle and trigonometry
40
7.
The geometry of addition and multiplication
44
8.
Logarithms
45
Chapter
3.
Complex Numbers and Geometry
49
1.
Lines, circles, and balls
49
2.
Analytic geometry
52
3.
Quadratic polynomials
53
4.
Linear fractional transformations
60
5.
The Riemann sphere
63
Contents
Chapter
4. Power
Series Expansions
67
1.
Geometric series
67
2.
The radius of convergence
70
3.
Generating functions
73
4.
Fibonacci numbers
74
5.
An application of power series
77
6.
Rationality
79
Chapter
5.
Complex Differentiation
83
1.
Definitions of complex analytic function
83
2.
Complex differentiation
85
3.
The Cauchy-Riemann equations
86
4.
Orthogonal trajectories and harmonic functions
89
5.
A glimpse at harmonic functions
90
6.
What is a differential form?
96
Chapter
6.
Complex Integration
99
1.
Complex-valued functions
99
2.
Line integrals
101
3.
Goursat s proof
109
4.
The Cauchy integral formula 111
5.
A return to the definition of complex analytic function
116
Chapter
7.
Applications of Complex Integration
119
1.
Singularities and residues
119
2.
Evaluating real integrals using complex variables methods
121
3.
Fourier transforms
128
4.
The Gamma function
131
Chapter
8.
Additional Topics
137
1.
The minimum-maximum theorem
137
2.
The fundamental theorem of algebra
138
3.
Winding numbers, zeroes, and poles
141
4.
Pythagorean triples
147
5.
Elementary mappings
150
6.
Quaternions
153
7.
Higher-dimensional complex analysis
155
Further reading
158
Bibliography
159
Index
161
|
| any_adam_object | 1 |
| author | D'Angelo, John P. 1951- |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 519f MAT 300f |
| ctrlnum | (OCoLC)734071192 (DE-599)BVBBV037465192 |
| 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 |
| format | Book |
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| id | DE-604.BV037465192 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T15:17:26Z |
| institution | BVB |
| isbn | 9780821852743 |
| language | English |
| lccn | 2010029859 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022617073 |
| oclc_num | 734071192 |
| open_access_boolean | |
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| owner_facet | DE-703 DE-634 DE-20 DE-824 DE-188 DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| physical | XI, 163 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Pure and applied undergraduate texts |
| series2 | Pure and applied undergraduate texts The Sally series |
| spellingShingle | D'Angelo, John P. 1951- An introduction to complex analysis and geometry Pure and applied undergraduate texts Functions of complex variables Geometry, Algebraic Sequences (Mathematics) Funktionentheorie (DE-588)4018935-1 gnd Lehrbuch (DE-588)4123623-3 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4123623-3 |
| title | An introduction to complex analysis and geometry |
| title_auth | An introduction to complex analysis and geometry |
| title_exact_search | An introduction to complex analysis and geometry |
| title_full | An introduction to complex analysis and geometry John P. D'Angelo |
| title_fullStr | An introduction to complex analysis and geometry John P. D'Angelo |
| title_full_unstemmed | An introduction to complex analysis and geometry John P. D'Angelo |
| title_short | An introduction to complex analysis and geometry |
| title_sort | an introduction to complex analysis and geometry |
| topic | Functions of complex variables Geometry, Algebraic Sequences (Mathematics) Funktionentheorie (DE-588)4018935-1 gnd Lehrbuch (DE-588)4123623-3 gnd |
| topic_facet | Functions of complex variables Geometry, Algebraic Sequences (Mathematics) Funktionentheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022617073&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035489189 |
| work_keys_str_mv | AT dangelojohnp anintroductiontocomplexanalysisandgeometry |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 001z 2001 B 939-12
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |