MARC details
| 000 -LEADER |
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04879nam a22005175i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
978-1-4471-0027-0 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20210921163821.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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| fixed length control field |
cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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121227s2003 xxk| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781447100270 |
| -- |
978-1-4471-0027-0 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-1-4471-0027-0 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA331-355 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBKD |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT034000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBKD |
| Source |
thema |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515.9 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Howie, John M. |
| Relator term |
author. |
| Relator code |
aut |
| -- |
http://id.loc.gov/vocabulary/relators/aut |
| 245 10 - TITLE STATEMENT |
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| Title |
Complex Analysis |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by John M. Howie. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
1st ed. 2003. |
| 264 #1 - |
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| -- |
London : |
| -- |
Springer London : |
| -- |
Imprint: Springer, |
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2003. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XI, 260 p. |
| Other physical details |
online resource. |
| 336 ## - |
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| -- |
text |
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txt |
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rdacontent |
| 337 ## - |
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| -- |
computer |
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c |
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rdamedia |
| 338 ## - |
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| -- |
online resource |
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cr |
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rdacarrier |
| 347 ## - |
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| -- |
text file |
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PDF |
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rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Springer Undergraduate Mathematics Series, |
| International Standard Serial Number |
1615-2085 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1. What Do I Need to Know? -- 1.1 Set Theory -- 1.2 Numbers -- 1.3 Sequences and Series -- 1.4 Functions and Continuity -- 1.5 Differentiation -- 1.6 Integration -- 1.7 Infinite Integrals -- 1.8 Calculus of Two Variables -- 2. Complex Numbers -- 2.1 Are Complex Numbers Necessary? -- 2.2 Basic Properties of Complex Numbers -- 3. Prelude to Complex Analysis -- 3.1 Why is Complex Analysis Possible? -- 3.2 Some Useful Terminology -- 3.3 Functions and Continuity -- 3.4 The O and o Notations -- 4. Differentiation -- 4.1 Differentiability -- 4.2 Power Series -- 4.3 Logarithms -- 4.4 Cuts and Branch Points -- 4.5 Singularities -- 5. Complex Integration -- 5.1 The Heine-Borel Theorem -- 5.2 Parametric Representation -- 5.3 Integration -- 5.4 Estimation -- 5.5 Uniform Convergence -- 6. Cauchy's Theorem -- 6.1 Cauchy's Theorem: A First Approach -- 6.2 Cauchy's Theorem: A More General Version -- 6.3 Deformation -- 7. Some Consequences of Cauchy's Theorem -- 7.1 Cauchy's Integral Formula -- 7.2 The Fundamental Theorem of Algebra -- 7.3 Logarithms -- 7.4 Taylor Series -- 8. Laurent Series and the Residue Theorem -- 8.1 Laurent Series -- 8.2 Classification of Singularities -- 8.3 The Residue Theorem -- 9. Applications of Contour Integration -- 9.1 Real Integrals: Semicircular Contours -- 9.2 Integrals Involving Circular Functions -- 9.3 Real Integrals: Jordan's Lemma -- 9.4 Real Integrals: Some Special Contours -- 9.5 Infinite Series -- 10. Further Topics -- 10.1 Integration of f?/f; Rouché's Theorem -- 10.2 The Open Mapping Theorem -- 10.3 Winding Numbers -- 11. Conformai Mappings -- 11.1 Preservation of Angles -- 11.2 Harmonic Functions -- 11.3 Möbius Transformations -- 11.4 Other Transformations -- 12. Final Remarks -- 12.1 Riemann's Zeta function -- 12.2 Complex Iteration -- 13. Solutions to Exercises -- Subject IndexBibliography -- Subject IndexIndex. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers, differentiation, integration, Cauchy's theorem, and its consequences, Laurent series and the residue theorem, applications of contour integration, conformal mappings, and harmonic functions. A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Functions of complex variables. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematical analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Analysis (Mathematics). |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Functions of a Complex Variable. |
| -- |
https://scigraph.springernature.com/ontologies/product-market-codes/M12074 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Analysis. |
| -- |
https://scigraph.springernature.com/ontologies/product-market-codes/M12007 |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9781852337339 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9781447100287 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Springer Undergraduate Mathematics Series, |
| -- |
1615-2085 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.1007/978-1-4471-0027-0">https://doi.org/10.1007/978-1-4471-0027-0</a> |
| 912 ## - |
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ZDB-2-SMA |
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ZDB-2-SXMS |
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ZDB-2-BAE |
