Twenty-One Lectures on Complex Analysis : (Record no. 5815)

MARC details
000 -LEADER
fixed length control field 03970cam a22002295i 4500
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240607170456.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 171129s2017 gw |||| o |||| 0|eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9783319681702
041 ## - LANGUAGE CODE
Language code of text/sound track or separate title eng
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515
Item number IsaT
100 1# - MAIN ENTRY--AUTHOR NAME
Personal name Isaev, Alexander.
245 10 - TITLE STATEMENT
Title Twenty-One Lectures on Complex Analysis :
Remainder of title A First Course /
Statement of responsibility, etc Alexander Isaev.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication Cham :
Name of publisher Springer,
Year of publication c2017.
300 ## - PHYSICAL DESCRIPTION
Number of Pages XII,194p.
490 1# - SERIES STATEMENT
Series statement Springer Undergraduate Mathematics Series
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note 1. Complex Numbers. The Fundamental Theorem of Algebra -- 2. R- and C-Differentiability -- 3 The Stereographic Projection. Conformal Maps. The Open Mapping Theorem -- 4. Conformal Maps (Continued). Möbius Transformations -- 5. Möbius Transformations (Continued). Generalised Circles. Symmetry -- 6. Domains Bounded by Pairs of Generalised Circles. Integration -- 7. Primitives Along Paths. Holomorphic Primitives on a Disk. Goursat's Lemma -- 8. Proof of Lemma 7.2. Homotopy. The Riemann Mapping Theorem -- 9. Cauchy's Independence of Homotopy Theorem. Jordan Domains -- 10. Cauchy's Integral Theorem. Proof of Theorem 3.1. Cauchy's Integral Formula -- 11. Morera's Theorem. Power Series. Abel's Theorem. Disk and Radius of Convergence -- 12. Power Series (Cont'd). Expansion of a Holomorphic Function. The Uniqueness Theorem -- 13. Liouville's Theorem. Laurent Series. Isolated Singularities -- 14. Isolated Singularities (Continued). Poles and Zeroes. Isolated Singularities at infinity -- 15. Isolated Singularities at infinity (Continued). Residues. Cauchy's Residue Theorem -- 16. Residues (Continued). Contour Integration. The Argument Principle 137 -- 17. The Argument Principle (Cont'd). Rouché's Theorem. The Maximum Modulus Principle -- 18. Schwarz's Lemma. (Pre) Compactness. Montel's Theorem. Hurwitz's Theorem -- 19. Analytic Continuation -- 20. Analytic Continuation (Continued). The Monodromy Theorem -- 21. Proof of Theorem 8.3. Conformal Transformations of Simply- Connected Domains -- Index.
520 ## - SUMMARY, ETC.
Summary, etc At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. To guarantee a student's progression, more advanced topics are spread out over several lectures. This text is based on a one-semester (12 week) undergraduate course in complex analysis that the author has taught at the Australian National University for over twenty years. Most of the principal facts are deduced from Cauchy's Independence of Homotopy Theorem allowing us to obtain a clean derivation of Cauchy's Integral Theorem and Cauchy's Integral Formula. Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Analysis (Mathematics).
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Mathematical analysis.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Analysis.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type Books
Holdings
Withdrawn status Lost status Damaged status Collection code Home library Current library Shelving location Date acquired Source of acquisition Purchase Price Bill number Full call number Accession Number Print Price Bill Date/Price effective from Koha item type
      Mathematics Indian Institute of Technology Tirupati Indian Institute of Technology Tirupati General Stacks 07/06/2024 Gifted 0.00 Free 515 IsaT 10503 3292.55 07/06/2024 Books