Authors:
- Clear and rigorous exposition is supported by engaging examples and exercises
- Provides a means to learn complex analysis as well as subtle introduction to careful mathematical reasoning
- Topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (21 chapters)
-
Front Matter
About this book
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 complexanalysis 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.
Reviews
Authors and Affiliations
-
Mathematical Sciences Institute, Australian National University, Acton, Australia
Alexander Isaev
About the author
Bibliographic Information
Book Title: Twenty-One Lectures on Complex Analysis
Book Subtitle: A First Course
Authors: Alexander Isaev
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-319-68170-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-68169-6Published: 07 December 2017
eBook ISBN: 978-3-319-68170-2Published: 29 November 2017
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XII, 194
Number of Illustrations: 30 b/w illustrations
Topics: Analysis