A First Course in Complex Analysis
by M. Beck, G. Marchesi, D. Pixton
Publisher: San Francisco State University 2012
Number of pages: 215
These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated 'from scratch'. This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.
Home page url
Download or read it online for free here:
by K. Chandrasekharan - Tata Institute of Fundamental Research
These notes provide an intorduction to the theory of the Riemann Zeta-function for students who might later want to do research on the subject. The Prime Number Theorem, Hardy's theorem, and Hamburger's theorem are the principal results proved here.
by George Cain
The textbook for an introductory course in complex analysis. It covers complex numbers and functions, integration, Cauchy's theorem, harmonic functions, Taylor and Laurent series, poles and residues, argument principle, and more.
by G. N. Watson - Cambridge University Press
This brief monograph offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications ...
by Leif Mejlbro - BookBoon
Polynomials are the first class of functions that the student meets. Therefore, one may think that they are easy to handle. They are not in general! Topics as e.g. finding roots in a polynomial and the winding number are illustrated.