C o o r d i n a t e s   (6,0,9)

Complex Analysis
Student: Joe Erickson (erickson@bucks.edu)


March 16, 2017 - A goodly amount of work has been done on Chapter 1, which still needs more work, but it's getting there.

October 3, 2015 - Rather than the Prime Number Theorem, Chapter 13 will be on the Fourier Transform. There will be a Chapter 14 on the Gamma and Zeta functions later on, which will contain a section on the Prime Number Theorem. Even further in the future there may be a Chapter 15 on Elliptic and Theta functions. The main reference for these new chapters will be Complex Analysis by Stein & Shakarchi. At least one chapter about functions of several complex variables is just a twinkling in my eye right now.

June 30, 2015 - All cross references in the book are now up to date.

May 6, 2015 - Except for the Appendix, the chapter links below no longer lead to individual chapter files, but rather go to the appropriate page of the book file. The book link itself (at top) goes to the first page of the file. The Appendix is a dead-end and something of a misnomer. It will someday be given a different designation as a stand-alone document.

May 3, 2015 - Table of contents for the book is done.

May 2, 2015 - Except for the Appendix, the separate chapters linked to below have been put together into a single book: Complex Analysis. Quite soon I'll include a title page, table of contents, and symbols glossary. A little further down the road there will be an index. Still further away is the inclusion of Chapter 13, but it will get done, along with the inclusion of additional proofs, examples and exercises throughout.

September 16, 2014 - The End Game is at hand, and the book nearly done! Courses at Drexel start in under a week, however, so I foresee setting up the chapter on the Prime Number Theorem and then sweeping up pockets of resistance as time allows over the course of the coming months. By and large, though, the project is finished. Still, there are other books out there, and I'll be taking a course in complex analysis sometime in the future.

June 11, 2014 - A significant reorganization of the material in the first four chapters has been done, with Chapter 4 splitting into two chapters. The titles of the first two sections in Chapter 1 have been changed, and a corresponding change in content will occur over time. I think this is the last big shake-up of the manuscript, and at this point work on Chapter 11 (on families of analytic functions) can finally begin.

May 18, 2014 - Chapter 1 has been broken into two chapters, and thus the newest chapter on analytic continuation is now Chapter 9. Cross-referencing is now in the process of being updated.

May 14, 2014 - Work has begun on Chapter 8, on analytic continuation.

April 8, 2014 - Chapter 2 has been broken into two chapters, and thus the newest chapter on Poisson integrals is now Chapter 7.

April 7, 2014 - Work on Chapter 6, on Poisson integrals, has begun.

March 7, 2014 - Work on Chapter 5, on conformal mappings, has begun.

November 11, 2013 - A proof of the Fundamental Theorem of Algebra is now in Chapter 2 of the notes.

June 20, 2013 - The material largely relating to formal power series has been relegated to an Appendix as part of a reorganization that will bring the narrative more into conformity with Ash & Novinger.

May 22, 2013 - I'm finding the approach taken in the book Complex Variables by Ash and Novinger more to my liking, and so from now on the exercises and narrative will tend to derive from it instead of Lang. A reshuffling of contents below is inevitable as a result.

March 22, 2013 - I've made every attempt to make the treatment of formal power series more "airtight" compared with Lang, with the final touches (I think) being made today. The goal is not to write a new textbook here, but rather to organize and develop certain concepts in a way that some (including myself) may find to be useful as a reference.

January 1, 2013 - I'm back in the complex analysis game after spending 10 months churning out notes for differential equations, linear algebra, and all three calculus courses.

February 11, 2012 - Mostly practice and some theory pertaining to complex analysis. The primary reference here will be the 4th edition of Serge Lang's Complex Analysis.