Skip to main content
Chaptra
Cover of A Course in Complex Analysis

A Course in Complex Analysis

Written by Wolfgang Fischer,Ingo Lieb

Not rated yet — tap a star to review it

280 pages, about 6 hours of reading

Mathematics

Chaptra reads alongside you — AI insights, chapter breakdowns and reader discussions for every book. Join free

About this book

This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem ...) and – a new feature in this context! – to exhibiting basic facts in the theory of several complex variables. Part of the book is a translation of the authors’ German text “Einführung in die komplexe Analysis”; some material was added from the by now almost “classical” text “Funktionentheorie” written by the authors, and a few paragraphs were newly written for special use in a master’s programme.

Read it with a club

Small groups reading the same books and talking as they go.

All clubs
A warm-lit wall of bookshelves

News

  • 1 member
  • 1,813 discussions
  • Active 8h ago

Read A Course in Complex Analysis alongside people who are reading it too.

Open the club

Also here: News Bulletin, Just Joking....

Chaptra Prime — paid clubs, every club feature, and unlimited reading support, for $5 a month or $60 once.

See Prime

Reading guide

Themes, characters and key ideas in A Course in Complex Analysis, written by Chaptra AI.

  • about 40 hours
  • advanced
  • Rigorous
  • Comprehensive
  • Challenging

A Course in Complex Analysis by Fischer and Lieb is a meticulously crafted textbook designed for advanced undergraduate and beginning graduate students, primarily within European university systems. It offers a rigorous introduction to the fundamental concepts and results of complex analysis, extending beyond standard material to include advanced topics like elliptic functions, Gamma- and Zeta functions (culminating in a proof of the prime number theorem), and an innovative introduction to several complex variables. Drawing from the authors' established German texts, this comprehensive volume emphasizes both theoretical depth and practical application, making it a valuable resource for aspiring mathematicians.

“Not applicable in the traditional literary sense for a mathematics textbook. Significant content consists of theorems, definitions, and proofs.”

Key themes

Rigor and Precision in Mathematical Proof
The book places paramount importance on the rigorous development of complex analysis, ensuring that all definitions are precise and all theorems are proven with meticulous detail. This foundational emphasis on logical consistency and exactitude is central to the authors' pedagogical philosophy, preparing students for advanced mathematical thought.
Generalization and Abstraction of Functions
A core theme is the extension of real analysis concepts to the complex plane, demonstrating how properties of functions become more constrained and powerful in a complex setting. This involves abstracting familiar ideas like differentiability and integration to a higher dimension, revealing profound connections and new phenomena.
Interconnectedness of Mathematical Fields
The textbook masterfully illustrates how complex analysis is not an isolated field but is deeply intertwined with other branches of mathematics, including number theory, real analysis, and topology. This theme highlights the unifying power of complex methods to solve problems in seemingly disparate areas.

Worth discussing

How does the inclusion of topics like elliptic functions and an introduction to several complex variables enhance the overall understanding of complex analysis?

Chapter-by-chapter breakdowns, character arcs and the full thematic analysis come with a free account.

Sign up freeLog in

Discussions

No one has started one yet

Join

Questions this book opens up

No discussions yet

Be the first to start a discussion about this book!

Sign up to start the discussion

Reviews

No reviews yet

Be the first to review this book!