More Explorations in Complex Functions

More Explorations in Complex Functions is a sequel to GTM 287, covering core material in complex analysis and tools used in other areas of mathematics and applications. It is intended for graduate students and researchers, independent readers, seminar attendees, or instructors for a second course in complex analysis. The text includes a mapping of dependence relations among chapters and exercises to complement the results.

Format: Hardback
Length: 403 pages
Publication date: 14 June 2023
Publisher: Springer International Publishing AG

More Explorations in Complex Functions is a captivating sequel to GTM 287, Explorations in Complex Functions. While both texts cover a wide range of topics, from fundamental concepts in complex analysis to tools that find applications in various branches of mathematics and real-world applications, they have minimal overlap. The primary target audience for these texts includes advanced graduate students and researchers in complex analysis, independent readers, seminar attendees, and instructors preparing for a second course in complex analysis. Instructors will find great value in the numerous possibilities for designing a second course that builds upon a standard first course in complex analysis. The book is accompanied by an extensive set of exercises that reinforce the results presented throughout. It is worth noting that this text contains more material than can typically be covered in a year-long course in complex analysis. A mapping of dependence relations among chapters allows instructors and independent readers to choose their reading pathway. Chapters 2, 4, 5, 7, and 8 provide the necessary function theory background for several stochastic equations of current interest, such as SLE. The text commences with two introductory chapters that serve as valuable resources. Chapters 3 and 4 offer standalone introductions to complex dynamics and univalent function theory, respectively, including the celebrated deBranges theorem. Chapters 5 to 7 can be viewed as a cohesive unit that progresses from harmonic functions to covering surfaces, leading to the uniformization theorem and Fuchsian groups. Chapter 8 stands as a standalone treatment of quasiconformal mapping, setting the stage for Chapter 9, an introduction to Teichmüller theory. The final chapters, 10 to 14, primarily serve as standalone introductions to topics of both theoretical and applied interest: the Bergman kernel, theta functions and Jacobi inversion, Padé approximants, and continuity.

Weight: 863g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031282874
Edition number: 1st ed. 2023