LEADER 00000nam a2200457 i 4500
001 978-3-030-42085-7
003 DE-He213
005 20201007142515.0
006 m o d
007 cr nn 008maaau
008 200530s2020 sz s 0 eng d
020 9783030420857|q(electronic bk.)
020 9783030420840|q(paper)
024 7 10.1007/978-3-030-42085-7|2doi
040 GP|cGP|erda
041 0 eng
050 4 QA331|b.M336 2020
082 04 515.94|223
100 1 Mac Nerney, John Sheridan,|eauthor
245 13 An introduction to analytic functions :|bwith theoretical
implications /|cby John Sheridan Mac Nerney ; edited by
William E. Kaufman, Ryan C. Schwiebert
250 Revised edition
264 1 Cham :|bSpringer International Publishing :|bImprint:
Springer,|c2020
300 1 online resource (xix, 92 pages) :|billustrations,
digital ;|c24 cm
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
347 text file|bPDF|2rda
505 0 0. Conventions, Set Theory, Number Systems -- 1. The
Complex Plane, Relations, Functions -- 2. Boundedness,
Convergence, Continuity -- 3. Paths, Integrals,
Derivatives -- 4. Connectedness, Convexity, Analyticity --
5. Triangles, Polygons, Simple Regions -- 6. Extensions,
Contours, Elementary Functions -- 7. Power-Series,
Residues, Singularities -- 8. Analytic Inverses, Standard
Regions, Convergence Continuation -- 9. Extended Complex
Plane, Linear-Fractional Transformations, Meromorphic
Functions -- 10. Analytic Relations, Analytic Continuation,
Functional Boundaries, Branch-Points -- Appendix A.
Homotopy Groups -- Appendix B. Automorphic Functions --
Appendix C. Excepted Values and Uniformization -- Appendix
D. Well-ordering -- Appendix E. Analytic Surfaces -- Mac
Nerney's Theorem Numbering in the original Edition --
Index
520 When first published in 1959, this book was the basis of a
two-semester course in complex analysis for upper
undergraduate and graduate students. J. S. Mac Nerney was
a proponent of the Socratic, or "do-it-yourself" method of
learning mathematics, in which students are encouraged to
engage in mathematical problem solving, including theorems
at every level which are often regarded as "too difficult"
for students to prove for themselves. Accordingly, Mac
Nerney provides no proofs. What he does instead is to
compose and arrange the investigation in his own unique
style, so that a contextual proof is always available to
the persistent student who enjoys a challenge. The central
idea is to empower students by allowing them to discover
and rely on their own mathematical abilities. This text
may be used in a variety of settings, including: the usual
classroom or seminar, but with the teacher acting mainly
as a moderator while the students present their
discoveries, a small-group setting in which the students
present their discoveries to each other, and independent
study. The Editors, William E. Kaufman (who was Mac
Nerney's last PhD student) and Ryan C. Schwiebert, have
composed the original typed Work into LaTeX ; they have
updated the notation, terminology, and some of the prose
for modern usage, but the organization of content has been
strictly preserved. About this Book, some new exercises,
and an index have also been added
650 0 Analytic functions
650 14 Functional Analysis
700 1 Kaufman, William E.,|eeditor
700 1 Schwiebert, Ryan C.,|eeditor
710 2 SpringerLink (Online service)
773 0 |tSpringer eBooks
856 40 |uhttps://doi.org/10.1007/978-3-030-42085-7