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: 
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 -- 
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