國立高雄大學圖資館 |

Language: English

Back

An introduction to analytic function...

Kaufman, William E.

An introduction to analytic functionswith theoretical implications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	An introduction to analytic functionsby John Sheridan Mac Nerney ; edited by William E. Kaufman, Ryan C. Schwiebert.
Reminder of title:	with theoretical implications /
Author:	Mac Nerney, John Sheridan.
other author:	Kaufman, William E.
Published:	Cham :Springer International Publishing :2020.
Description:	xix, 92 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Analytic functions.
Online resource:	https://doi.org/10.1007/978-3-030-42085-7
ISBN:	9783030420857$q(electronic bk.)

An introduction to analytic functionswith theoretical implications /
Mac Nerney, John Sheridan.

An introduction to analytic functionswith theoretical implications /[electronic resource] :by John Sheridan Mac Nerney ; edited by William E. Kaufman, Ryan C. Schwiebert. - Revised edition. - Cham :Springer International Publishing :2020. - xix, 92 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9783030420857$q(electronic bk.)

Standard No.: 10.1007/978-3-030-42085-7doiSubjects--Topical Terms:

185973
Analytic functions.

LC Class. No.: QA331 / .M336 2020

Dewey Class. No.: 515.94

An introduction to analytic functionswith theoretical implications /
LDR:03302nmm a2200337 a 4500 001 579861
003 DE-He213
005 20201007142515.0
006 m
007 cr
008 201229s2020
020 $a 9783030420857$q(electronic bk.)
020 $a 9783030420840$q(paper)
024 7 $a 10.1007/978-3-030-42085-7 $2 doi
035 $a 978-3-030-42085-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA331 $b .M336 2020
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.94 $2 23
090 $a QA331 $b .M169 2020
100 1 $a Mac Nerney, John Sheridan. $3 869355
245 1 3 $a An introduction to analytic functions $h [electronic resource] : $b with theoretical implications / $c by John Sheridan Mac Nerney ; edited by William E. Kaufman, Ryan C. Schwiebert.
250 $a Revised edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xix, 92 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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 $a 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 $a Analytic functions. $3 185973
650 1 4 $a Functional Analysis. $3 274845
700 1 $a Kaufman, William E. $3 869356
700 1 $a Schwiebert, Ryan C. $3 869357
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-030-42085-7
950 $a Mathematics and Statistics (Springer-11649)