An Introduction to Analytic Functions : With Theoretical Implications. 1st ed. 2020

種類:

電子ブック

責任表示:

by John Sheridan Mac Nerney ; edited by William E. Kaufman, Ryan C. Schwiebert

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Mac Nerney, John Sheridan.
• Kaufman, William E.
• Schwiebert, Ryan C.
• SpringerLink (Online service)

ISBN:

9783030420857 [303042085X]    

注記:

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

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