| Titre : | Complex analysis | | Type de document : | texte imprimé | | Auteurs : | Elias M. STEIN, Auteur ; Rami SHAKARCHI, Auteur | | Editeur : | Princeton (N.J.) : Princeton University Press | | Année de publication : | Cop. 2003 | | Collection : | Princeton Lectures in Analysis num. II | | Importance : | XVII-379 p. | | ISBN/ISSN/EAN : | 978-0-691-11385-2 | | Langues : | Anglais | | Mots-clés : | analyse complexe | | Résumé : | With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.
With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. | | Note de contenu : | index, glossaire, bibliogr. |
Complex analysis [texte imprimé] / Elias M. STEIN, Auteur ; Rami SHAKARCHI, Auteur . - Princeton (N.J.) : Princeton University Press, Cop. 2003 . - XVII-379 p.. - ( Princeton Lectures in Analysis; II) . ISBN : 978-0-691-11385-2 Langues : Anglais | Mots-clés : | analyse complexe | | Résumé : | With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.
With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. | | Note de contenu : | index, glossaire, bibliogr. |
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Affiner la recherche Interroger des sources externesAnalytic continuation of group representations (Cop. 1971)
