{"title":"Wolfgang Tutschke","description":null,"products":[{"product_id":"solution-of-initial-value-problems-in-classes-of-generalized-analytic-functions-book-wolfgang-tutschke-9783540502166","title":"Solution of Initial Value Problems in Classes of Generalized Analytic Functions","description":"The purpose of the present book is to solve initial value problems in classes of generalized analytic functions as well as to explain the functional-analytic background material in detail. From the point of view of the theory of partial differential equations the book is intend­ ed to generalize the classicalCauchy-Kovalevskayatheorem, whereas the functional-analytic background connected with the method of successive approximations and the contraction-mapping principle leads to the con­ cept of so-called scales of Banach spaces: 1. The method of successive approximations allows to solve the initial value problem du CTf = f(t,u), (0. 1) u(O) = u , (0. 2) 0 where u = u(t) ist real o. r vector-valued. It is well-known that this method is also applicable if the function u belongs to a Banach space. A completely new situation arises if the right-hand side f(t,u) of the differential equation (0. 1) depends on a certain derivative Du of the sought function, i. e. , the differential equation (0,1) is replaced by the more general differential equation du dt = f(t,u,Du), (0. 3) There are diff. erential equations of type (0. 3) with smooth right-hand sides not possessing any solution to say nothing about the solvability of the initial value problem (0,3), (0,2), Assume, for instance, that the unknown function denoted by w is complex-valued and depends not only on the real variable t that can be interpreted as time but also on spacelike variables x and y, Then the differential equation (0.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52426485727505,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52426486317329,"sku":"NLS9783540502166","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540502166.jpg?v=1759157968"},{"product_id":"grundlagen-der-funktionentheorie-book-wolfgang-tutschke-9783322979339","title":"Grundlagen der Funktionentheorie","description":"Dieses Buch stellt eine Einf hrung in die (komplexe) Funktionentheorie dar. Die Funktionentheorie ist eine nach den verschiedensten Richtungen sehr weit entwickelte mathematische Theorie, deren Grundlage die Theorie der komplexen Differentiation ist. Einer der wichtigsten S tze der Funktionentheorie ist der Cauchysche Integralsatz. Er besagt, da  das komplexe Kurvenintegral einer komplexwertigen Funktion 1 (z)  ber eine geschlossene Kurve gleich Null ist, wenn I(z) in jedem Punkt ihres Definitionsgebietes im komplexen Sinne differen- zierbar ist. Allerdings gilt diese Aussage nur, wenn  ber die Struktur des Defini- tionsgebietes bestimmte Voraussetzungen gemacht werden. Hierin zeigt sich die enge Verbindung von Funktionentheorie und Topologie der Ebene. Diesen Zusammenhang kann man verwenden, um die Funktionentheorie gleich von Anfang an durch Heranziehung topologischer Aussagen aufzubauen. Ein sol- cher Satz, der an die Spitze der Funktionentheorie gestellt werden kann, ist der Jordansche Kurvensatz. Seine Verwendung ist f r die Funktionentheorie  u erst bequem, da in den Begriff des einfach zus mmenh ngenden Gebietes, zu dessen Definition man die Aussage de'\u0026gt; Jordanschen Kurvensatzes ben tigt, sozusagen alle topologischen Schwierigkeiten hineingesteckt werden. Ein Nach- teil dieser Ans tze ist, da  manche Analogien zur reellen Analysis, die erhalten bleiben k nnten, verlorengehen. SARS und ZYGMUND waren meines Wissens die ersten, die auf diesen Umstand hingewiesen und in ihrem Buch  56] die Funktionentheorie ohne Verwendung des Jordanschen Kurvensatz3s aufgebaut haben. Diese Idee wurde von L. AHLFoRs  1] erneut aufgegriffen. R. NEVAN- LINNA und V. PAATERO gaben in  48] einen Aufbau der Funktionentheorie mit Hilfe von Elementardeformationen, wodurch unn tige topologische Schwierig- keiten umgangen werden.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52427302994193,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52427303715089,"sku":"NLS9783322979339","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783322979339.jpg?v=1759160573"},{"product_id":"stammfunktionen-komplexwertiger-funktionen-book-wolfgang-tutschke-9783112584279","title":"Stammfunktionen Komplexwertiger Funktionen","description":"Keine ausführliche Beschreibung für \"Stammfunktionen komplexwertiger Funktionen\" verfügbar.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52454213779729,"sku":"NLS9783112584279","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783112584279.jpg?v=1759370481"},{"product_id":"das-reziprozittstheorem-fr-eine-klasse-pseudoholomorpher-funktionen-mehrerer-kom-book-wolfgang-tutschke-9783112584217","title":"Das Das Reziprozittstheorem Fr Eine Klasse Pseudoholomorpher Funktionen Mehrerer Komplexer Variabler","description":"Keine ausführliche Beschreibung für \"Das Reziprozitätstheorem für eine Klasse pseudoholomorpher Funktionen mehrerer komplexer Variabler\" verfügbar.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52454262407441,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52454262898961,"sku":"NLS9783112584217","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783112584217.jpg?v=1759370629"},{"product_id":"die-neuen-methoden-der-komplexen-analysis-und-ihre-anwendung-auf-nichtlineare-di-book-wolfgang-tutschke-9783112504116","title":"Die Neuen Methoden Der Komplexen Analysis Und Ihre Anwendung Auf Nichtlineare Differentialgleichungssysteme","description":"Keine ausführliche Beschreibung für \"Die neuen Methoden der komplexen Analysis und ihre Anwendung auf nichtlineare Differentialgleichungssysteme\" verfügbar.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52454369263889,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52454369853713,"sku":"NLS9783112504116","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783112504116.jpg?v=1759370953"},{"product_id":"konstruktion-von-globalen-lsungen-mit-vorgeschriebenen-singularitten-bei-partiel-book-wolfgang-tutschke-9783112499771","title":"Konstruktion Von Globalen Lsungen Mit Vorgeschriebenen Singularitten Bei Partiellen Komplexen Differentialgleichungssystemen","description":"Keine ausführliche Beschreibung für \"Konstruktion von globalen Lösungen mit vorgeschriebenen Singularitäten bei partiellen komplexen Differentialgleichungssystemen\" verfügbar.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52456230387985,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52456230977809,"sku":"NLS9783112499771","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783112499771.jpg?v=1759376710"},{"product_id":"introduction-to-complex-analysis-book-wolfgang-tutschke-9781584884781","title":"An Introduction to Complex Analysis","description":"Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole.  To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison.  Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52902742524177,"sku":"NLS9781584884781","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53250860089617,"sku":"NIN9781584884781","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781584884781.jpg?v=1765585647"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-wolfgang-tutschke.oembed","provider":"World of Books ","version":"1.0","type":"link"}