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Analysis I

Introduction

The present book is the first volume of a two-volume work on analysis and deals with the functions of a real variable. In complex analysis it is essentially limited to power series. In particular, it contains the material that is usually offered in the first semester of an introductory analysis lecture for mathematicians, physicists and computer scientists, and goes beyond this in some places. The book is aimed at students for whom it is a helpful companion to the lecture and a source for deepening the subject, mathematicians at work, especially teachers in secondary schools, and finally everyone who knows something about Would like to learn about analysis and its significance in the larger scientific and cultural context. This brings us to one of the main concerns of the textbook series "Basic Knowledge of Mathematics", the historical reference. The mathematical concepts and contents of analysis have not fallen from the sky of pure knowledge, and no thinker in the ivory tower has devised them. European intellectual history begins where nature is no longer understood as an enigmatic event controlled by uncanny higher powers, but as rationally explainable: by the Ionian philosophers of the 6th century BC. Analysis arose in pursuit of this goal of penetrating the world rationally and finding its laws. Your story is a piece of cultural history.

Keywords

Analysis differential equation function limit sky integral integral calculus power series Riemann integral rings sun continuity complex numbers real number complete induction

Authors and affiliations

  1. 1.Mathematisches Institut IUniversit├Ąt KarlsruheKarlsruhe 1Germany

Bibliographic information

  • Book Title Analysis I.
  • AuthorsWolfgang Walter
  • Series TitleBasics of Mathematics
  • DOIhttps: //doi.org/10.1007/978-3-662-05708-7
  • Copyright InformationSpringer-Verlag Berlin Heidelberg1985
  • Publisher NameSpringer, Berlin, Heidelberg
  • eBook PackagesSpringer Book Archive
  • Softcover ISBN978-3-540-12780-2
  • eBook ISBN978-3-662-05708-7
  • Series ISSN1431-4215
  • Edition Number1
  • Number of PagesXII, 388
  • Number of Illustrations39 b / w illustrations, 0 illustrations in color
  • Topics Real Functions
  • Buy this book on publisher's site