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Mathematical analysis

Mathematical analysis

Approximation and discrete processes

Mariano Giaquinta, Giuseppe Modica

288 pages, parution le 02/06/2004

Résumé

This fairly self-contained work embraces a broad range of topics in analysis at the graduate level, requiring only a sound knowledge of calculus and the functions of one variable. A key feature of this lively yet rigorous and systematic exposition is the historical accounts of ideas and methods pertaining to the relevant topics. Most interesting and useful are the connections developed between analysis and other mathematical disciplines, in this case, numerical analysis and probability theory.

The text is divided into two parts: The first examines the systems of real and complex numbers and deals with the notion of sequences in this context. After the presentation of natural numbers as a subset of the reals, elements of combinatorics and a discussion of the mathematical notion of the infinite are introduced. The second part is dedicated to discrete processes starting with a study of the processes of infinite summation both in the case of numerical series and of power series. The volume closes with an introductory chapter on the study of discrete dynamical systems and a summary of mathematicians and other scientists referenced in the work.

Mathematical Analysis: Approximation and Discrete Processes is replete with beautiful illustrations, examples, exercises at the end of each chapter, and a comprehensive index to aid the reader. It may be used in graduate seminars and courses or as a reference text by mathematicians, physicists, and engineers.

L'auteur - Mariano Giaquinta

Scuola Normale Superiore, Pisa, Italy

L'auteur - Giuseppe Modica

The University of Florence, Florence, Italy

Sommaire

  • Real numbers and natural numbers
  • Sequences of real numbers
  • Integer numbers: congruences, counting and infinity
  • Complex numbers
  • Polynomials, rational functions and trigonometric polynomials
  • Series
  • Power series
  • Discrete processes
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Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Mariano Giaquinta, Giuseppe Modica
Parution 02/06/2004
Nb. de pages 288
Format 16 x 24
Couverture Relié
Poids 703g
Intérieur Noir et Blanc
EAN13 9780817643133
ISBN13 978-0-8176-4313-3

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