Mathematical Analysis

Approximation and Discrete Processes

Mariano Giaquinta, Giuseppe Modica

388 pages, parution le 27/01/2005

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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

Preface
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
Mathematicans and Other Scientists
Bibliographical Notes
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Mariano Giaquinta, Giuseppe Modica
Parution	27/01/2005
Nb. de pages	388
Format	15,5 x 23,5
Couverture	Broché
Poids	556g
Intérieur	Noir et Blanc
EAN13	9780817643379
ISBN13	978-0-8176-4337-9