Mathematical Analysis

Approximation and Discrete Processes

Authors: Giaquinta, Mariano, Modica, Giuseppe

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eBook 101,14 €
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  • ISBN 978-0-8176-4414-7
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Hardcover 123,76 €
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  • ISBN 978-0-8176-4313-3
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Softcover 123,76 €
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  • ISBN 978-0-8176-4337-9
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About this Textbook

This volume! aims at introducing some basic ideas for studying approxima­ tion processes and, more generally, discrete processes. The study of discrete processes, which has grown together with the study of infinitesimal calcu­ lus, has become more and more relevant with the use of computers. The volume is suitably divided in two parts. In the first part we illustrate the numerical systems of reals, of integers as a subset of the reals, and of complex numbers. In this context we intro­ duce, in Chapter 2, the notion of sequence which invites also a rethinking of the notions of limit and continuity2 in terms of discrete processes; then, in Chapter 3, we discuss some elements of combinatorial calculus and the mathematical notion of infinity. In Chapter 4 we introduce complex num­ bers and illustrate some of their applications to elementary geometry; in Chapter 5 we prove the fundamental theorem of algebra and present some of the elementary properties of polynomials and rational functions, and of finite sums of harmonic motions. In the second part we deal with discrete processes, first with the process of infinite summation, in the numerical case, i.e., in the case of numerical series in Chapter 6, and in the case of power series in Chapter 7. The last chapter provides an introduction to discrete dynamical systems; it should be regarded as an invitation to further study.

Reviews

"This self-contained book aims to introduce the main ideas for studying approximation processes, more generally discrete processes at graduate level. The use of computers induces a growing need for studying discrete processes.... A key feature this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations.... Each chapter has a short summary where the most important facts discussed are collected and described. There is also a large number of exercises inserted at various points into the text....The book is meant principally for graduate students in mathematics, physics, engineering, and computer science, but it can be used at technological and scientific faculties by anyone who wants to approach these topics. It may also be used in graduate seminars and courses or as a reference text by mathematicians, physicists, and engineers."   —Zentralblatt MATH

"Mathematical Analysis does contain a substantial amount of material that is unusual in terms of an introductory text in real analysis…These are all interesting topics that have gained increasing importance in modern applications of mathematics, albeit outside the traditional area of analysis. It is very nice to have these topics developed outside a specialized textbook, in, e.g., combinatorics, dynamical systems, or number theory. The authors do a very good job presenting this material…Mathematical Analysis includes substantial amounts of historical background…The book also contains a lot of examples…I can happily recommend Mathematical Analysis as a good resource for instructors of introductory analysis courses, especially in terms of providing some unusual applications of analysis and developments of some basic classic topics that are often shortchanged in standard texts."  —SIAM Review

“This is the second volume of a series on analysis. … a real hodgepodge that could only be the primary textbook for a course specifically based on it. … In this series Giaquinta and Modica have set themselves the formidable task of constructing from scratch an analysis sequence of several years length. … they have more regard for classical topics and arguments than most authors writing analysis books today. … I enjoyed reading this volume … .” (Warren Johnson, The Mathematical Association of America, January, 2010)
 


Table of contents (8 chapters)

  • Real Numbers and Natural Numbers

    Giaquinta, Mariano (et al.)

    Pages 1-30

    Preview Buy Chapter 30,19 €
  • Sequences of Real Numbers

    Giaquinta, Mariano (et al.)

    Pages 31-70

    Preview Buy Chapter 30,19 €
  • Integer Numbers: Congruences, Counting and Infinity

    Giaquinta, Mariano (et al.)

    Pages 71-120

    Preview Buy Chapter 30,19 €
  • Complex Numbers

    Giaquinta, Mariano (et al.)

    Pages 121-144

    Preview Buy Chapter 30,19 €
  • Polynomials, Rational Functions and Trigonometric Polynomials

    Giaquinta, Mariano (et al.)

    Pages 145-186

    Preview Buy Chapter 30,19 €

Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-0-8176-4414-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 123,76 €
price for Spain (gross)
  • ISBN 978-0-8176-4313-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 123,76 €
price for Spain (gross)
  • ISBN 978-0-8176-4337-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Analysis
Book Subtitle
Approximation and Discrete Processes
Authors
Copyright
2004
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-4414-7
DOI
10.1007/978-0-8176-4414-7
Hardcover ISBN
978-0-8176-4313-3
Softcover ISBN
978-0-8176-4337-9
Edition Number
1
Number of Pages
XII, 388
Topics