| Mathematical Analysis: Approximation and Discrete Processes 2004 Edition Contributor(s): Giaquinta, Mariano (Author), Modica, Giuseppe (Author) |
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ISBN: 0817643133 ISBN-13: 9780817643133 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: April 2004 Annotation: This 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 introductory chapters on the study of discrete dynamical systems and discrete probability. 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Differential Equations - General - Mathematics | Applied |
| Dewey: 515 |
| LCCN: 2004043696 |
| Physical Information: 0.93" H x 6.2" W x 9.42" (1.55 lbs) 388 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |