Mathematical Analysis: Approximation and Discrete Processes
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2004
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This volume! aims at introducing some basic ideas for studying approximation processes and, more generally, discrete processes. The study of discrete processes, which has grown together with the study of infinitesimal calculus, 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 introduce, in Chapter 2, the notion of sequence which invites also a rethinking of the notions of limit and continuity 2 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 numbers 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 |
| Beschreibung: | 1 Online-Ressource (XII, 388 p) |
| ISBN: | 9780817644147 9780817643379 |
| DOI: | 10.1007/978-0-8176-4414-7 |
Internformat
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| 245 | 1 | 0 | |a Mathematical Analysis |b Approximation and Discrete Processes |c by Mariano Giaquinta, Giuseppe Modica |
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Datensatz im Suchindex
| _version_ | 1804153089423310848 |
|---|---|
| any_adam_object | |
| author | Giaquinta, Mariano |
| author_facet | Giaquinta, Mariano |
| author_role | aut |
| author_sort | Giaquinta, Mariano |
| author_variant | m g mg |
| building | Verbundindex |
| bvnumber | BV042419147 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863956695 (DE-599)BVBBV042419147 |
| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-0-8176-4414-7 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:04Z |
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| isbn | 9780817644147 9780817643379 |
| language | English |
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| publisher | Birkhäuser Boston |
| record_format | marc |
| spelling | Giaquinta, Mariano Verfasser aut Mathematical Analysis Approximation and Discrete Processes by Mariano Giaquinta, Giuseppe Modica Boston, MA Birkhäuser Boston 2004 1 Online-Ressource (XII, 388 p) txt rdacontent c rdamedia cr rdacarrier This volume! aims at introducing some basic ideas for studying approximation processes and, more generally, discrete processes. The study of discrete processes, which has grown together with the study of infinitesimal calculus, 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 introduce, in Chapter 2, the notion of sequence which invites also a rethinking of the notions of limit and continuity 2 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 numbers 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 Mathematics Functions of complex variables Differential Equations Mathematical statistics Functions of a Complex Variable Ordinary Differential Equations Applications of Mathematics Statistical Theory and Methods Mathematik Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Differentialrechnung (DE-588)4012252-9 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktion (DE-588)4195664-3 gnd rswk-swf Integralrechnung (DE-588)4027232-1 gnd rswk-swf Differentialungleichung (DE-588)4149785-5 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Differentialrechnung (DE-588)4012252-9 s Integralrechnung (DE-588)4027232-1 s Differentialungleichung (DE-588)4149785-5 s 3\p DE-604 Funktion Mathematik (DE-588)4071510-3 s Mehrere Variable (DE-588)4277015-4 s 4\p DE-604 Funktionentheorie (DE-588)4018935-1 s 5\p DE-604 Funktion (DE-588)4195664-3 s 6\p DE-604 Analysis (DE-588)4001865-9 s 7\p DE-604 Modica, Giuseppe Sonstige oth https://doi.org/10.1007/978-0-8176-4414-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Giaquinta, Mariano Mathematical Analysis Approximation and Discrete Processes Mathematics Functions of complex variables Differential Equations Mathematical statistics Functions of a Complex Variable Ordinary Differential Equations Applications of Mathematics Statistical Theory and Methods Mathematik Mehrere Variable (DE-588)4277015-4 gnd Analysis (DE-588)4001865-9 gnd Differentialrechnung (DE-588)4012252-9 gnd Funktionentheorie (DE-588)4018935-1 gnd Funktion (DE-588)4195664-3 gnd Integralrechnung (DE-588)4027232-1 gnd Differentialungleichung (DE-588)4149785-5 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| subject_GND | (DE-588)4277015-4 (DE-588)4001865-9 (DE-588)4012252-9 (DE-588)4018935-1 (DE-588)4195664-3 (DE-588)4027232-1 (DE-588)4149785-5 (DE-588)4071510-3 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Mathematical Analysis Approximation and Discrete Processes |
| title_auth | Mathematical Analysis Approximation and Discrete Processes |
| title_exact_search | Mathematical Analysis Approximation and Discrete Processes |
| title_full | Mathematical Analysis Approximation and Discrete Processes by Mariano Giaquinta, Giuseppe Modica |
| title_fullStr | Mathematical Analysis Approximation and Discrete Processes by Mariano Giaquinta, Giuseppe Modica |
| title_full_unstemmed | Mathematical Analysis Approximation and Discrete Processes by Mariano Giaquinta, Giuseppe Modica |
| title_short | Mathematical Analysis |
| title_sort | mathematical analysis approximation and discrete processes |
| title_sub | Approximation and Discrete Processes |
| topic | Mathematics Functions of complex variables Differential Equations Mathematical statistics Functions of a Complex Variable Ordinary Differential Equations Applications of Mathematics Statistical Theory and Methods Mathematik Mehrere Variable (DE-588)4277015-4 gnd Analysis (DE-588)4001865-9 gnd Differentialrechnung (DE-588)4012252-9 gnd Funktionentheorie (DE-588)4018935-1 gnd Funktion (DE-588)4195664-3 gnd Integralrechnung (DE-588)4027232-1 gnd Differentialungleichung (DE-588)4149785-5 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| topic_facet | Mathematics Functions of complex variables Differential Equations Mathematical statistics Functions of a Complex Variable Ordinary Differential Equations Applications of Mathematics Statistical Theory and Methods Mathematik Mehrere Variable Analysis Differentialrechnung Funktionentheorie Funktion Integralrechnung Differentialungleichung Funktion Mathematik Einführung Lehrbuch |
| url | https://doi.org/10.1007/978-0-8176-4414-7 |
| work_keys_str_mv | AT giaquintamariano mathematicalanalysisapproximationanddiscreteprocesses AT modicagiuseppe mathematicalanalysisapproximationanddiscreteprocesses |