E-Book, Englisch, 316 Seiten
Reihe: Textbooks in Mathematics
Hrbacek / Lessmann / O'Donovan Analysis with Ultrasmall Numbers
Erscheinungsjahr 2014
ISBN: 978-1-4987-0266-9
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, 316 Seiten
Reihe: Textbooks in Mathematics
ISBN: 978-1-4987-0266-9
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon–delta methods. Students can fully prove fundamental results, such as the Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness.
The book is suitable for a calculus course at the undergraduate or high school level or for self-study with an emphasis on nonstandard methods. The first part of the text offers material for an elementary calculus course while the second part covers more advanced calculus topics.
The text provides straightforward definitions of basic concepts, enabling students to form good intuition and actually prove things by themselves. It does not require any additional "black boxes" once the initial axioms have been presented. The text also includes numerous exercises throughout and at the end of each chapter.
Zielgruppe
Researchers interested in non-standard analysis and the theory of infinitesimal numbers; first-year graduate and advanced undergraduate students in analysis or real analysis courses.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Elementary Analysis
Basic concepts
Continuity and limits
Differentiability
Elementary integration
Higher Analysis
Basic concepts revisited
Derivatives
Sequences and series
Topology of Real Numbers
Differential Equations
Integration
