Analysis with Ultrasmall Numbers
Seiten
2024
Chapman & Hall/CRC (Verlag)
978-1-032-92239-3 (ISBN)
Chapman & Hall/CRC (Verlag)
978-1-032-92239-3 (ISBN)
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This text 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. Readers can fully prove fundamental results, such as the Extreme Value Theore
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.
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.
Karel Hrbacek, Olivier Lessmann, Richard O'Donovan
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. Appendix. Index.
| Erscheint lt. Verlag | 14.10.2024 |
|---|---|
| Reihe/Serie | Textbooks in Mathematics |
| Zusatzinfo | 21 Illustrations, black and white |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 600 g |
| Themenwelt | Kunst / Musik / Theater ► Design / Innenarchitektur / Mode |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Technik ► Umwelttechnik / Biotechnologie | |
| ISBN-10 | 1-032-92239-7 / 1032922397 |
| ISBN-13 | 978-1-032-92239-3 / 9781032922393 |
| Zustand | Neuware |
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CHF 41,95
