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.
| ISBN: | 9781032922393 |
| Publication date: | 14th October 2024 |
| Author: | Karel Hrbacek, Olivier Lessmann, Richard ODonovan |
| Publisher: | Chapman & Hall/CRC an imprint of CRC Press |
| Format: | Paperback |
| Pagination: | 322 pages |
| Series: | Textbooks in Mathematics |
| Genres: |
Engineering: general Product design Calculus and mathematical analysis |
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 features in the following genres: Engineering: general, Product design, Calculus and mathematical analysis
Analysis With Ultrasmall Numbers is available in Paperback, Ebook, Hardback
Analysis With Ultrasmall Numbers was written by Karel Hrbacek, Olivier Lessmann, Richard ODonovan and published by Chapman & Hall/CRC an imprint of CRC Press
Analysis With Ultrasmall Numbers has 322 pages
Yes it is part of Textbooks in Mathematics series
£56.69