Analysis with Ultrasmall Numbers Textbooks in Mathematics Series
Auteurs : Hrbacek Karel, Lessmann Olivier, O'Donovan Richard
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.
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.
Date de parution : 11-2014
15.6x23.4 cm
Thèmes d’Analysis with Ultrasmall Numbers :
Mots-clés :
Observable Neighbor; Ultrasmall Numbers; mathematics using ultrasmall numbers; Closure Principle; modern approach to infinitesimals; Extended Context; calculus course at the undergraduate or high school level; Increment Equation; infinitesimal methods; Observable Relative; prove fundamental results from axioms; Open Interval; Extreme Value Theorem; Holds; Riemann Integrable; Continuous Function; Dense Open Sets; Dense; Uniform Continuity; Natural Numbers; Induction; Real Numbers; Oblique Asymptote; T− 1; Rolle’s Theorem; Quadratic Polynomial; Definite Integral; Set A; Vertical Asymptote; Smooth; Nonnegative Integer