![]() The derivative of ƒ is then the ( standard part of the) slope of that line (see figure). Similarly, an infinite-magnification microscope will transform an infinitesimal arc of a graph of ƒ, into a straight line, up to an infinitesimal error (only visible by applying a higher-magnification "microscope"). ![]() When one examines a curve, say the graph of ƒ, under a magnifying glass, its curvature decreases proportionally to the magnification power of the lens. Similarly, an infinite-resolution telescope is used to represent infinite numbers. In his textbook, Keisler used the pedagogical technique of an infinite-magnification microscope, so as to represent graphically, distinct hyperreal numbers infinitely close to each other. The usual definitions in terms of ε–δ techniques are provided at the end of Chapter 5 to enable a transition to a standard sequence. Keisler defines all basic notions of the calculus such as continuity (mathematics), derivative, and integral using infinitesimals. Keisler also published a companion book, Foundations of Infinitesimal Calculus, for instructors, which covers the foundational material in more depth. ![]() Keisler's textbook is based on Robinson's construction of the hyperreal numbers. The book is available freely online and is currently published by Dover. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes given as An approach using infinitesimals. Elementary Calculus: An Infinitesimal Approach AuthorĮlementary Calculus: An Infinitesimal approach is a textbook by H.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |