Год выпуска: 2011 Автор: Magid Maatallah Издательство: LAP Lambert Academic Publishing Страниц: 148 ISBN: 9783846523773
Описание
Calculus: the related areas of differentiation, integration, sequences and series, that are united in their reliance on the idea of limits. Additional topics: complex numbers and trigonometric functions. This simplifies the discussion of the ‘classical’ functions of calculus (i.e. trigonometric, hyperbolic, exponential, logarithmic) and their relations. Relation between calculus and analysis: • Calculus: intuitive and operational ideas, no emphasis on strict step-by-step logical derivation e.g. derivative as limit of a ratio, integral as limit of a sum initially (Newton, Leibniz) without rigorous definition of ‘limit’. • Analysis: logical, rigorous proofs of the intuitive ideas of calculus Rationale behind this division of work: • Hard to prove a theorem without being already familiar with the unproven (but strongly believed in) result. • Hard to understand the need for the rigorous style of analysis until one has sufficient experience with calculus to realize the need...
