Calculus I

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 to prove theorems, and to appreciate the beauty and elegance of such a logical formal treatment.