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Keep in mind your objectives for the course, for example:
a) The derivative and integral are very simple concepts, appealing to
intuition from geometry (slope of the tangent and area) or from
physics (velocity and work). A basic task is to find out how they
should be formulated mathematically (i.e. with more precision, gene-
rality and abstraction) in order to make them accessible to mathematical
(algebraic) manipulations.