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Not US, but for GCSE A's further math equivalent, calculus primarily involved applying intermediate rules (chain rules, trig identities, etc.) to evaluate diffe
by jhanschoo 4y ago
Not US, but for GCSE A's further math equivalent, calculus primarily involved applying intermediate rules (chain rules, trig identities, etc.) to evaluate differentiation/integrals on elementary functions, and a bit on geometric and arithmetic series.
Analysis discusses less well behaved functions and spaces than these.
- zozbot234 4y agoYou can do the first part without even relying on analysis in a mathematical sense. You simply define a differential algebra, by introducing a derivation function that just happens to respect the correct rules. Then "calculus" is the topic of how to perform computations in such an algebra. Note however that you do need analysis to rigorously address other parts of a typical "calculus course", especially those dealing with infinities, sequences and etc.