OP wrote:
>
> On p. 58 & 59 of Spivak's Calculus, he says "Given two distinct
> points (a,b) and (c,d), find the linear function f whose graph goes
> through (a,b) and (c,d). This amounts to saying that f(a) = b and
> f(c) = d. If f is to be of the form f(x) = Aa + B, then we must have:
>
> Aa + B = b;
> Ac + B = d;
>
> therefore A = (d - b)/(c - a) and B = b - [(d - b)/(c - a)]a, so [etc.]"
It sounds as if Spivak expects his reader to know (at least the
rudiments of) linear algebra before he embarks on calculus; which is not
an unreasonable assumption.
Some authors, such as Protter and Morrey[1, 2] do the two in parallel,
but their books seem to be out of print.
How are things done now: in parallel or linear algebra followed by
calculus?
[1] Calculus and Analytic Geometry, A First Course, Addison-Wesley.
[2] Modern Mathematical Analysis, Addison-Wesley.
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