[Qem]

Can you recommend a introductory calculus book that builds it up from dual numbers?

[enriquto]

The Silvanus P. Thompson book suggested by the sibling comment is lovely and very clear.

For a more algebraic treatment, and its important applications to automatic differentiation, I'd suggest starting with the relevant wikipedia articles:

https://en.wikipedia.org/wiki/Dual_number

https://en.wikipedia.org/wiki/Automatic_differentiation

[zozbot234]

You could try Calculus made easy by S. P. Thompson.