You may be having trouble finding things because calculus done with full rigor is called "analysis". The classic introductory-but-extremely-dense text is Rudin's _Principles of Mathematical Analysis_. If you're reading on your own, though, I expect you'll get a lot more out of a friendlier book; my first analysis course was taught out of Strichartz's _The Way of Analysis_.

N.B.: Most everything in either book will be completely new to you. 1st-year calculus courses have absolutely no interest in teaching you what goes on under the hood; there's just no time. But I think the analogy to Feynman's lectures holds up pretty well.

Looks like The Way of Analysis is what I need, thank you :)

wow..thanks!

Apostol's Calculus texts (2 volumes) are the best with the supporting theory. I'm more from an engineering perspective, for readers looking for a book from that direction is Kline's "Calculus: An Intuitive and Physical Approach".

Introductory general biology texts have a lot more variation in how the material is presented, but have to cover such an incredible amount of facts that there is actually less effective difference. Some biology texts tend to be more ecologically oriented (Campbell), where others are more cellular and chemically oriented (Curtis), but the difference tends to get lost somewhat with the need to cover everything, and the sheer mass of material each HAS to cover.

You might try Pauling's "General Chemistry" text for a more theoretical treatment in chemistry.

Both Kline's calculus and Pauling's chemistry texts were from the 1960s and reprinted by Dover in the 1990s; you might try checking the Dover catalog to see if there are any more similar reprints out.

Michael Spivak's Calculus text:

http://www.amazon.com/gp/product/0914098918

volume 1 of the best series out there...

http://www.amazon.com/Calculus-Vol-One-Variable-Introduction...

If you'd like to read a refresher on the calculus of multiple variables, I think you'd enjoy Div, Grad, Curl and All That. It's in the same sort of informal style of Feynman's Lectures. It's not rigorous like Rudin, but it gives you a good intuitive understanding of the subject.