Calculus + vector calculus¶
Five ranked references. Rank 1 is the default spine, not a requirement to read all five.
1 | Calculus, Volumes I-II¶
Tom M. Apostol | Primary rigorous spine | Undergraduate
Treats calculus as a mathematical theory tied to linear algebra and physics, not a bag of tricks.
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2 | Calculus¶
Michael Spivak | Proof-oriented depth | Undergraduate
For understanding why single-variable calculus works; develops mathematical maturity.
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3 | Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach¶
John H. Hubbard, Barbara Burke Hubbard | Multivariable / geometry | Upper undergraduate
Unifies derivatives, manifolds, forms, and linear algebra in a way that transfers directly to physics and control.
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4 | Calculus, Volumes 1-3¶
OpenStax | Open primary | Undergraduate
Complete standard sequence with a legal free web/PDF edition and large problem sets.
Amazon search | Full open text
5 | Active Calculus: Single Variable + Multivariable¶
Matthew Boelkins et al. | Open active-learning path | Undergraduate
Built around doing mathematics, explaining, and solving problems rather than passive reading.
Amazon search | Full open text