Answer: Calculus James Stewart is the best for a beginner.
I started to learn Calculus studying engineering with James Stewart Calculus ( maybe the best for beginners and is really didactic ), Problems in Mathematical Analysis Demidovich ( best for me because simplicity, fast, but few multivariable focus and difficult for learn ), Nikolai Piskunov - Differential and Integral Calculus (again difficult to learn but teachers used for prepare his test), Calculus with Analytic Geometry Swokosky, Louis Leithold Calculus and Purcell Calculus. this books are the popular base books for an engineering degree in mostly all universities.
However the best way for approach Calculus to Artificial Intelligence is focus in the chapter that are directly related to IA and we have:
- Multivariable Calculus (also could help for understand faster linear algebra, eigen values&vectors, $ R ^n $ spaces,etc )
- Directional Derivatives ( For Gradient Descent )
- Infinite Sequences and Series
- Partial Derivates ( you need know one variable derivatives for go to Partial Derivatives )
- Vector Calculus
- Of course all that need a deep understanding of integrals and derivatives no forget.
- none of this can be learned without knowing algebra, matrices, geometry, trigonometry and logic math ( Elementary Subjects )
I can tell you my experience learning Calculus James Stewart 7th and build a summary about the topics.
- Multivariable Calculus 6 Chapters about that.
- Directional Derivatives Section 14.6
- Infinite Sequences and Series Chapter 11
- Vector Calculus Chapter 16
- Jacobian Transformation ( 15.10 Change of Variables in Multiple Integrals)
- Of course all that need a deep understanding of integrals and derivatives no forget. 6 Chapters about that.
As a reference this is the index:
I am looking forward for more books about advanced calculus especially with focus in multidimensional calculus or applied math for artificial intelligence, I have found more books about statistics approach than calculus/math approach.