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Calculus is a branch of mathematics that primarily deals with the rate of change of outputs of a function w.r.t the inputs.

It contains several concepts including limits, first-order derivatives, higher-order derivatives, chain rule, derivatives of special and standard functions, definite integrals, indefinite integrals, derivative tests, gradients, higher-order gradients, and so on...

Calculus has been heavily used in optimization and maybe in several other aspects of artificial intelligence.

What are the Calculus textbook(s) recommended that cover all the concepts required for a researcher in artificial intelligence?

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    $\begingroup$ I don't have any books in mind (hence the comment rather than the answer), but from my experience most of ML has not been too bad with the calculus, it's mostly just multi-variable calculus (which is really just summing the gradients). If you cover that and basic calculus you'll be good for most mainstream algorithms $\endgroup$
    – Recessive
    Commented Aug 24, 2021 at 0:22

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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:

  1. Multivariable Calculus (also could help for understand faster linear algebra, eigen values&vectors, $ R ^n $ spaces,etc )
  2. Directional Derivatives ( For Gradient Descent )
  3. Infinite Sequences and Series
  4. Partial Derivates ( you need know one variable derivatives for go to Partial Derivatives )
  5. Vector Calculus
  6. Jacobian
  7. Of course all that need a deep understanding of integrals and derivatives no forget. Calculus.
  8. 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:

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.

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