Is it important to keep one's goal in mind when learning calculus?

Question

I am learning calculus primarily as a prerequisite to understanding machine learning and other statistics/finance applications (Black Scholes, etc.), but I've found that most of the web content helpful for building a conceptual understanding of calculus is geared toward physics applications.

Obviously the computational skills will carry over seamlessly; the derivative operator doesn't care what's going on in the world around it.

What I'm curious about is how important it is to guide your study of the conceptual side of calculus (including in non-introductory areas like multivariable calculus and differential equations) toward your end goal.

I ask in part because some schools have "Business Calculus" or similarly named courses. Does the deeper conceptual understanding of the subject carry over just as the computational understanding, or is it helpful to steer this study in an intentional direction?

Answer 1

Throughout your studies in machine learning, there will be a lot of questions that can easily be answered with the tools of calculus:

• What's the maximal/minimal value of a certain attribute? (Simple derivative can give you an answer.)
• What's the ideal vector for a character to move on (for example in game learning environment)? (Again, derivatives.)
• How can I improve a system, or give guidance for the algorithm? (Being able to write up a function that determines the speed/efficiency/other attributes of the algorithm based on input values, then solving for its maximum/minumum.)

There are also a lot of in-world examples where knowing Calculus can give you a huge advantage, so I'd say it's generally a great skill to have.