Calculus

Learning

I would recommend 3Blue1Brown's introduction to calculus. Again, since it's relatively short, I'd recommend just watching the whole thing through.

Concepts/Questions

• If there's one thing you really need to get, it's the chain rule.

  • What is the derivative of g(h(x))?

• Derivative

  • How can you think of the derivative (as a graph)?

  • If you are driving a car, what is the derivative of your position with respect to time?

  • If you've taken Physics, what is the derivative of velocity with respect to time?

  • Good intuitions for thinking about derivatives

    • Best constant approximation for the rate of change at a point.

    • As tiny nudges/wiggles (extremely useful for thinking about neural nets).

  • What is a partial derivative?

Practice

https://www.khanacademy.org/math/calculus-1

Answers to the questions from the last section:

• The derivative of g, evaluated at h(x), times the derivative of h wrt x.

• It is approximately the graph of slope of the tangent line (not that tangent line itself) at a point (works because dt approaches 0).

• Speed

• Acceleration

• Derivative of a function wrt one of the variables with the other ones held constant.