Math 0-1: Calculus for Data Science & Machine Learning

Review practical function concepts for this course, including real numbers as inputs, function notation, variable letters, linear and polynomial forms, root, exponential, logarithmic, trig, hyperbolic functions, and base changes.

Explore the precise epsilon-delta definition of the limit, including delta, and how for every epsilon there exists a delta ensuring |f(x)-l|<epsilon as x approaches a, noting this is optional.

Explore indeterminate forms in limits, including zero over zero and infinity over infinity, with intuitive examples and notes on how limits can resolve them.

Learn derivative checking by comparing finite difference estimates with true derivatives for x squared, x cubed, 1/x, and sqrt(x) using small h in Python.

An alternative derivation of the exponential rule uses the limit definition of e, then derives d/dx e^x from first principles, and extends to general bases via natural log.

learn the product rule and prove d/dx [f(x) g(x)] = f(x) g'(x) + f'(x) g(x). derive the quotient rule via limits and connect it to the chain rule.

Explore applications of implicit differentiation and prove the power rule, product rule, and quotient rule using logarithmic differentiation and derivative of absolute value, with step-by-step derivations.

Learn to locate minimums and maximums using derivatives and first/second derivative tests, with x^2, x^3, and x^4 examples for calculus in data science and machine learning.

Explore partial differentiation, gradients, jacobians, and differentials in multiple dimensions; apply the chain rule, directional derivatives, and gradient descent and ascent in unconstrained and constrained optimization with Lagrange multipliers.

Explore the appendix and FAQ as optional, supplementary sections that provide context and answers, and use the Q&A to ensure you have zero unanswered questions.