Calculus Lessons

This calculus course begins with Calculus 1. It opens with a short algebra and trigonometry review, covering functions, inverses, trigonometry, and exponentials and logarithms, the skills calculus uses constantly, then moves into limits: what a limit means, how to find one from a graph and with algebra, one-sided and infinite limits, continuity, the squeeze theorem, the formal epsilon-delta definition, and L'Hôpital's rule. The derivatives chapter then builds the derivative from its limit definition and works through differentiability, the power, product, quotient and chain rules, the derivatives of trigonometric, exponential, logarithmic and inverse trigonometric functions, and implicit and logarithmic differentiation.

Limits come first because every later idea in calculus is defined through them. A derivative is the limit of an average rate of change, and an integral is the limit of a sum, so time spent on limits now makes derivatives and integrals far easier later. Each lesson works examples by hand, shows the graph where a picture helps, and links to practice problems with step-by-step solutions.

Review lessons borrowed from the algebra course are marked with a label, so you can skip the ones you already know. If you are short on time, the lessons on functions, domain and range, and trigonometric functions are the ones most worth revisiting before you start on limits.