20 lessons spanning Differential, Integral, and Multivariable Calculus — each with theory, worked examples, practice questions, and a downloadable worksheet.
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A limit describes the value a function approaches as its input gets closer ...
A function is continuous if you can draw its graph without lifting your pen...
Differentiation finds the derivative of a function — a measure of how fast ...
Instead of using the limit definition every time, a handful of rules let us...
The chain rule lets us differentiate composite functions — one function nes...
Some equations mix x and y together so that y cannot easily be isolated. Im...
Derivatives are not just abstract slopes — they describe real rates of chan...
Optimization uses derivatives to find the best possible outcome — the maxim...
Integration is the reverse of differentiation — instead of finding a rate o...
A definite integral computes a specific numeric value — often representing ...
An indefinite integral represents an entire family of antiderivatives, diff...
One of the most powerful applications of integration is finding the exact a...
Integration extends to three dimensions, letting us calculate the volume of...
Beyond the basic power rule, several techniques handle more complex integra...
When a function depends on more than one variable, partial derivatives meas...
Multiple integrals extend integration to functions of two or more variables...
Vector calculus studies functions that output vectors (called vector fields...
The gradient turns a scalar function of several variables into a vector tha...
Divergence measures how much a vector field is spreading out from (or conve...
Curl measures the rotation or 'swirling' tendency of a vector field at a po...
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