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Series · 33 lessons
Calculus: Derivatives
From continuity to inverse hyperbolic functions. Thirty-three short, interactive courses that build up the derivative one idea at a time.
- Continuity
- The derivative
- Differentiation rules
- Trigonometric functions
- Implicit differentiation & related rates
- Exponentials & logarithms
- Inverse & hyperbolic functions
Binary search
How many steps does it take to find one number in a billion? Halve the search space and discover the power of logarithms.
Bayes’ theorem
How should new evidence change your mind? Turn conditional probability into something you can see and understand.
Eigenvectors & eigenvalues
When a matrix transforms space, some vectors stay on the same line. Find them and discover the geometry behind the numbers.
Oscillation & resonance
How can a gentle push make a swing go higher? Adjust the driving frequency and discover when the response is strongest.
Breadth-first search
How do you find the shortest path through a network? Explore one layer at a time and watch the answer emerge.
Taylor polynomials
Trace complex curves with simple polynomials. Zoom in and out to discover where a local approximation holds up.
Lenz’s law
Which way does current flow as a magnet approaches a coil? Follow the changing magnetic flux to find out.
Derivatives & extrema
Does a zero slope always mean a peak? Follow a curve and connect its derivative to its maxima and minima.
Motion in a magnetic field
How does an invisible magnetic field bend a particle’s path? Follow the force to understand circular motion.
Two’s complement & overflow
How do computers represent negative numbers? Explore a world of limited bits and discover what happens when numbers overflow.
Solar elevation angle
Why is the equator hot and the poles cold? Tilt a beam of sunlight and watch the same energy spread over more ground.
Rain shadow
Why is one side of a mountain lush and the other a desert? Lift a pocket of air and follow its water vapor over the peak.