Visualizations · Mathematics
Limits, derivatives, integrals and vector calculus
What approaching a value means
What a derivative visually means
Derivative of composite function
Derivative of product of functions
Extrema and saddle points
Where function is convex/concave
Existence of point with average slope
Finding minima and maxima
Limits of indeterminate forms
Numerical root finding
Integral as infinitely many rectangles
Area under the curve
Connection of derivative and integral
Integration method for products
Integration by substitution
Integral between two functions
Volume of solid of revolution
Volume by cylindrical shells
Length of a curve via integral
Polynomial approximation of functions
Taylor series around zero
How transformations locally scale area
Surface flux = divergence inside
Local curl → boundary circulation
Work done by force along a path
Why work is path-independent
Constrained optimization
Why gradient points steepest
∞ points can have zero area
Building functions from sine waves
Optimization on loss landscapes