∫ Calculus

Compressed to runnable code, SVG diagrams, and plain English. Scheme first, Python in the fold.

	Chapter
1.	Functions and Graphs	Domain, range, composition, inverses: the vocabulary everything else builds on	∫
2.	Trigonometry	Unit circle, sin/cos/tan, identities, inverse trig: periodic functions decoded	∫
3.	Limits and Continuity	What 'approaching' means, made precise with epsilon-delta	∫
4.	The Derivative	Instantaneous rate of change as a limit of secant slopes	∫
5.	Derivative Rules	Power, product, quotient, chain: the shortcuts that make differentiation mechanical	∫
6.	Applications of Derivatives	Optimization, related rates, curve sketching: what derivatives are for	∫
7.	The Integral	Riemann sums, definite integrals, and the Fundamental Theorem that ties it all together	∫
8.	Techniques of Integration	Substitution, parts, partial fractions: the toolkit for antiderivatives	∫
9.	Applications of Integrals	Area, volume, arc length, work: what integrals are for	∫
10.	Vectors and Geometry	Dot products, cross products, lines, planes: calculus goes multidimensional	∫
11.	Partial Derivatives	Derivatives of functions with multiple inputs: hold one variable fixed, vary the other	∫
12.	Optimization	Lagrange multipliers and gradient descent: finding extrema with constraints	∫
13.	Multiple Integrals	Double and triple integrals: area becomes volume, volume becomes mass	∫
14.	Line and Surface Integrals	Integrating along curves and over surfaces: work, flux, circulation	∫
15.	Fundamental Theorems	Green, Stokes, Divergence: the boundary-interior duality that unifies calculus	∫

Neighbors

∞ Real Analysis — the rigorous foundations that justify what calculus does
📐 Linear Algebra — multivariable calculus and linear transformations share the same substrate
⚛ Physics — calculus was invented to describe motion
🤖 Machine Learning — gradient descent lives in calculus
🎛 Control Theory — differential equations throughout