📐 Foundations & Limits
00
Prerequisites: Functions & Graphs
Function families, trigonometry, log/exp, inverse functions, domain/range, piecewise functions
01
Limits & Continuity
Limit definition, one-sided limits, infinite limits, continuity, Intermediate Value Theorem, limits at infinity
⚡ Derivatives
02
Derivatives: Concepts & Rules
Limit definition, tangent lines, differentiability, power/product/quotient/chain rules
03
Applications of Derivatives
Extrema, Mean Value Theorem, increasing/decreasing, concavity, optimization, related rates, linearization, L'Hôpital's rule
∫ Integrals
04
Definite & Indefinite Integrals
Antiderivatives, Riemann sums, Fundamental Theorem of Calculus, properties of definite integrals
05
Techniques of Integration
Substitution, integration by parts, partial fractions (BC depth), improper integrals
06
Applications of Integrals
Area under/between curves, volume (disk/washer/shell), average value, arc length (BC)
📈 Differential Equations
🔷 BC ONLY · Infinite Series & Parametric
08
Parametric, Polar & Vector Functions
Parametric curves, polar coordinates, vector-valued functions, velocity/acceleration
09
Infinite Sequences & Series
Convergence tests (geometric, integral, comparison, ratio/root), alternating series
10
Power Series & Taylor/Maclaurin Series
Radius/interval of convergence, Taylor polynomials, Lagrange error bound, series manipulations
✍️ Practice & Mock Exams