AP Calculus Textbook

Limits → Derivatives → Integration → Series

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AP Calculus AB AP Calculus BC
Unit 1 — Foundations
1

Limits and Continuity

Limit definition, evaluation techniques, Squeeze Theorem, continuity, IVT

AB BC 10 problems 3 interactive graphs
2

Derivatives

Definition, power rule, product rule, quotient rule, higher-order derivatives

AB BC 25 problems 7 interactive graphs
3

Chain Rule & Implicit Differentiation

Chain rule, implicit differentiation, inverse trig derivatives

AB BC 8 problems 3 interactive graphs
Unit 2 — Applications of Derivatives
4

Applications of Derivatives

Related rates, linear approximation, Mean Value Theorem

AB BC 8 problems 3 interactive graphs
5

Curve Sketching & Optimization

Critical points, concavity, inflection points, optimization problems

AB BC 8 problems 3 interactive graphs
Unit 3 — Integration
6

Integration

Antiderivatives, Riemann sums, Fundamental Theorem of Calculus, u-substitution

AB BC 8 problems 3 interactive graphs
7

Techniques of Integration

Integration by parts, trig integrals, partial fractions, improper integrals

AB BC 8 problems 3 interactive graphs
8

Applications of Integration

Area between curves, disk and washer methods for volume, displacement vs. distance

AB BC 8 problems 3 interactive graphs
Unit 4 — BC Topics
9

Differential Equations

Slope fields, separable equations, Euler's method, logistic growth

BC 8 problems 3 interactive graphs
10

Parametric, Polar & Vectors

Parametric equations, polar coordinates, vector-valued functions

BC 8 problems 3 interactive graphs
11

Infinite Sequences & Series

Convergence tests, power series, Taylor & Maclaurin series

BC 8 problems 3 interactive graphs

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