Preparing for the Calculus AP Exam with Calculus: Graphical, Numerical Algebraic, 2nd Edition

Calculus Prerequisites

Precalculus — A Preparation for Calculus

Functions

Transformations

Polynomial Functions

Rational Functions

Exponential Functions

Sinusoidal Functions

More Trigonometric Functions

Inverse Trigonometric Functions

Parametric Relations

Numerical Derivatives and Integrals

Functions, Graphs, and Limits

Analysis of Graphs

Limits of Functions

Asymptotic and Unbounded Behavior

Function Magnitudes and Their Rates of Change

Continuity

Intermediate and Extreme Value Theorems

Parametric, Polar, and Vector Functions

Derivatives

Concept of the Derivative

Differentiability and Continuity

Slope of a Curve at a Point

Local Linearity

Instantaneous Rate of Change

Relationships Between the Graphs of f and f’

The Mean Value Theorem

Equations Involving Derivatives

Correspondences Between the Graphs of f, f’ and f”

Points of Inflection

Concavity of Functions

Extreme Value of Functions

Analysis of Parametric, Polar, and Vector Curves

Optimization

Related Rates

Implicit Differentiation

Derivative as a Rate of Change

Slopefields

Euler's Method

L’Hopital’s Rule

Derivatives of Basic Functions

Derivative Rules

Chain Rule Explorations

Chain Rule

Derivatives of Parametric, Polar, and Vector Functions

Integrals

Riemann Sums

Definite Integral of a Rate of Change

Basic Properties of Definite Integrals

Applications of Integrals

Fundamental Theorem of Calculus

Antiderivative Basics

Integration by Substitution

Integration by Parts

Integration by SimplePartial Fractions

Improper Integrals

Initial Value Problems

Separable Differential Equations

Numerical Approximations to Definite Integrals

Polynomial Approximations and Series

Concept of Series

Geometric, Harmonic and Alternating Series

Integral Test, Ratio Test, Comparison Test

Taylor Polynomials

Maclaurin and Taylor Series

Manipulating Taylor Series

Power Series

Radius and Interval of Convergence

Lagrange Error Bound