Course Outline
This course covers all of the topics required for the AP Calculus AB exam.

Chapter 1: Introduction
The problems that Calculus solves, introduction to derivatives,
finding rates of change from graphs, from equations, and from data,
Numerical derivatives, Introduction to Integrals,
Approximating integrals from graphs, from equations and from data,
the Trapezoid Rule

Chapter 2: Limits
A graphical approach to limits, Describing function behavior with limits, Asymptotes,
Rational Functions, Polynomial end behavior, The Limit Theorems, Evaluating limits,
Continuity, The Intermediate Value Theorem

Chapter 3: Derivatives
A graphical look at derivatives, Difference Quotients, the Derived Function,
Notation, Numerical calculations of derivatives, Tangents and Linear Approximation,
Differentiability and Continuity, the Chain Rule, the Product Rule, the Quotient Rule,
Leibniz' Proofs, Derivatives of Trig Functions, Implicit Differentation,
Derivatives of Inverse Functions, Derivatives of Inverse Trig Functions

Chapter 4: Applications of Derivatives
The Extreme Value Theorem, Rolle's Theorem and the Mean Value Theorem, First and Second
Derivatives, Concavity and Inflection Points, Graphs and Curve Sketching, The Calculus of Motion,
MaxMin problems, Related Rates, Practice

Chapter 5: Integrals
Antiderivatives, Integrals, Infinitesimals, Riemann Sums, Definite Integrals,
The Fundamental Theorem of Calculus, Properties of Definite Integrals, Numerical Methods,
Integration by Substitution, Average Value

Chapter 6: Exponential Functions and Differential Equations
Derivatives of exponential functions, Derivatives of logarithmic functions,
Derivatives and integrals of base b exponents, Integrals with variable limits,
Logarithmic Differentiation, Integrals of trig functions, Intro to Differential Equations,
Examples and applications, Slope Fields, Euler's Identity

Chapter 7: Applications of Integrals
The area of a plane region, The Calculus of Motion, Real world applications, Integrating
to find volumes, Plane Slicing, Solids of Revolution, Cylindrical Shells
