# AP Calculus AB

• Welcome to AP Calculus AB.  AP Calculus AB is a year long course designed to prepare you for the AP Calculus AB Exam in early May.  The course will be taught with a balanced approach using a "Rule of Four:  Numerical Analysis, Graphical Analysis, Analytic/Algebraic Analysis, and Verbal/Written Analysis."

Here are the units that we will study:

1.  Limits and Continuity (3 - 4 weeks)

Rates of Change

Limits at a Point

Limits Involving Infinity

Discontinuity

Rates of Change and Tangent Lines

2.  The Derivative (5 - 6 weeks)

Derivative of a Function

Differentiability

Rules for Differentiation

Applications of the Derivative

Derivatives of Trigonometric Functions

The Chain Rule

Implicit Differentiation

Derivatives of Inverse Trigonometric Functions

Derivatives of Exponential and Logarthmic Functions

3.  Applications of the Derivative (3 - 4 weeks)

Extreme Values

Implications of the Derivative (Theorems about Continous and Differentiable Functions)

Connecting f' and f" with the graph of f(x).

Optimization Problems

Linearization Models

Related Rates

4.  The Definite Integral (3 - 4 weeks)

Approximating Areas

Accumulation Functions

Properties of Definite Integrals

The Fundamental Theorem of Calculus

5.  Differential Equations and Mathematical Modeling (3 - 4 weeks)

Slope Fields

Antiderivatives

Integration using U-substitution

Integration by Parts

Separable Differential Equations

Logistic Growth

6.  Applications of Definite Integrals (3 weeks)

Integral as Net Change

Area Between Curves

Calculating Volume

7.  Review / Test Preparation (3 - 5 weeks)

Multiple Choice Practice

Free-Response Practice

8.  After the Exam (4 - 5 weeks)

Limits of Sequences & Series, Taylor and MacLaurin Polynomials

Review/Research Projects