TVS Initiative

AP Calculus AB
(Two Semesters or Block)

Description: This is a college level course covering derivatives, integrals, limits, approximation, and applications and modeling.

Prerequisites: Algebra II, Geometry, Trigonometry and Pre-Calculus (or Math Analysis)

Textbook: Calculus with Infotrac (Optional) ISBN: 0534437362

Supplemental text: Calculus Concepts and Contexts, 2nd Edition, James Stewart, Brooks/Cole, 2001.

Required Material: TI 83 Plus Calculator

Course cost: $350 / student / semester + required materials

Course Outline

Semester 1
1. FUNCTION & GRAPHS

Functions & function notation
Absolute Value & Piecewise Defined Functions
Inequalities
Composition & Combination of Functions
Exponential & logarithmic functions
Transformation of Functions
Trigonometric Functions
Polynomial & Rational Functions
2. LIMITS & CONTINUITY

Intuitive Definition of a Limit
Algebraic Techniques for Finding Limits
One-Sided Limits
Infinite Limits
Limits at Infinity
Limits of Special Trigonometric Functions
Continuity
3. DERIVATIVES

Definition of the Derivative
Differentiation Rules
The Chain Rule
Derivatives of Exponential Functions
Derivative of Logarithmic Functions
Derivatives of Inverse Functions
Differentiability & Continuity
Implicit Differentiation
Logarithmic Differentiation
Limits & Continuity of Vector-Valued Functions
4. APPLICATION OF THE DERIVATIVE

Tangent & Normal Lines
Position, Velocity, & Acceleration (PVA)
Related rates
Relative Extrema & the First Derivative Test
Concavity & the Second Derivative Test
Absolute Extrema & Optimization
Rolle's Rule & the Mean Value Theorem
Differentials

Semester 2
1. ANTI-DERIVITIVES

Differential Equations and Slope Fields
Antiderivatives
The Chain Rule for Antiderivatives
Antiderivatives of Logarrithms
Antiderivatives of Inverse Trig Functions
Trigonometric Substitutions
The Definite Integral
Fundamental Theorem of Calculus
2. APPLICATION

Net Change and Displacement
Volume
Separable Differential Equations
Work
Other Applications of Definite Integrals