AP CALCULUS LESSONS

Summer Work	Class Contract	Limits and Their Properties	Differentiation	Applications of Differentiation
Integration	Logarithmic, Exponential, and Other Transcendental Functions	Applications of Integration	Integration Techniques, L'Hopital's Rule, and Improper Integrals	Infinite Series
Conics, Parametric Equations,  Polar Functions, & Vectors		First Semester Exam Review A Second Review

Integration

• Antiderivatives & Indefinite Integration
• Sequences & Area Under a Curve by summing rectangles
• Riemann Sums
• Fundamental Theorem of Calculus
• Integration by Substitution
• Trapezoidal Rule

Review Semester Exam -- a good review source

Exponential,Logarithmic, and Inverse Trigonometric Functions

• Logarithms
• The Derivative of the Natural Logarithm
• Integrate, using the Natural Logarithm & Integrate the rest of the Trigonometric                      Functions
• Derivatives of Inverse Functions
• Derivatives of Natural Exponential Functions
• Integrate Exponential Functions
• Derivatives & Integrals of Bases Other than e; Savings Account Formulas
• Slope Fields
• Exponential Growth & Differential Equations Solved by Separating Variables
• Inverse Trigonometric Functions
• Derivatives of Inverse Trigonometric Functions
• Integrals Involving Inverse Trigonometric Functions

Applications of Integrals

• Area Between Curves
• Volumes by disk method
• Volumes, using washers
• Volumes, using known cross-sections
• Volumes, using shells
• Arclength
• Work
• Moments and Centroids

Integration Techniques

• Integration by Parts
• Trigonometric Integrals (more complex ones)
• Trigonometric Substitution
• Partial Fractions
• Improper Integrals
• Review

Infinite Series

• Sequences and Series
• Limits of Sequences
• Series and Convergence
• Geometric Series
• p-Series
• The Ratio and Root Tests
• Alternating Series
• Improper Integrals & Series
• Power Series
• Special Functions
• Review

Parametric Equations and Polar Coordinates

Vectors

Functions in Two Variables

• Limits
• Cobwebs
• Review

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