Calculus CP                Susan Hebert & Lisa Sypek

 1.  Precalculus Review

2.  Limits and Their Properties

• Finding Limits Graphically and Numerically
• Evaluating Limits Analytically
• Continuity and One-Sided Limits
• Infinite Limits

3.  Differentiation

• The Derivative and the Tangent Line Problem
• Basic Differentiation Rules and Rates of Change
• The Product and Quotient Rule
• Higher Order Derivative
• The Chain Rule
• Derivative of Logarithmic Functions
• Derivative of Exponential Functions
• Implicit Differentiation
• Related Rates

4.  Applications of Differentiation

• Extrema on an Interval
• Mean Value Theorem
• Increasing, Decreasing Function and the First Derivative Test
• Concavity and the Second Derivative Test
• Limits @ Infinity
• Curve Sketching
• Optimization Problems
• Differential Equations

5.  Integration

• Antiderivatives and Indefinite Integration
• Area Under a Curve
• Reimann Sums and Definite Integrals
• The Fundamental Theorem of Calculus
• Integration by Substitution
• Integration of Logarithmic Functions
• Integration of Exponential Functions

6.  Integration techniques and L'Hôpital's Rule

• Basic Integration Rules
• Integration by Parts
• Intermediate Forms and L'Hôpital's Rule