Unit 0: Review

• Lines
• Functions and Graphs
• Exponential Functions
• Functions and Logarithms
• Trigonometric Functions

Unit 1: Limits and Continuity

• Finding Limits Graphically and Numerically
• Evaluating Limits Analytically
• One-sided Limits
• Continuity and Intermediate Value Theorem
• Infinite Limits
• Limits at Infinity

Unit 2: Differentiation Definition and Fundamental Properties

• The Derivative and the Tangent Line Problem
• Basic Differentiation Rules
• Equations of a tangent Line
• The Natural Logarithmic Functions: Differentiation
• The Product and Quotient Rules

Unit 3: Differentiation: Composite, Implicit and Inverse Functions

• The Chain Rule
• Implicit Differentiation
• Inverse Functions
• Inverse Trigonometric Functions and Differentiation

Unit 4: Contextual Applications of Differentiation

• Velocity and Acceleration
• Related Rates - Introduction
• Related Rates - Advanced Examples
• Indeterminate Forms and L'Hopital's Rule

Unit 5: Analytical Applications of Differentiation

• Rolle's Theorem
• The Mean Value Theorem
• Extrema on an Interval
• Extrema on a Closed Interval
• Increasing and Decreasing Functions and the First Derivative Test
• Concavity and the Second Derivative Test
• A Summary of Curve Sketching
• Optimization Problems

Unit 6: Integration and Accumulation of Change

• Left and Right Side Approximations
• Area - Midpoint and Trapezoidal Approximations
• Riemann Sums and Definite Integrals
• Antidifferentiation and Indefinite Integration
• The Fundamental Theorem of Calculus
• Integration by Substitution
• The Natural Logarithmic Functions: Integration
• Exponential Functions: Differentiation and Integration
• Bases Other Than e and Applications
• Inverse Trigonometric Functions and Integration
• Trigonometric Integrals
• Trigonometric Substitution

Unit 7: Differential Equations

• Slope Fields
• Separation of Variables
• Differential Equations: Growth and Decay

Unit 8: Applications of Integration

• Area of a Region Between Two Curves
• Area of a Region Between Two Curves - Advanced Examples
• Volume: Solids with Known Cross Sections
• Volume: The Disk Method
• Volume: The Shell Method