Unit 0: Review

• Lines
• Functions and Graphs
• Exponential Functions
• Functions and Logarithms
• TTrigonometric Functions

UUnit 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 Part 1: 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

Unit 6 Part 2: More Integration Techniques

• Exponential Functions: Differentiation and Integration
• Bases Other Than e and Applications
• Inverse Trigonometric Functions and Integration
• Trigonometric Integrals
• Trigonometric Substitution
• Integration by Parts (BC Only)
• Partial Fractions (BC Only)
• Improper Integrals (BC Only)

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
• Arc Length (BC Only)

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC Only)

• Parametric Equations
• Differentiation of Parametric Equations
• Vector-Valued Functions
• Differentiation and Integration of Vector-Valued Functions
• Velocity and Acceleration Using Parametric and Vector Valued Functions
• Polar Coordinates and Polar Graphs
• Polar Form of a Derivative
• Areas in Polar Coordinates

Unit 10: Infinite Sequences and Series (BC Only)

• Sequences
• Infinite and Geometric Series
• The Integral Test and p-Series
• Comparisons of Series and the Ratio Test
• Alternating Series
• Taylor Polynomials and Approximations
• Power Series
• Taylor and Maclaurin Series
• Representation of Functions by Power Series