Chapter 1: Functions, Graphs and Limits

  1. The Cartesian Plane and the Distance Formula
  2. Graphs of Equations
  3. Lines in the Plane and Slope
  4. Functions
  5. Limits
  6. Continuity

Chapter 2: Differentiation

  1. The Derivative and the Slope of a Graph
  2. Some Rules for Differentiation
  3. Rates of Change: Velocity and Marginals
  4. The Product and Quotient Rules
  5. The Chain Rule
  6. Higher-Order Derivatives
  7. Implicit Differentiation
  8. Related Rates

Chapter 3: Applications of the Derivative

  1. Increasing and Decreasing Functions
  2. Extrema and the First Derivative Test
  3. Concavity and the Second Derivative Test
  4. Optimization Problems
  5. Asymptotes
  6. Curve Sketching: A Summary

Chapter 4: Exponential and Logarithmic Functions

  1. Exponential Functions
  2. Natural Exponential Functions
  3. Derivatives of Exponential Functions
  4. Logarithmic Functions
  5. Derivatives of Logarithmic Functions
  6. Exponential Growth and Decay

Chapter 5: Integration and its Applications

  1. Antiderivatives and Indefinite Integrals
  2. The General Power Rule
  3. Exponential and Logarithmic Integrals
  4. Area and the Fundamental Theorem of Calculus
  5. The Area of a Region Bounded by Two Graphs

Chapter 6: Techniques of Integration

  1. Integration by Substitution
  2. Integration by Parts
  3. Improper Integrals