• Chapter 1: Functions
  • Chapter 2: Limits and Continuity
  • §2.1, 2.2, 2.3: Informal and formal limits
  • §2.4: One-sided limits
  • §2.5: Continuity
  • §2.6: Limits involving ∞; Asymptotes of Graphs
  • Chapter 3: Differentiation
  • §3.1: Tangents and Derivative at a point
  • §3.2: The Derivative as a Function
  • §3.3: Differentiation Rules
  • §3.4: The Derivative as a Rate of Change
  • §3.5: Derivatives of Trigonometric Functions
  • §3.6: The Chain Rule
  • §3.7 Implicit Differentiation
  • §3.8: Related Rates
  • §3.9: Linearization and Differentials
  • Chapter 4: Applications of Derivatives
  • §4.1: Extreme Values of Functions
  • §4.2: The Mean Value Theorem
  • §4.3: Monotonic Functions and the First Derivative Test
  • §4.4: Concavity and Curve Sketching
  • §4.5: Applied Optimization Problems
  • §4.6: Newton's Method
  • §4.7: Antiderivatives
  • Chapter 5: Integration
  • §5.1: Estimating with Finite Sums
  • §5.2: Sigma Notation and Limits of Finite Sums
  • §5.3: The Definite Integral
  • §5.4: The Fundamental Theorem of Calculus
  • §5.5 Indefinite Integrals and the Substitution Method
  • §5.6 Substitution and Area Between Curves
  • Chapter 6: Applications of Definite Integrals
  • §6.1, §6.2: Volumes by slices and shells
  • §6.3: Lengths of Plane Curves
  • §6.4: Surface Area
  • §6.5: Work, and force from fluid pressure
  • §6.6: Moments and Centers of Mass
  • Chapter 7: Transcendental Functions
  • §7.1: Inverse Functions and Their Derivatives
  • §7.2 and §7.3: Natural Logarithms and Exponentials
  • §7.4: Exponential Change and Separable Differential
  • §7.5: Indeterminate Forms and L'Hopital's Rule
  • §7.6: Relative Rates of Growth
  • §7.7: Inverse Trigonometric Functions
  • §7.8: Hyperbolic Functions