Course Outline

Textbook: James Stewart, Calculus, Early Transcedentals , third edition.

• Chapter 5 - Integrals
  • 5.1 Sigma Notation
  • 5.2 Area
  • 5.3 The Definite Integral
  • 5.4 The Fundamental Theorem of Calculus
  • 5.5 The Substitution Rule

• Chapter 6 - Applications of Integration
  • 6.1 Areas between Curves
  • 6.2 Volume
  • 6.3 Volume by Cylindrical Shells
  • 6.4 Work
  • 6.5 Average Value of a Function

• Chapter 7 - Techniques of Integration
  • 7.1 Integration by Parts
  • 7.2 Trigonometric Integrals
  • 7.3 Trigonometric Substitution
  • 7.4 Integration of Rational Functions by Partial Fractions
  • 7.5 Rationalizing Substitutions
  • 7.6 Strategy for Integration
  • 7.7 Using Tables of Integrals
  • 7.8 Approximate Integration
  • 7.9 Improper Integrals

• Chapter 8 - Further Applications of Integration
  • 8.1 Differential Equations
  • 8.2 Arc Length
  • 8.3 Area of a Surface of Revolution

• Chapter 9 - Parametric Equations and Polar Coordinates (new material only)
  • 9.2 Tangents and Areas
  • 9.3 Arc Length and Surface Area
  • 9.5 Areas and Lengths in Polar Coordinates

• Chapter 10 - Infinite Sequences and Series
  • 10.1 Sequences
  • 10.2 Series
  • 10.3 The Integral Test
  • 10.4 The Comparison Tests
  • 10.5 Alternating Series
  • 10.6 Absolute Convergence and the Ratio and Root Tests
  • 10.7 Strategy for Testing Series