Chapter 7: Integration

  1. Definition of the Riemann Integral; integrable and non-integrable functions
    2. Criteria for integrability;
  2. Uniform continuity; all continuous functions are integrable
  3. Elementary properties of the integral (linearity, triangle inequality, etc)
  4. The Fundamental Theorem of Calculus
  5. Improper integrals; the Integral Summation Test
  6. Definition of the Riemann-Stieltjes integral
  7. Functions of bounded variation